Chapter 5 Space Environment and Orbital Mechanics
Section 1: Space Environment 5-1 Overview
Introduction Space is often incorrectly thought of as a vast, empty vacuum that begins at the outer reaches of the Earth's atmosphere and extends throughout the universe. In reality, space is a dynamic place that is filled with energetic particles, radiation, and trillions of objects both very large and very small. Compared to what we experience on Earth, it is a place of extremes. Distances are vast. Velocities can range from zero to the speed of light. Temperatures on the sunny side of an object can be very high, yet extremely low on the shady side, just a short distance away. Charged particles continually bombard exposed surfaces. Some have so much energy that they pass completely through an object in space. Magnetic fields can be intense. The environment in space is constantly changing. All of these factors influence the design and operation of space systems.
Where Space Begins There is no formal definition of where space begins. International law, based on a review of current treaties, conventions, agreements and tradition, defines the lower boundary of space as the lowest perigee attainable by an orbiting space vehicle. A specific altitude is not mentioned. By international law standards aircraft, missiles and rockets flying over a country are considered to be in its national airspace, regardless of altitude. Orbiting spacecraft are considered to be in space, regardless of altitude.
U.S. definition The U.S. government defines space in the same terms as international law.
Lowest altitude for a satellite The Earth's atmosphere does not suddenly end at a particular altitude and space begins. In fact, the Earth's atmosphere continues out for more than 1,000 miles into space. In practical terms, the lowest altitude for a satellite in a circular orbit is about 93 miles (150 km) but, without propulsion, the satellite would quickly lose speed and fall back to Earth.
5-2 Earth's Atmosphere
Introduction The atmosphere limits the lowest altitude at which a satellite can be placed into orbit. The atmosphere absorbs, diffuses, deflects, or delays certain frequencies of signals sent to and from a satellite. Satellites launched from the Earth's surface must pass through the atmosphere to attain orbit. Manned spacecraft and some unmanned payloads must reenter the atmosphere in order to safely return to the surface.
Atmospheric Regions The Earth's atmosphere is divided into numerous regions which have different characteristics. The boundaries between the regions are not distinct. Some regions overlap and others are made up of a number of sub-regions. Definitions are complicated by the fact that different scientific fields define these regions in different ways using various criteria, such as pressure or temperature. Altitude alone does not define where one region ends and another begins because the regions are constantly fluctuating in size depending on the time of day, the season of the year, the degree of activity of the sun and many other factors.

Troposphere The troposphere is the lowest region of the atmosphere. It starts at the Earth's surface and extends to the tropopause, the upper boundary of the troposphere. Almost all clouds and weather occur in the troposphere. It contains about 99% of the atmosphere's water vapor and 90% of the air. Above an altitude of 2 miles (3.2 km), a person who has not become adapted requires supplemental oxygen or a pressurized environment. Approximately half of the Earth's atmosphere is below an altitude of 3 miles (5 km). The temperature generally drops with increased altitude at about 17/ F per mile (10/ C per km) until the tropopause is reached, the point at which the atmospheric temperature begins to rise with altitude. Normally, gases expand with increased temperature. In the troposphere, the air temperature is higher near the surface yet the air density is higher due to gravity. The result is that the troposphere is unstable. This instability generates the majority of the Earth's weather. The altitude of the tropopause varies from 9 to 12 miles (15 to 20 km) at the equator to about 6 miles (10 km) in polar areas.
5-2 Earth's Atmosphere, cont'd
Stratosphere The layer above the troposphere is the stratosphere. It extends from the tropopause to the stratopause, the upper boundary at about 30 to 33 miles (48 to 53 km) altitude. The temperature of the stratosphere increases slightly with altitude which results in vertical stability. Air flow in the stratosphere is mostly horizontal. The point at which the temperature maximum of about 32/ F (0/ C) is reached is called the stratopause. Approximately 99 percent of the atmosphere is in the stratosphere and troposphere. This region is characterized by the near absence of water vapor and clouds. At altitudes above 9 miles (14.5 km) breathing supplemental oxygen through a mask is no longer effective because natural pressure inside a person's body equals the outside atmospheric pressure, thus not allowing the blood to absorb oxygen. Also, bubbles of water vapor and nitrogen appear in the body fluids, first on the mucous membranes of the mouth and eyes and later in the veins and arteries. Blood starts to "boil" as the bubbles continue to expand. This is called the bends and is extremely painful. Pressurization by means of a pressure cabin or a pressure suit and helmet is required above this altitude. Above an altitude of 15 miles (24 km) compressing outside air into the cabin or pressure suit usually generates too much heat. Everything required to sustain life must be carried on board. Ozone, an isotope of oxygen, is present in the ozone layer which varies in altitude from 12 to 21 miles above the Earth. Traces of ozone are found as low as 6 miles and as high as 35 miles. Ozone is poisonous, therefore, in the stratosphere the outside atmosphere cannot be used to pressurize a crew cabin. The ozone layer is important because it absorbs a large portion of the sun's ultraviolet radiation which is harmful to humans and most other life forms. The radius of the Earth is about 3,960 miles, thus the upper limit of the stratosphere represents only 0.75% of the distance to the center of the Earth, yet it contains 99% of the Earth's atmosphere. This points out just how thin the Earth's atmosphere really is. The small band around the picture of the Earth represents the combined thickness of the troposphere and stratosphere relative to the size of the Earth.
Mesosphere The mesosphere extends from the stratopause at the lower boundary to the mesopause, the upper boundary at about 50 miles (80 km) altitude. The temperature of the atmosphere in the mesosphere decreases as the altitude increases. The mesopause is where the minimum temperature is reached. The temperature at the mesopause is about ­130/ F (­90/ C). Above about 30 miles (48 km) altitude there is not enough atmosphere for even a high altitude ramjet to operate. Above this altitude both fuel and oxidizer must be carried for a rocket engine to provide thrust.
Thermosphere The thermosphere extends from an altitude of 50 miles (80 km) to between 200 miles (320 km) and 375 miles (600 km). The temperature increases with altitude from about ­130/ F (­90/ C) to the thermopause where the maximum temperature occurs. The maximum temperature is about 2,960/ F (1,475/ C) during the day and about 440/ F (225/ C). U.S. astronaut wings are awarded to anyone who travels to an altitude of 50 miles or higher, regardless of whether they completed an orbit of the Earth. At an altitude above 60 miles (100 km) wings and other lift and control surfaces no longer work since the atmosphere is too thin to generate lift and aerodynamic stabilization. This is an area of complete silence outside the craft because the atmosphere is too thin to carry sound waves. All but one­millionth of the atmosphere lies below 60 miles altitude. An altitude of 93 miles (150 km) is the lowest altitude at which a satellite in a circular orbit can orbit the Earth for at least one revolution without propulsion. At this altitude it takes 87.5 minutes to complete one revolution of Earth. This altitude is the most commonly accepted definition of where space begins but it is not explicitly stated in any treaty or international agreement. An altitude of 80 miles (129 km) is about the lowest altitude (perigee) at which a satellite in an elliptical orbit can pass through the Earth's atmosphere and still remain in orbit. At an altitude of approximately 100 miles (160 km) the sky is totally black. Stars do flicker and the area between stars is black since there is not enough air to scatter light rays.
5-2 Earth's Atmosphere, cont'd
Exosphere The exosphere begins where the thermosphere ends and extends out into space. In this region the density of atoms and molecules of the atmospheric gases is very low. Typically, individual atoms travel about 1600 miles in 20 minutes before colliding with another atom. After the collision, some atoms have enough velocity to escape the Earth's gravity and enter interplanetary space. The density is so low that all of the atmospheric particles which surround the Earth at an altitude of 1,000 miles could be contained in 1 cm3 at sea level. Satellites orbiting in the exosphere at an altitude of about 620 miles (1000 km) are, however, slowed by atmospheric drag caused by friction from collisions with individual molecules.

5-3 Atmospheric Drag
Definition Satellites in orbit around the Earth experience atmospheric drag. Atmospheric drag is the resistive force of the molecules of the atmosphere. The amount of drag is dependent on the density of the atmosphere, the shape and size of the object, the material it is made of, and other factors.
Result of Atmospheric Drag Atmospheric drag causes a satellite to slow down, thus the satellite "falls" to a lower altitude to gain velocity. The atmosphere is more dense at the lower altitude resulting in even more atmospheric drag which causes the satellite to slow down even more. The result is that the orbit continues to decay. Satellites with a perigee of 600 miles or less are the most severely affected. When the speed of the satellite is reduced, the altitude of the apogee is lowered and the period is shortened.
