CHAPTER 4
4-2 The Chinese had a working calendar at least as early as the fourteenth century B.C. They also maintained accurate records of comets, meteor showers, meteorites, and other phenomena. Egyptian astronomers were able to roughly predict the flooding of the Nile River each year near the time when the star Sirius could be seen rising in the dawn sky just before the sun. The Bronze age people in Northwestern Europe built many monuments such as Stonehenge, which was certainly used as a crude calendar. One of the earliest known attempts to describe the location of the planets, Sun, Moon, and their motions with respect to each other was by Pythagoras. He assumed that the Earth was stationary at the center of a system comprised of the seven known moving objects visible to the unaided eye−the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. Pythagoras theorized that all revolved about the Earth in complex spherical orbits. This was known as the geocentric theory. Aristotle (384-322 B.C.), one of the most famous of Greek philosophers, understood such phenomena as the phases of the Moon and eclipses. Aristotle considered the theory that the apparent daily motion of the sky could be explained by a hypothesis of the rotation of either the Earth or of the celestial sphere. Perhaps most importantly though, Aristotle considered the possibility that the Earth revolves around the Sun, instead of the more popular idea that the Earth was the center of the universe. Aristarchus of Samos (310-230 B.C.), another famous Greek astronomer, was the first to profess a belief in the heliocentric theory−that the Earth moves about the Sun. He also believed that the stars must be extremely distant to account for the fact that their apparent positions in the sky remain the same all year long. However, because Aristarchus’ ideas were too revolutionary, they were rejected, and the geocentric theory continued to be accepted for centuries. About A.D. 140, Claudius Ptolemy amplified the geocentric theory by developing an elaborate geometrical representation of the solar system, which predicted the apparent motion of the planets with considerable accuracy. According to his theory, the planets revolve about imaginary planets, which in turn revolve around the Earth. Ptolemy’s hypothesis, with some later modifications, was accepted as absolute authority throughout the Middle Ages. MODERN ASTRONOMY It was not until some 1800 years after Aristarchus had first proposed the heliocentric theory, that a Polish monk named Nicolaus Copernicus (1473-1543) published a book in defense of the heliocentric system. Copernicus postulated that the Earth was one of the six (then known) planets that revolve around the Sun. Starting nearest the Sun, he ordered the planets Mercury, Venus, Earth, Mars, Jupiter, and Saturn. He further deduced that the closer a planet is to the Sun, the greater its orbital speed. Thus, the retrograde (or, backward) motion of Mars, Jupiter, and Saturn was easily explained. He also calculated the approximate scale of the
4-3 solar system. Contrary to what has been a popular belief, Copernicus did not prove that the Earth revolves about the Sun. A Danish astronomer, Tycho Brahe (1546-1601), established an astronomical observatory in 1576, where for 20 years he carried out the most complete and accurate astronomical observations made up to that time. In 1600 Brahe was joined by a young German mathematician named Johannes Kepler (1571-1630). Brahe put Kepler, an early convert to the heliocentric theory, to work on finding a satisfactory theory of planetary motion. LAWS OF MOTION Kepler’s most detailed study was of Mars, for which Brahe’s observational data was the most extensive. For 10 years he attempted to fit combinations of circular motion to the observed motion of Mars. Finally, Kepler tried to represent the orbit of Mars with an oval and soon discovered that the orbit could be fitted by a curve known as an ellipse. KEPLER’S LAWS OF PLANETARY MOTION Kepler found that Mars has an orbit that is an ellipse, with the Sun at one focus (the other focus of the ellipse is empty, an unoccupied point in space). Kepler generalized that what is true for Mars must be true for the other planets as well. This generalization has become known as Kepler’s First Law of Planetary Motion. Kepler’s First Law of Planetary Motion (Law of Ellipses) Each planet moves in an elliptical orbit with the Sun a t one focus and the other focus empty. This law also applies to man-made objects orbiting the Earth (i.e., satellites). The orbit of each satellite is an ellipse with the center of the Earth at one focus and the other focus unoccupied. This law simply implies that the purpose of the occupied focus (i.e., the Earth) is to provide gravitational attraction to the satellite to keep the satellite in its elliptical orbit (see Figure 4-1). Figure 4-1. Kepler’s 1st Law applied to an Earth satellite.
4-4 Kepler’s Second Law of Planetary Motion (Law of Areas) The line joining a planet to the Sun sweeps over equal areas in equal time intervals. As applied to an Earth-orbiting satellite, the line joining it to the Earth sweeps over equal areas in equal periods of time (see Figure 4-2). This law implies that the speed of a satellite changes depending on its distance from its gravitational attraction source, the center of the Earth. A satellite’s speed is greatest at the point in the orbit closest to the Earth, and is slowest at the point farthest from the Earth. If a satellite is traveling in a circular orbit, then the speed of the satellite is constant. Figure 4-2. Kepler’s 2nd Law. It is important to understand that the orbit followed by a satellite is not dependent on its mass. A large, heavy satellite could be in the same orbit with a small, light satellite with each sweeping out equal areas in equal periods of time. Kepler’s Third Law of Planetary Motion (Law of Harmonics) For any planet, the square of its period of revolution about the Sun is directly proportional to the cube of its mean distance from the Sun. When applied to earth satellites, this
4-5 law explains that the farther a satellite is from the Earth, the longer it will take to complete its orbit, the greater the distance it will travel, and the slower its average speed.
4-6 This law is expressed as follows: p2/d3 = K where p is the period d is the distance K is a constant with the same value for all satellites GALILEO GALILEI An Italian mathematician, Galileo Galilei (1564-1642), contributed greatly to the understanding of the behavior of objects at rest or in motion. In addition to being the first person to develop and use a telescope, he accumulated a great deal of evidence in support of the heliocentric theory. In 1632, he published the "Dialogue of the Two Great World Systems," which examined all arguments for and against the heliocentric theory. NEWTON’S LAWS OF MOTION AND UNIVERSAL GRAVITATION While declaring his three laws of planetary motion, Kepler deduced that a force from the Sun pulled on the planets, but he did not determine the mathematical nature of this force. Galileo discovered some of the basic laws governing the behavior of physical objects. Sir Isaac Newton (1643-1727), regarded as the father of classical mechanics, drew upon the work of both Kepler and Galileo to formulate the Law of Universal Gravitation and the three Laws of Motion. While Kepler’s laws provided a conceptual model of orbital motion, Newton’s laws provided the foundation for the mathematical description of orbits and why a satellite remains in orbit. Newton’s First Law of Motion (Law of Inertia) A body in motion will keep moving at the same speed and in the same direction unless acted upon by an external force. This explains why a satellite moves in a curved path around the Earth, because the Earth’s gravitational pull acts as an external force on it. Newton’s Second Law of Motion (Law of Momentum) If the sum of forces acting on an object is not zero, the object will have an acceleration proportional to the magnitude and in the direction of the net force. This provides some of the explanation for changes in a satellite’s orbit due to external forces other than the Earth’s gravity, and the need to adjust a satellite’s orbit.
4-7 Newton’s Third Law of Motion (Law of Action & Reaction) For every