Friction and Heat Friction from air molecules can heat the satellite to very high temperatures. The heat is either deflected by heat shields or distributed throughout the satellite. Eventually the satellite either burns up or it is controlled during reentry so that it remains intact. The only way to avoid reentry is to periodically boost the satellite to a higher altitude.
Sun Effects When the Sun is very active it emits more energy which heats the outer portions of the atmosphere causing it to expand farther out into space. This results in more atmospheric drag at higher orbital altitudes.
Satellite Orbits Satellite orbits with a perigee of less than 70 miles encounter so much atmospheric drag that they are not practical. Orbits with a perigee above 350 miles experience so little atmospheric drag that the orbit usually will not decay before the satellite fails for other reasons.
Value of Atmospheric Drag The approximate value of atmospheric drag can be calculated and considered in updating a satellite's position and deciding on orbital maneuvers to maintain a satellite in orbit. Long term predictions are difficult because of the inability to predict what the Sun will do.
Ionosphere The ionosphere is a region which is defined by its high density of ionized molecules, rather than by temperature changes. It begins within the mesopause, between 31 and 50 miles in altitude and extends to about 240 miles (400 km). The atoms and molecules in this layer are bombarded by solar x­rays and ultraviolet radiation from the sun and become electrically charged, or ionized, in a process known as photo-ionization. This process produces an excess of free electrons and ionized atoms. X­rays and extreme ultraviolet (EUV) radiation from the sun and ultra­high­frequency galactic cosmic rays from the stars of outer space are the prime mechanisms in the formation of the ionosphere. The amount of radiation available to ionize atmospheric molecules varies between day and night, high and low latitude, and with the activity level of the sun. Sunspots, solar flares and other disturbances on the surface of the Sun produce fluctuations in the output of the Sun's energetic rays and particles. These fluctuations cause Sudden Ionospheric Disturbances (SIDs). Interaction between the ionosphere and the concentrated magnetic field of the Earth at the North and South Poles causes the undulating brilliant colors of the aurora borealis (north lights) and the aurora australis (southern lights).
Effects of the Ionosphere The ionosphere can absorb, delay or reflect certain frequencies of radio signals, therefore, the characteristics of the ionosphere have significant impact on the design and operation of communications systems between satellites and ground stations. The ionosphere is also important for ground­to­ground radio communications systems because they rely on the ability of the ionosphere to reflect radio waves to achieve long range.
5-3 Atmospheric Drag, cont'd
Ionosphere Regions The variation of electron density with height has led to the subdivision of the ionosphere into the D­region (30­60 miles), the E­region (55­100 miles), and the F­region, which is further subdivided into F1 (100­160 miles) and F2 (160­600 miles). The D­region contains relatively few electrons, but still can affect AM radio transmissions. During the daytime, these transmissions are absorbed in the D­region, because the air is more densely ionized due to photo-ionization. The D­region is particularly sensitive to the effects of solar disturbances both at night or during the day. The E­region, like the D­region, has an electron density that varies according to solar effects. The ionization effects are reduced, but not eliminated, at night. The F­region is the region most affected by solar activity. The F1 region exists only during daylight and is even more pronounced during periods of high solar activity. The highest electron density level in the ionosphere is found in the F2 region. This region is present throughout the day as well as at night. It is the F2 region that reflects or attenuates certain frequencies of radio signals most consistently.
Ionosphere Effects Communications The frequencies used for communications between satellites and ground stations (both control stations and users) are limited by atmospheric attenuation (absorption, also known as signal strength loss through heating, and refraction, also known as scattering).
AM Radio Transmissions During the day AM radio transmissions (530 kHz to 1.65 MHz) are absorbed by the D­region. At night the D­region dissipates rapidly, thus AM radio transmissions pass through the D­region and are reflected back to the Earth by the ions in the E­region. This is why AM radio stations have greater range at night. Commercial short-wave radio transmissions (6 to 30 MHz) are reflected by the E and F regions of the ionosphere. These transmissions are also reflected by surface of the Earth, therefore multiple hops are not uncommon. Since frequencies below 30 MHz are absorbed by the D­region of the ionosphere and reflected by the E and F­regions, they are not well suited for communications with satellites. Background atmospheric, solar and cosmic noise limit the utility of frequencies lower than 300 MHz. The upper limit of frequencies is 300 gigahertz (GHz) because above this frequency water and carbon dioxide in the atmosphere very efficiently absorb the electromagnetic radiation convert it to heat. There are also some specific frequencies bands between 300 MHz and 300 GHz that are subject to absorption by molecules in the atmosphere.
Refraction Most radio signals within the 300 Mhz to 300 GHz band will pass through the atmosphere, allowing communications between the ground and satellite. In the F2­region, however, radio signals can still experience some interference in the form of refraction. Refraction is the bending of the signal path just as light is refracted through a prism due to the difference in the density of the air outside the prism and the glass inside. In such a situation, the signal travels farther than just the straight line distance between the transmitter and the receiver. This delays reception of the signal which has an impact on systems which rely on precise time, such as the Global Positioning System.
5-4 The Sun
Introduction The Sun constantly emits particles, known as corpuscular radiation, and electromagnetic radiation in the form of light and radio frequency noise. The constant stream of these forms of radiation is called the solar wind. In addition, at seemingly irregular intervals, there are solar flares, the explosive ejection of particles (mostly protons and electrons) accompanied by sporadic emissions of electromagnetic radiation.
Solar Activity Solar activity is also characterized by cycles of various lengths. The Sun has a rotation period of 28 days, which exposes Earth to the surface features of the Sun, such as sunspots. The number of sunspots is characterized by an 11­year cycle. Sunspots are normally associated in a complex, but not completely understood, way with solar flares, i.e., the more the sunspots, the more the solar flares. A change in polarity of the overall solar magnetic field is characterized by a 22 year cycle. It seems to govern the frequency of flares.
Electromagnetic Radiation of the Sun The spectrum of solar electromagnetic radiation extends from the radio frequency (RF) range to the x­ray frequencies, expanding to slightly higher frequencies during solar flares. The total energy incident on Earth's atmosphere is called the "solar constant". This radiation can be harmful to an unprotected human and can change the surface properties of various materials. The radiation received from the Sun varies according to the Sun's rotation period. The sun emits three general classes of radiation in the RF range. First, there is a constant background noise over the whole radio spectrum from the "quiet sun". Second, there is a slowly varying component related to sunspots. Third, there is sporadic emission related to centers of activity, such as solar flares. Solar activity during solar maximum can be catastrophic, especially if solar flares are involved. The greatest concerns are possible interference with communications and the threat to humans.
The Solar Wind Because of the high temperature of the Sun's corona, solar protons and electrons acquire velocities in excess of the escape velocity from the sun. The result is that there is a continuous outward flow of charged particles in all directions from the sun. This flow of particles is called the solar wind<$ISun;Solar Wind>. By the time the solar wind reaches Earth's orbit, it is traveling at 185 ­ 435 mi/sec (300 to 700 km/sec). The density is 1 ­ 10 particles per cubic centimeter. The velocity and density of the solar wind vary with sunspot activity. The solar wind causes a radiation pressure on satellites in orbit around the Earth. Radiation pressure is a significant source of perturbations, especially for satellites with large area to mass ratios. Typically such a large ratio is the result of large solar panels Radiation pressure causes frictional drag. It is present only on the daylight side of Earth. The satellite is essentially shielded from solar wind when it is on the night side of Earth. This causes irregular perturbations of a satellite's orbital elements and corresponding ground traces.
Solar Flares High speed solar protons emitted by a solar flare are probably the most potent of the radiation hazards to space flight. Flares themselves are among the most spectacular disturbances seen on the Sun. A flare may spread in area during its lifetime, which may last from several minutes to a few hours. There is a relationship between the number of sunspots and the frequency of flare formation, but the most intense flares do not necessarily occur at solar cycle maximum. There are many events that may occur on Earth following a solar flare. In addition to increase in visible light, minutes later there is a Sudden Ionosphere Disturbance (SID) in Earth's ionosphere. This, in turn, causes short wave fade­out, resulting in the loss of long­range over­the­horizon communications for 15 minutes to 1 hour. During the first few minutes of a flare, there may be a radio noise storm. The first few minutes of this storm causes noise over a wide range of frequencies that can be heard as static in radio transmissions.
5-4 The Sun cont'd
Cosmic Rays One type of corpuscular radiation is the cosmic ray. Cosmic rays originate from two sources: the Sun (solar cosmic rays), and other stars throughout the universe (galactic cosmic rays). This radiation is primarily high velocity protons and electrons. The galactic cosmic rays are extremely energetic, but do not pose a serious threat, due to the low flux, the rate at which they enter the atmosphere. The solar cosmic rays are not a serious threat to humans, except during periods of solar flare activity, when the radiation can increase a thousand-fold over short periods. Manned operations during such conditions require heavy on­board shielding, which is generally impractical today, due to high launch costs. The only alternative is to curtail the mission and bring the crew back. Cosmic ray particles can also cause direct damage to internal components through collision. Shielding is not feasible due to the high energy of the particles and the weight of the shielding required. Some of the methods currently used to solve this problem include parts selection, triple redundancy, error detection and correction and regular reload/reset. Cosmic rays have the most impact on polar and geosynchronous orbits. This is due to the fact that they are outside or near the edge of the protective shielding provided by Earth's magnetic field.
Thermal Energy Thermal energy emitted by the Sun is intense. Satellites in orbit around the Earth do not have the benefit of the shielding provided by the atmosphere. Parts of satellites exposed to sunlight can heat to very high temperatures if they absorb the radiant energy. Sunlight reflected by the Earth is also a significant source of radiant energy for satellites in low Earth orbit. On the shadow side, heat can radiate from the satellite into cold space with the result that surface temperatures can be hundreds of degrees below zero. Thermal energy is also generated by internal components of a satellite such as batteries, transmitters, computers and other devices. This thermal energy must be dissipated so that it does not damage the components. Thermal management control systems are an integral part of the design of a satellite. Techniques include passive and active systems. A simple passive technique is to spin the satellite to equalize exposure. Highly reflective surfaces and radiators are other passive techniques. Some active techniques include the use of heaters or refrigerators. In some satellites, the problem of management of thermal energy is compounded by the fact that sensors may need to be maintained at near absolute zero temperature while mono-propellants for small rockets may need to be maintained at a temperature of about 100/ F.
5-5 Earth's Magnetic Field
Introduction The Earth has a magnetic field which emanates from its south magnetic pole, extends out into space and comes back to its north magnetic pole. The north and south magnetic poles are near the north and south celestial poles about which the Earth rotates. This is not true of some other planets. The magnetic field around the Earth is similar to one that would be formed if a bar magnet extended through the center of the Earth with the tips at the north and south magnetic poles. According to accepted theory, Earth's magnetic field arises from electrical currents flowing in the molten metallic core of the planet.
Magnetosphere The Earth's magnetic field extends out into space forming the magnetosphere. As the solar wind expands out from the sun, it encounters the magnetic field of Earth. On the sunward side of Earth, the solar wind compresses the magnetic field in toward the Earth, increasing the magnetic field strength in the compressed areas. On the opposite side of Earth, the solar wind acts to stretch out the magnetic field thus giving it a teardrop shape.
Magnetopause The boundary of the magnetosphere is the magnetopause. It is where the pressure of the solar wind is balanced by Earth's magnetic field pressure. The magnetopause is most defined on the sunward side where it is located approximately 10 Earth radii (10 times 3962 mi) from the Earth. This boundary fluctuates between 7 to 14 Earth radii during magnetic disturbances resulting from large variations in the solar wind.
Magnetotail On the side of Earth opposite from the Sun, the solar wind draws the magnetic field out into a long tail, called the magnetotail. This tail extends out to 1,000 earth radii or more. Located within the magnetotail is a region of high density, high energy plasma, known as the plasma sheet. It may extend out past 300 earth radii. Within the plasma sheet is the neutral sheet. This is where the magnetic field lines reverse direction from a component towards Earth (Northern lobe) to a component away from Earth (Southern lobe).
Shock Wave When the solar wind encounters Earth's magnetic field, it is deflected and a shock wave is produced. The location and shape of this shock wave is similar to that of the wave caused by the bow of a boat as it moves across the surface of a body of water. This shock wave is called the bow shock and marks the transition from undisturbed to disturbed solar wind. Its front lies on the sunward side between 10 and 15 earth radii from Earth.
Van Allen Radiation Belts Within the magnetosphere are found the Van Allen radiation belts, named after Dr. James Van Allen, who was responsible for the interpretation of the data from the Explorer I satellite, launched by the U.S. Army. Their existence was not discovered until early 1958, when Explorer I data was used to map particles trapped by Earth's magnetic field. Data from this satellite and other satellites revealed the strange shape of the magnetosphere and toroidal shaped pockets of trapped charged particles. Other scientific satellites have added even more detail. The Van Allen radiation belts consist of concentric doughnut shaped regions of energetically charged particles. The Van Allen belts have an inner and outer portion filled with high energy protons and electrons. The protons are most intense at about 2,200 miles. The electron flux breaks at about 10,000 miles. The area of low particle density separating the two belts is often called the "Slot". Although the cross sectional view shown in shows two distinct belts, they are not really that distinct. The density of electrons in the slot is just somewhat lower than in the two Van Allen radiation belts.
Inner Van Allen Radiation Belt The inner Van Allen radiation belt starts at an altitude between 250 miles to 750 miles, depending upon the latitude. It extends to about 6,200 miles. This is where the "slot" begins. The inner belt extends from about 40/ north latitude to about 40/ south latitude.
Outer Van Allen Radiation Belt The outer Van Allen belt begins at about 6,200 miles (depending on latitude) and extends to between 37,000 and 57,000 miles. The upper boundary is dependent upon the activity of the sun. When electrons, protons, and perhaps some other charged particles encounter Earth's magnetic field, many of them are trapped by the field. They bounce back and forth between the magnetic north and south poles, following the magnetic field lines.
5-5 Earth's Magnetic Field, cont'd
Spacecraft in Van Allen Radiation Belts Experience has shown that spacecraft (manned or unmanned) in low circular orbits (120­340 mi) receive an insignificant amount of radiation from the Van Allen zones. A satellite in a geosynchronous orbit, however, would be close enough to the center of the outer zone (22,500 mi) to accumulate a hazardous dose. For manned space systems, the spacecraft must be shielded and an orbit that minimizes radiation exposure must be selected.
Electromagnetic Forces As a satellite orbits the Earth, it travels through the magnetic fields which cause the satellite to act like a magnet. The electrical or electronic components within or outside the satellite set up magnetic fields, which react with the Earth's magnetic field. Another reason a satellite may act as a magnet is due to a negative electrical charge that is generated by the satellite passing through the partly ionized medium which produces a negative charge on the satellite's skin. The negative charge is higher on the day side of the orbit than on the night side. The motion of a charged satellite made of conductive materials through Earth's magnetic field also results in the satellite acquiring an electrical potential gradient which is proportional to the intensity of the magnetic field and the velocity of the satellite as it passes through the field. These cause a magnetic drag to act upon the satellite. The drag can cause torquing of the satellite.
Auroras The aurora borealis (northern lights) and the aurora australis (southern lights) are multicolored bands of visible light effects seen in the nighttime sky. Auroras occur in the upper atmosphere of both the north and south poles where the Earth's magnetic field bends towards the Earth's surface. The bottom of the auroral curtain is about 62 miles (100 km) in altitude, extending up to about 190 miles (300 km). Seen from above by research satellites, the auroral curtain appears along oval belts around the Earth's geomagnetic poles. The average radius is about 1,400 miles from the poles (about 70/ north or 70/ south latitude) and extend thousands of miles to the east and west. Typically, the auroral band is only about one mile or less thick.
Light of Auroras The light of the auroras is caused by electrical discharges powered by the interaction of the Earth's magnetic field and the solar wind. The solar wind supplies the necessary charged particles which perturb the magnetosphere so that the particles are "dumped" into the atmosphere near Earth's magnetic poles. As these particles collide with gas molecules in the upper atmosphere, light energy is released, causing auroral displays. Increased activity in the auroras indicates major solar activity that can affect military communications.
Geographic Anomalies The center of Earth's magnetic field is offset from the center of Earth by 270 miles towards the Western Pacific Ocean. This leads to two areas on Earth where the magnetic field strength will be either stronger or weaker than expected. These areas are geographic anomalies.
  • The South Atlantic anomaly is a region of unusually low magnetic field strength. At this location where the low strength field lines dip to a low altitude, many particles enter the atmosphere and collide with the higher density atmospheric particles. As a result of these collisions, we have ionospheric effects similar to those produced in the auroral regions. This will disrupt high frequency (HF) transmissions.
  • The Southeast Asian anomaly is an area of unusually high magnetic field strengths. As a result of this strong field, the trapped particles will have a higher density at any given altitude. This leads to an enhanced F2 region in the ionosphere. This can adversely affect communication transmissions that pass through this region.
The solutions to the problems caused by these anomalies are to use a frequency not affected by the disturbed conditions or to avoid transmissions within either region.
5-6 Space Environment Effects on Satellites
Introduction The environment in space has significant effect on satellites. The discussion below highlights the principal effects experienced by satellites orbiting the Earth.
Satellite Charging Satellite charging is a variation in the electrostatic potential of a satellite with respect to the surrounding low density plasma around the satellite or to another part of the satellite. The extent of the charging depends on both design and orbit. The two primary mechanisms responsible for charging are plasma bombardment and photoelectric effects.
Van Allen Radiation Belts Plasma bombardment occurs due to varying plasma density, resulting in the surface of the satellite becoming electrostatically charged. This can occur in the proximity of the Van Allen radiation belts and the magnetotail. Charging from plasma bombardment usually results in a negative charge on the surface of the satellite. The photoelectric effect results from solar radiation which liberates electrons on a satellite's surface, resulting in a positive charge on the satellite's sunlit side. A satellite will usually have a negative potential on shaded areas (due to plasma charging) and a positive potential on sunlit areas (due to the photoelectric effect). If the surface of the satellite is conductive, a current will develop to cancel these potentials. For a non-conducting surface, the charge separation will be maintained until voltage exceeds the resistive threshold of the material. This leads to a sudden electrostatic discharge.
Satellite Discharging The satellites most vulnerable to charging/discharging are those located at geosynchronous altitude. Discharges as high as 20,000 volts (V) have been experienced. Satellites in geosynchronous orbits typically move both in and out of the upper regions of the Van Allen Radiation Belts and the Earth's magnetotail. This results in a low plasma density around the satellite which does not allow the charge to bleed off or neutralize before a discharge occurs.
Hardware Damage Sudden electrostatic discharge (high current or arc) can cause hardware damage, such as:
  • Blown fuses or exploded transistors, capacitors and other electronic components.
  • Vaporized metal parts.
  • Structural damage
  • Breakdown of thermal coatings
Electric Problems These discharges can result in electrical or electronic problems, such as:
  • False commands
  • On/Off circuit switching
  • Memory changes
  • Solar cell degradation
  • Degradation of optical sensors
Deep Charging Deep charging of a satellite occurs when cosmic ray particles pass through a satellite and ionize atoms within, through collisions. Some of these particles are solar in origin, but the majority are galactic and with no preference to time or light conditions. They do show some dependence on the solar cycle.
Particle Collision High energy solar flare particles and galactic cosmic rays can cause direct damage to the surface of a satellite. The damage can include vaporization of surface materials and structural damage. These particles can also enter star or horizon sensors and mimic reference points. This can lead to false readings resulting in loss of attitude: antennas and solar panels pointing in the wrong direction, miscorrection of orbit.
Outgassing Although the environment in space is not benign, the density of particles above 100 miles altitude is extremely low. There is almost no atmospheric pressure, similar to a complete vacuum. As a result, satellites and the materials they are made of experience phenomena which are not encountered on Earth. In a vacuum, some materials experience outgassing. Outgassing is a phenomena where molecules of material evaporate into space. Although many materials experience outgassing, composite materials and those made with volatile solvents are particularly susceptible. These include electronic microchips, plastics, glues and adhesives. Outgassing can result in changes to the physical properties of a material, In addition, the evaporating molecules can form a thin film over other components of the satellite, thereby affecting their performance. Outgassing can be minimized through careful selection of component materials but eventually some components will exhibit different characteristics and properties.
5-6 Space Environment Effects on Satellites, cont'd
Space Debris Space debris is defined as any non-operational man­made object of any size in space. The size of space debris varies from complete inoperative satellites and expended rocket bodies to small chips of paint. Of the almost 10,000 man­made items in space currently tracked and catalogued, only about 5% are operational space systems. The rest is space debris. Space debris smaller than approximately 2 cm (0.78 inches) cannot be detected and tracked reliably, therefore it is reasonable to assume that there is significantly more space debris than we know about. It has been estimated that as many as 100 satellites have broken up while in orbit, sometimes due to explosions of propulsion systems, and at other times due to impact with other space debris. The result is a an estimated 40,000 to 80,000 pieces of debris in orbit around the Earth. There is even a wrench that became space debris when it drifted away from an astronaut during a space walk. Most debris is small but it can be traveling at relatively high speeds.
Debris in Different Orbits Debris in low Earth orbit tends to have much higher velocities relative to other objects in orbit than those at geostationary orbit altitude (22,300 miles). In a collision between two objects, the force of impact is determined by the relative velocity and the masses of the objects. A dense object like the wrench could do catastrophic damage if it were to hit a satellite at even a low relative velocity. At high impact velocities of 30,000 mph, even small objects are capable of inflicting significant damage. A small paint chip damaged a window on the space shuttle when it impacted at about 8,000 miles per hour. Shielding, energy absorbing panels and other design considerations can make a satellite more resistant to damage from impacts with small space debris. At altitudes below 200 miles, atmospheric drag tends to cause much debris to reenter the Earth's atmosphere where it is usually vaporized. This self­cleaning space debris located at the altitude of geostationary orbits tend to have lower relative velocities (200 ­ 1,000 mph) and the density is much less. Atmospheric drag at this altitude is almost zero, therefore the debris is present for a much longer time.
Meteoroids It is estimated that approximately 20,000 tons of natural material is added to the Earth each year from impacts of meteoroids and asteroid fragments with the Earth's atmosphere. Most of these particles are the size of dust particles, however, some are much larger. When meteoroids enter the Earth's atmosphere they usually burn up due to the friction with the air molecules. Larger meteoroids generate enough light to be seen as meteors streaking across the night sky. Occasionally, larger objects don't completely vaporize. When a piece strikes the surface of the Earth it is called a meteorite. These particles represent a constant natural danger to satellites in orbit around the Earth. The Long Duration Exposure Facility (LDEF) was a U.S. research satellite that remained in orbit for six years before it was recovered by the Shuttle and returned to the Earth. Examination of the exposed surfaces indicate thousands of impacts by micro-meteoroids. Microscopic examination has revealed extensive damage to metal surfaces. Most meteoroids are too small and traveling too fast to be detectable in time for satellite controllers to direct a satellite to change it's orbit to avoid collision. Shielding and other design considerations are the most effective means to protect satellites from catastrophic damage.
Section 2: Orbital Mechanics
5-7 Orbital Mechanics
Overview Satellites move predictably according to the laws of physics. Satellites do not escape Earth's gravity. In fact, it is Earth's gravity that holds them in orbit. Without gravity there would not be any satellites because nothing would stay in orbit. Many different types of orbits can be achieved by changing a satellite's orbital parameters. For example, it is possible to position a satellite over the equator at an altitude where the time for it to revolve around the Earth is exactly one day. The result is the satellite will appear to be stationary to an observer on the surface of the rotating Earth below. It is also possible to create an orbit so that a satellite will pass within view of every point on the Earth at the same time every day and night. Some orbits are not possible. For example, it is not possible to position a satellite in low Earth orbit so that it will loiter or hover over a particular spot.
Intent of This Section The orbit chosen for a satellite is determined by the mission it is designed to perform. The intent of this section is to present information in non­mathematical terms that allow the reader to develop an understanding of the motion of Earth satellites. This provides a basis for understanding the capabilities and limitations of various orbits, particularly with respect to the service that the satellite provides to the user.
5-8 Kepler's Laws of Planetary Motion
Introduction In the early 1600's, Johannes Kepler formulated three Laws of Planetary Motion. Although his laws were intended to explain the motion of the planets around the Sun, they also apply to any satellite orbiting around another object.
Kepler's First Law: Law of Ellipses "The orbit of each planet is an ellipse with the sun at one focus." As it applies to satellites in orbit around the Earth Kepler's first law can be restated as, "The orbit of each satellite is an ellipse with the center of the Earth at one focus." The other focus is an imaginary point in space.

Kepler's Second Law: Law of Areas "Every planet revolves so that the line joining it to the sun sweeps over equal areas in equal times anywhere in the orbit." For earth orbiting satellites this can be restated as, "A satellite orbits so that the line joining it with the center of Earth sweeps over equal areas in equal times anywhere in the orbit." In a circular orbit a satellite travels at the same speed at all points. In an elliptical orbit the speed of the satellite varies. As the satellite approaches closer to the Earth its speed increases. The maximum speed is attained at the point of closest approach called the perigee. As the satellite moves away from the Earth it slows down. The slowest velocity occurs at the point farthest from the Earth, the apogee.

5-8 Kepler's Laws of Planetary Motion, cont'd
Kepler's Third Law: Law of Harmonics "The square of the sidereal periods (the time it takes to complete one orbit of the Sun) of any two planets are to each other (proportional) as the cube of their mean distances from the center of the Sun." For a satellite in orbit around the Earth this can be restated as, "The squares of the orbital periods (time it takes a satellite to complete one orbit) of two satellites are proportional to each other as the cubes of their mean distances from the center of the Earth." The square of the period divided by the cube of the mean distance from the center of the Earth is a constant for all objects. The constant number is not dependent upon the mass of the satellite. Kepler's third law of planetary motion has many implications. First, satellites of different masses with exactly equal orbits have equal speeds. The mass of a satellite does not determine its period or orbital speed. Second, satellites with orbits of equal semi­major axis length have equal periods, whether or not their eccentricities are the same. Finally, comparing two satellites with orbits of equal eccentricity, the orbit with the longer semi­major axis has a larger circumference, and the satellite in the larger circumference orbit has a lower speed. Thus, satellites farther away from the Earth have more distance to travel and move more slowly than satellites closer to the Earth.

5-9 Newton's Laws
Introduction Sir Isaac Newton was a British scientist who, in the late 1600's, formulated his laws of motion and a law of universal gravitation. Kepler's laws provided mathematical formulas for the orbits of satellites but did not explain what forces cause satellites to move in space the way that they do.
Newton's Firs Law: Law of Inertia "Every body continues in a state of rest or of uniform motion in a straight line unless it is compelled to change that state by a force impressed on it." An object at rest will remain at rest and an object in motion will remain in motion in a straight line, unless it is acted upon by an outside force.
Newton's Second Law: Law of Momentum "When a force is applied to a body, the time rate of change of its momentum is proportional to, and in the direction of, the applied force." Momentum is the property of a moving body that determines what force is required to bring the body to rest in a given amount of time.
Newton's Third Law: Law of Action-Reaction "For every action there is a reaction, equal in magnitude, but opposite in direction, to the action." The effect of this law is most easily demonstrated where friction is not present or is extremely low. This is the law which explains how rockets work. The rocket exhaust gases are light but are ejected at high velocity. This results in a force which accelerates the larger mass of the rocket. The maximum velocity of the rocket is the maximum velocity of the rocket gases, however, the propellant is usually expended before that velocity is attained.
Newton's Law of Universal Gravitation Newton also formulated the Law of Universal Gravitation. It states, "Between any two objects in the universe there exists a force of attraction that is in proportion to the product of the masses of the objects and is in inverse proportion to the square of the distance between them."
F=G m1m2/d2
The gravitational attraction between two objects is greater for more massive objects and decreases as the square of the distance between the objects increases. "G" is the Universal Gravitational Constant which is the same everywhere in the universe. Newton based his derivation on large objects rotating mutually about each other, such as the Earth and the Moon. It applies equally to man­made satellites orbiting the Earth except that the mass of the man­made satellite is so small compared to the mass of the Earth that the offset of the center of rotation of the two objects from the center of the Earth's mass is so small it is ignored. It is the force of gravity that allows satellites to orbit. Gravity is the force that continually acts on the satellite to continually change its direction in order to circle Earth. Without gravity, the satellite would fly off into space in a straight line, maintaining constant velocity.
Gravitational Effects The law of universal gravitation states that all objects with mass in the universe exert a gravitational attraction on all other objects. The number of objects in the universe is almost infinite but the gravitational forces from objects farther away than the immediate solar system are very insignificant. The force of the Earth's gravity at sea level results in an acceleration of about 32 ft/sec2. This is called a "1 g force". For a satellite in orbit 200 miles above the Earth the effects of gravity from the most significant sources are shown below:
Gravitational Effect of an Earth Satellite with a 200 mile Altitude
Source of Gravitational Force
Strength of Gravitational Force
Earth 0.89 g 28.600 ft/sec2
Earth's Oblateness 0.0001 g 0.030 ft/sec2
Sun 0.0006 g 0.019 ft/sec2
Moon 0.0000033 g 0.001 ft/sec2
5-9 Newton's Laws, cont'd
Gravitational Attraction on a Satellite Satellites do not escape Earth's gravity but are held in orbit by it. Without the constant force of Earth's gravitational attraction on the satellite it would go off into deep space in a straight line. As the distance from the Earth increases the Earth's gravitational force decreases, thus the gravitational effects of other bodies in the solar systems become relatively more significant.
Misconception A misconception is that centrifugal force somehow affects the orbit of a satellite. It does not. Centrifugal force only exists when there is a physical link between two objects and one is moving around the other. A ball tied to the end of a string and swung around in a circle is an example. If the string breaks, the ball moves in a straight line except that the Earth's gravity pulls it toward the center of the Earth. The ball follows an arching path until it hits the ground. Obviously, there is no string, rope or equivalent attached to each satellite. The principle force that holds satellites in orbit is gravity.
5-10 Putting a Satellite Into Orbit Around the Earth
Introduction To put a man­made object into orbit around the Earth requires that a number of conditions be met. The most critical are velocity and altitude. At sea level an object falls 16 feet in the first second of travel due to gravity. The curvature of the Earth is about 16 feet every five miles. To put a satellite into orbit around the Earth the satellite must be accelerated to a velocity parallel to the surface of so that the curvature of the Earth compensates for the distance the satellite falls toward the center of the Earth. Near the surface of the Earth an object would have to travel about five miles per second (about 18,000 miles per hours). Of course, friction from the atmosphere near the Earth's surface is substantial. At 18,000 miles per hour air friction would quickly heat the object to a high temperature and it would burn up before traveling very far. To avoid air friction, the object must be boosted to an altitude high enough to avoid most of the atmosphere. These factors determine the basic altitude and velocity necessary to put an object into orbit around the Earth. The minimum speed for an object to be placed into orbit around the Earth is about 17,500 miles per hour and the minimum altitude of a circular orbit is about 90 miles.  At this altitude the atmospheric density is still enough to cause the satellite to slow down so that it would fall out of orbit after only a couple of revolutions. It would either burn up during the high speed reentry through the atmosphere or it would impact on the surface. In addition, an object placed into orbit will return to the last place where propulsion was provided.
Use of Rockets Rockets are used to accelerate a payload to the required velocity and altitude to place an object into orbit around the Earth. Other means of propulsion are possible but none have proven more capable or efficient. A rocket accelerates the payload to the required velocity and altitude. In addition, a rocket provides propulsion until it burns out which is usually at an altitude high enough for the payload to go into orbit. Since an object in orbit will return to the last point that propulsion was provided, it is important that burnout occur at an altitude high enough to avoid the Earth's surface and most of the atmosphere.
Thrusters After a satellite is placed into an initial orbit, it is common to use additional rockets or thrusters to position the satellite into its final orbit.
5-11 Location Reference Systems
Introduction Location reference systems are used to describe where a place or object is located. Of the many reference systems available, the Geographic Coordinate Reference Systems (often referred to as the Earth­Fixed Greenwich Reference Systems) and the Geocentric (or Earth Centered) Inertial Coordinate System stand out because of their use in locating points on the surface of the Earth or describing the motion of Earth orbiting objects.
Fundamental Plane Although each location reference system has its own unique terminology, all have a fundamental plane, a point of origin or a reference point located on the fundamental plane, and a principle direction on the fundamental plane. Once the fundamental plane, origin, and principle direction have been established, it is possible to make distance and angular measurements from them. These measurements are sometimes called displacements.
Geographic Coordinate Reference Systems These systems are used to describe locations on most maps of the Earth's surface. The fundamental plane is the equatorial plane of the Earth. The point of origin is the center of the Earth. The principal direction is a line from the center of the Earth through the point where the prime meridian intersects the fundamental plane. The prime meridian is 0/ longitude, an imaginary line on the surface of the Earth from the North Pole to the South Pole which passes through Greenwich, England.  Altitude is usually stated as distance above sea level. Sea level is approximately one Earth radius from the center of the Earth (point of origin). The Military Grid Reference System (MGRS), the Universal Transverse Mercator (UTM) coordinate system and latitude/longitude are examples of Geographic Coordinate Reference Systems. The Earth is constantly spinning about its axis, therefore the principle direction also rotates. This makes these location reference systems unsuitable for describing the location and motion of objects orbiting the Earth.

Geocentric Inertial Coordinate System The Geocentric (Earth­Centered) Inertial Coordinate System is used to determine the orientation of an object orbiting the Earth in space. The origin is the Earth's center, the fundamental plane is the equatorial plane and the principal direction is a line to the First Point of Aries which is the direction from the center of the Earth to the center of the Sun when the Earth is at the vernal equinox. This can also be drawn as a line from the vernal (spring) equinox to the autumnal (fall) equinox. The Earth rotates daily about its axis at an angle (23/ 7') to the orbital (ecliptic) plane of the Earth as it rotates yearly about the Sun, thus the Earth's equatorial plane is at an angle to the ecliptic plane. Twice a year the Earth's orbit crosses the point where the ecliptic plane and the Earth's equatorial plane intersect. These points are called equinoxes because the length of daylight and night are the same. The Autumnal (Fall) Equinox occurs on 21 September, the first day of Fall. The Vernal (Spring) Equinox occurs on the first day of spring, 23 March. Using the direction to the First Point of Aries as the principle direction provides a way to describe the location of a satellite in orbit around the Earth without regard to the Earth's rotation about its axis.

5-12 Orbital Element Set
Introduction A set of orbital parameters or elements is used to describe the size and shape of a satellite's orbit, the orientation of the orbital plane, the orientation of the orbit within the orbital plane, and to locate the satellite within the orbit at any specified time. Element sets or "elsets" are used to calculate where a satellite is at a specified time and to predict where it will be in the future. Predictions are only approximations because many of the minor forces which influence a satellite's orbit are not included in the calculations. If the values in the element set are current, the predictions can be quite accurate. The values in the orbital element set must be updated more frequently for satellites in low Earth orbit than for those in geostationary orbit.
NORAD/NASA Sets There are numerous ways to express these parameters but the most two most common are the Keplerian orbital element set and the NORAD two­line element set. The NORAD two­line element set is also called the NASA two­line element set.
Keplerian Orbital Elements The Keplerian orbital element set consists of the following seven parameters to describe the motion of a satellite:
  • Semi­major axis
  • Eccentricity
  • Inclination
  • Right ascension of the ascending node
  • Argument of perigee
  • Epoch time
  • True anomaly
Semi-Major Axis All satellites move along an elliptical path. An ellipse has two foci. The sum of the distances between a point on the ellipse to each of the foci is the same for all points on the ellipse. A circle is a special ellipse where the two foci are in the same place. The maximum distance from the center of an ellipse to a point on the ellipse is called the semi­major axis; the minimum distance from the center to a point on the ellipse is called the semi­minor axis. The semi­major axis helps to describe the size of an orbit.

Eccentricity The shape of an ellipse is determined by its eccentricity. Eccentricity describes the amount an ellipse deviates from a circular shape. Eccentricity is the ratio of the distance from a focus to the center of the ellipse divided by the length of the semi­major axis. The center of a circle is the same point as the focus, therefore the eccentricity of a circle equals 0. All elliptical orbits have an eccentricity equal to or greater than 0 but less than 1. An eccentricity equal to 1 describes a parabolic path. An eccentricity greater than 1 describes a hyperbolic path which does not represent an orbit.
5-12 Orbital Element Set, cont'd
Inclination The inclination of an orbit is the angular measurement (0/ to 180/) of the extent to which the orbital plane tilts up into the northern hemisphere from the equatorial plane, measured at the ascending node. The ascending node is the point in the orbit where the satellite crosses from the southern hemisphere to the northern hemisphere. The value of the inclination of an orbit is also the value of the northernmost and southernmost latitudes of the satellite ground track. The inclination of an orbit helps to describe its orientation in space.
Description of Orbits Orbits are sometimes described by their inclination.

Prograde Inclination greater than or equal to 0 but less than 90; the satellite orbits Earth in the same direction as Earth's rotation.
Retrograde Inclination greater than 90 but less than or equal to 180; the satellite orbits Earth opposite to Earth's rotation. Sun synchronous orbits, common for weather and remote sensing satellites, are retrograde orbits.
Polar Inclination equal to 90; the satellite orbits from the north pole to the south pole and back to the north pole. Orbits with an inclination very close to 90 (88 ­ 92) are often referred to as being polar.
Equatorial Inclination equal to 0 or 180; the satellite's orbital plane and the equatorial plane of the Earth are the same therefore, the satellite is in orbit directly above the equator of Earth.
Right Ascension of the Ascending Node The right ascension of the ascending node is the angular measurement (0 to 360) in the equatorial plane from the First Point of Aries to the ascending node. The ascending node is the point where the satellite's orbit intersects the Earth's equatorial plane when the satellite is crossing from south to north. The line of nodes is an imaginary line between the ascending node and the descending node. Since an orbital plane always intersects the center of the Earth, the line of nodes will always pass through the center of the Earth. The right ascension of the ascending node helps to describe the orientation of a satellite's orbit in space.
Augment of Perigee The argument of perigee is an angular measurement (0 to 360) from the ascending node along the orbital path to the point of perigee. The apogee is directly opposite the perigee, a difference of 180/. The line of apsides is an imaginary line between the apogee and the perigee of an orbit. It will also pass through the center of the Earth. The argument of perigee helps to describe the orientation of a satellite's orbit in its orbital plane.

5-12 Orbital Element Set, cont'd
Epoch Time Epoch time is an arbitrary time used as a reference point at which other orbital parameters are measured. The US Space Command states the epoch time when the satellite is at the ascending node. In traditional Keplerian element sets, epoch time is usually stated when the satellite is at its perigee. An orbit number or revolution number associated with the epoch time is usually included in the orbital element set.
True Anomaly True anomaly is the angular measurement (0 to 360) from the center of the Earth in the direction of a satellite's motion from the point of perigee along the orbital path to the location of the satellite at a specific epoch time.
Mean Anomaly The mean anomaly is the angle measured from the center of an ellipse from the perigee to the satellite's position through which it would move in a specified period of time if it moved at its mean angular rate of motion. The mean angular rate of motion is the period of the orbit divided by 360 (one complete revolution). The mean anomaly is the same as the true anomaly for a satellite in a perfectly circular orbit.
Period The element set describes the average orbit for a satellite. Due to perturbations, the satellite's actual orbit will deviate somewhat from a perfect ellipse. The period of a satellite is not an orbital element, but it is extremely useful. There are four different ways to describe the period of a satellite:
  • Nodal Period: The time it takes a satellite to travel once from ascending node to ascending node. In most space discussions, "period" is used when referring to the nodal period.
  • Keplerian Period: The period defined by Kepler's third law. This period does not take perturbations into account and is only an average.
  • Anomalistic Period: The time it takes a satellite to travel once from perigee to perigee.
  • Sidereal Period: The time it takes a satellite to cross the equatorial plane at 0/ right ascension from the last time it crossed at 0/ right ascension.
NORAD (or NASA) Two-Line Element Set The NORAD two­line element set was developed by the North American Air Defense (NORAD)Command and the same format is now used by NASA and the US Space Command. The components of the NORAD two­line element set are shown below. The numerical values are updated frequently and are available from many government, commercial and private computer bulletin board systems (BBS). The NORAD two­line element set is used by a variety of commercial, shareware and public domain computer programs that calculate and display the motion of a satellite and usually draw a graphic picture of the satellite's ground track. These programs can be used to predict when a satellite will be within view of a particular location on the Earth.
5-12 Orbital Element Set, cont'd
Line 1 The Satellite No. is assigned by US Space Command as a sequential reference number. The letter following the satellite number on Line 1 indicates the security classification of the element set. "U" represents unclassified. The International Designator is a reference number assigned by the International Astronomical Union, an international organization with headquarters in Paris, France. The first two numbers represent the year of launch. The second two or three numbers are sequential numbers assigned as space objects are registered. This is followed by a letter. Sometimes one launcher places more than one satellite into orbit. The letter "A" represents the first object, "B" the second object and so on. The Epoch is a modified Julian date/time. The first two numbers are the year followed by three digits indicating the Julian date (the number of the day of the year). The decimal number represents the time of day since midnight GMT (0000Z). In the example, the epoch was set in 1991, on the 189th day (8 July). The time of day was 1300.45Z (0.54185552 x 24 = 13.004532). The first derivative of mean motion is the rate of change of the mean motion. The smaller the number, the more stable the mean motion of the satellite. The second derivative of mean motion is the rate of change of the first derivative of mean motion. A decimal point is implied but not shown before the first number. This number is usually zero. The number following the "­" represents the power of 10­1 of the number preceding it. For example "­0" at the end of the number represents 100. (100 = 1).
  • BSTAR is a number calculated by U.S. Space Command as a measure of the drag coefficient of the satellite. It is only used in technical computations.
  • The ELSET number is a sequential number assigned by US Space Command indicating the version number of the element set. The number increases by one each time a new element set is published. After the number "999" is reached, the number starts again at "1".
Line 2 The second line of the element set begins with a repeat of the satellite number. The unit of measurement for the inclination, right ascension of the ascending node, argument of perigee and mean anomaly is degrees. The eccentricity is a decimal number (the decimal point is implied) between 0 and .999999. The value for mean motion is the number of orbits that the satellite completes in one day. To determine the period divide 1440 minutes per day (24 hrs/day x 60 min/hr) by the value of the mean motion. In the example, the period of the NOAA 12 satellite is 101.304 minutes (1440/14.21464718 = 101.304). The number of revolutions is the number of revolutions that the satellite had completed at the stated epoch time since the satellite was launched.
Satellite Ground Tracks The ground track (also called ground trace) of an orbiting satellite is the trace of its path across the surface of the Earth. The path on the surface of the Earth is the trace of the satellite's nadir, or the point directly below the satellite where the orbital plane intersect the Earth's surface. A satellite ground track drawn on a map shows what areas the satellite will pass directly over.
Effect of Earth's Rotation If the Earth did not rotate, a satellite's ground track would simply repeat itself until some force changed the orbit. Of course, the Earth does rotate about its axis once (360) each day. This equates to an angular rotation speed of about 15 per hour. The result is that each successive orbit track will be offset 15 to the west for each hour of the satellite's period. A period of 90 minutes results in an offset of 22.5 (15/hr x 1.5 hr = 22.5)for each successive orbit.
Effect of Inclination The inclination of an orbit determines the highest north and south latitude of the ground track. Since all satellite orbital planes must pass through the center of the Earth, a satellite's ground track must be over or pass through the Equator. For a prograde orbit, the inclination of the orbit equals the highest north or south latitude of the ground track. A polar orbit has an inclination at or near 90. For a retrograde orbit (90 to 180 inclination), the highest inclination of the orbit equals 180 minus the highest latitude of the nadir.
Continued on next page 5-12 Orbital Element Set, cont'd
Effect of Altitude As the altitude of an orbit increases, the period becomes longer and the satellite's speed is lower. The result is that it takes more complete orbits to make a complete track around the globe.
Effect of Eccentricity The ground track of a satellite in a circular orbit (eccentricity = 0) is similar to a continuous sine wave. The portion above the equator is identical to the portion below. As the eccentricity of an orbit increases from zero to 1, the perigee remains close to the Earth while the apogee increases in distance. For highly eccentric orbits, the ground track of the portion near the perigee is wider than near the apogee. This is because the maximum speed of the satellite occurs at perigee and, therefore, the satellite ground track covers a greater portion of the Earth's surface. It also means at perigee a satellite is in view of a ground observer for less time. An advantage of a highly eccentric orbit is that as the satellite approaches the apogee of the orbit, it slows down and seems to linger over a geographic area.
Effect of Launch Site Location For launches due east (90 azimuth) or due west (270 azimuth) from a launch site, the resulting orbital inclination will equal the latitude of the launch site. For launches on any other azimuth, the inclination will always be greater than the latitude of the site. Thus, the choice of launch site determines the minimum inclination of the launch orbit. To attain an inclination that is lower than the latitude of the launch site requires additional orbital maneuvers, usually after the satellite has achieved orbit.

A satellite launched on an azimuth between 0 and 180 will have an inclination of between 0 and 90, hence a prograde orbit. Satellites launched on azimuths between 180 and 360 will have an inclination between 90 and 180, hence a retrograde orbit. Launching due north or due south (0 and 180 azimuth, respectively) will result in a polar orbit. It doesn't matter where the launch site is, the orbit will be polar. The Earth spins to the east at 1,037 miles­per­hour (mph) at the equator and 0 mph at the poles. A substantial savings in rocket propellant is possible by locating the launch site on or near the equator and launching to the east. This gives the launcher up to 1,037 mph more velocity without burning fuel if launched due east. To launch a satellite into a retrograde orbit it is desired to launch from as high a latitude as possible so that the launcher has to overcome as little of the Earth's rotational speed as possible.

5-13 Orbital Pertubations
Introduction Kepler's laws of planetary motion and Newton's laws of motion and law of universal gravitation describe how two objects move in a uniform environment. The universe, however, is not uniform. The Earth does not have a uniform density and it is not a perfect sphere. The Earth has an atmosphere and a magnetic field which extend out into space. The Sun emits vast amounts of matter and energy that vary significantly. The solar system is made up of many massive objects. The result is that there are variations in the movement and path of objects in orbit around the Earth. These variations are called perturbations. Perturbations are the effect of a variety of outside forces which act on a satellite to change its orbit.
Asymmetry of Earth Although the Earth is commonly portrayed as a perfect sphere, with a uniform shape and density, it is not. The Earth is asymmetric (uneven) in numerous ways. The material within the Earth is not distributed evenly throughout its body. For this reason, its gravitational pull is not equal in all directions.
Oblateness of Earth The Earth is oblate which means that it is fatter at the equator and somewhat flattened at the poles. The Earth's oblateness is caused by its daily rotation about its axis. The average radius of the Earth is 3,958.94 miles (6,371.00 km) but the radius to the equator is 3,963.38 miles (6,378.14 km) while the radius to the poles is 3,950.09 miles (6,356.76 km). The north polar region is more pointed than the south polar region producing somewhat of a pear shape. The equator itself is slightly elliptical (e = 1.6 x 10­5) rather than a perfect circle. The oblateness of Earth causes satellites in an inclined orbit to precess. Satellites in a prograde orbit precess to the west. Satellites in a retrograde orbit precess to the east. The amount of precession is more pronounced in low altitude satellites. This precession can be an advantage to help maintain a satellite in a sun synchronous orbit without expending any fuel for course changes.
Homogeneous-ness of the Earth The Earth is not homogeneous. It does not have uniform density, therefore the force of gravity from the Earth's mass is not quite the same in all directions. There is a region over the Andes Mountains in South America where gravity is somewhat weaker. This is often referred to as a "gravity hill." A satellite in geostationary orbit over this region requires more station keeping because the satellite tends to drift away to other areas with stronger gravity potential. There is an area over the Indian Ocean where gravity is somewhat stronger. This is often referred to as a "gravity well". Satellites in geostationary orbit over this region tend to remain there with very little station keeping. The area over the Indian Ocean is useful for holding inactive satellites in a temporary storage location.
5-14 Orbit Types
Introduction Orbits are put in categories or types depending on many different parameters such as altitude, eccentricity, inclination, synchronization with the Sun or other parameters. Sometimes the parameters are combined to describe the orbit. An example is a "polar, circular, low Earth orbit". In other cases they are given names such as a Clarke orbit (geostationary) or a Molniya orbit (highly elliptic, inclined, semi­synchronous).

Low Earth Orbit (LEO) There is no formal definition of what constitutes a Low Earth Orbit (LEO) but it is generally considered to have an apogee (maximum altitude) of no more than approximately 530 miles. Inclination of the orbital plane can be any value. Most low Earth orbits are nearly circular, therefore the eccentricity is very close to zero. At low altitudes, atmospheric drag significantly limits the lifetime of satellites unless they are periodically boosted into a higher orbit. Orbital lifetime, without any propulsion, is about one year at an altitude of 200 miles. Orbital lifetime at 500 miles altitude is more than 10 years. A considerable amount of space debris has collected in the higher altitudes, thus increasing the chances of having a collision with a piece of space debris or a meteoroid large enough to do significant damage to an orbiting satellite. Low Earth orbits are commonly used for observation, environmental monitoring, small communications satellites, and science instrument payloads. Manned orbiting satellites, such as the U.S. Space Shuttle and the Russian Mir, generally remain below an altitude of 300 miles so that heavy shielding to protect the crew from radiation from the Van Allen radiation belts is not needed. Satellites in LEO have the advantage that they pass relatively close to areas on the Earth. The disadvantage is that the satellite is in view of the ground user for only a short period of time as it passes quickly overhead. A satellite in LEO cannot provide continuous coverage to a specific geographic point or area. Some of the larger satellites in low Earth orbit are observable with the naked eye, especially in the early morning or late evening when it is dark on the surface of the Earth but the satellite is in sunlight. If an observer on the ground is able to see a low Earth orbiting satellite, it looks like a small dot in the sky, traveling quickly from one horizon to another, not necessarily directly overhead.
Sun-Synchronous Orbit A special case of a LEO is the sun­synchronous orbit. It is a retrograde, near­polar orbit, oriented in such a manner that the "sun­time" at any given point on Earth is the same each time the satellite passes over it. The inclination needed to achieve a sun synchronous orbit is determined by the altitude and the eccentricity of the orbit. Most commonly the inclination is about 98/. This orbit will always maintain the same relative orientation to the position of the sun. Thus, shadows cast by objects on the surface of Earth at any given latitude are always the same length when the satellite passes overhead. Thus, any change, such as new construction, is easily observed. Some weather and remote sensing environmental satellites use this type of orbit.
Semi-Synchronous Orbit A semi­synchronous orbit has a period equal to half of a day. It is possible to have an inclined, nearly circular semi­synchronous orbit which repeats an identical ground trace twice each day. A satellite with this period is considered to be in a medium altitude orbit. Satellites in this orbit are subject to high doses of radiation in the Van Allen radiation belts. Satellites in this orbit must be designed to withstand the increased radiation levels encountered while passing through the belts. A common application of this type of orbit is for the Global Positioning System (GPS) satellites.
Highly Elliptical Orbit There is no universal definition for a highly elliptical orbit, however, those with an eccentricity greater than 0.5 are generally considered to be highly elliptical. A satellite in a highly elliptical orbit spends most of the time on the side with the apogee. There is no specific inclination, altitude nor period associated with highly elliptical orbits.
5-14 Orbit Types, cont'd
Molniya Orbit A Molniya orbit is a specific form of a highly elliptical, semi­synchronous orbit. It has a 64 inclination, 0.7 eccentricity, and perigee over the southern hemisphere. A satellite in a Molniya orbit spends 11.7 hours of its 12 hour period in the northern hemisphere. This makes the Molniya orbit well suited for communications satellites intended to provide coverage in the extreme north where access to geostationary satellite is generally not feasible.
Geosynchronous Orbit A geosynchronous orbit has a period equal to that of Earth's rotation, 1 day. A satellite with this period is considered to be in a high altitude orbit; its mean orbital radius is about 22,300 miles. A geosynchronous orbit can have any inclination. Varying the inclination of the orbit produces ground traces that fluctuate about a point on the equator in the pattern of a figure eight; the larger the inclination, the larger the figure eight, until, when at polar inclination, a figure eight ground trace with its top at the north pole and bottom at the south pole is produced. Some types of communication, weather, and surveillance/warning satellites use geosynchronous orbits.
Geostationary Orbit A geostationary orbit is a special kind of geosynchronous orbit. The satellite's orbital plane is very close to the equatorial plane of the Earth thus the inclination is near 0. The orbit is as circular as possible, and eccentricity is almost zero. The orbital period of the satellite is the same as the period of the Earth's rotation around its axis (1 day). To an observer on the ground the satellite appears to be stationary in the sky. The satellites can be positioned so that they are positioned over any east/west longitude along the equator. The most significant advantage is that the satellite provides continuous coverage of specific areas of the Earth and antennas do not need to track the satellite. Geostationary orbits are used extensively for communications, weather and some detection satellites. Close to the North and South Poles, a user's antenna aimed at a geostationary satellite would have a very low elevation. The signal would have to travel through much more atmosphere and the amount of interference from ground clutter makes the use of geostationary satellites impractical at latitudes greater than 70. In the Southern Hemisphere, only Antarctica is affected. In the Northern Hemisphere, the northernmost part of Alaska along the Arctic Ocean, extreme northern Canada, Greenland, extreme northern Scandinavia and northern Siberia have restricted access to geostationary satellites nor can sensors on geostationary satellites observe these areas effectively.
Deep Space Orbit Deep space orbits have altitudes above geosynchronous altitude. Satellites in this type of orbit appear to move through the sky in the same manner as the moon, rising in the east and setting in the west, but slowly moving westward along the backdrop of the night time sky. It is generally used by scientific satellites, to perform tasks such as monitoring the outer solar terrestrial environment.
Libration Points (Lagrangian Poits) Libration points, often called Lagrangian points after the 18th century French mathematician and astronomer, Joseph Lagrange, are points where the forces of gravity from two large objects in mutual orbit are balanced. All libration points are on the orbital plane of the two objects. Libration points are points where a minimum of energy is required to maintain an object in orbit. The figure shows the location of the five Lagrangian points for the Earth­Moon. Although the forces of gravity are balanced at L1, L2 and L3, they are not stable orbital positions. If a satellite at any of these three points begins to drift, it will tend to continue to drift away. L4 and L5 are, however, stable orbital positions. Forces which tend to cause a satellite located at L4 or L5 to drift away are compensated for and the satellite returns to a stable position. The are also other Lagrangian points for the Sun­Earth, Sun­Venus, Sun­Mars, Sun Jupiter and Sun­Saturn.

5-15 Orbital Maneuvers
Introduction A satellite is rarely launched directly into its final orbit. After being launched into an initial parking orbit, at least one orbital maneuver is needed to get the satellite into the correct orbit to begin its mission. Orbital maneuvers are necessary to maintain a satellite in its proper orbit or to change the orbital parameters based on revised mission requirements. Changing the orbital parameters of a satellite requires careful planning and precise execution. Satellites carry a limited amount of fuel to power maneuvering engines. Once the fuel has been expended there is no way to change a satellites orbit or even to correct for small changes resulting from perturbations.
Categories of Maneuvers There are two basic categories of orbital maneuvers: in­plane maneuvers and out­of­plane maneuvers:
  • In-plane maneuvers
  • Out-of-plane maneuvers
In-Plane Maneuvers In­plane maneuvers can change the size and shape of the orbital plane but do not change its orientation. In­plane maneuvers include changing the altitude of the apogee or perigee, the eccentricity of the orbit, the length of the semi­major axis, and the argument of perigee.
Hohmann Transfer Maneuver The most energy efficient in­plane maneuver is known as the Hohmann Transfer. It is a two impulse maneuver between two coplanar orbits. The first burn is made at the perigee of the initial orbit to increase the speed of the satellite and change the eccentricity of the orbit. The magnitude and direction of the change, called the "delta vee", must be precisely controlled. If the new, more elliptical orbit is the desired final orbit, then no other burn is needed. If the final desired orbit is a circular orbit with a higher altitude than the original orbit, another burn must be made at the apogee of the transfer orbit. The second burn places the satellite in a higher, more circular orbit. The Hohmann Transfer is efficient but can take up to half of one period to execute. This technique is often used to boost communications satellites from an initial low Earth orbit into a geostationary orbit.
Fast Transfer Maneuver Another method of changing orbits is the Fast Transfer method, used when time is a factor. This method also uses two impulses. The difference between this method and the Hohmann Transfer is that the satellite approaches its new orbit at a higher angle and velocity. Thus, the second burn must be stronger to brake the satellite into the new orbit. Fast transfer is used by various surveillance satellites when new targeting requirements are critical.
Out-Of-Plane Maneuvers Out­of­plane maneuvers change the orientation of a satellite's orbital plane. As with a spinning gyroscope, making a change to the orbital plane of a satellite can require large amounts of energy. Two common out­of­plane maneuvers are changes to the inclination and to the right ascension of the ascending node. To change only the inclination of a satellite's orbit, one burn is made at either the ascending node or the descending node. To change only the right ascension of the ascending node requires one burn anywhere in the original orbit except at the ascending or descending nodes.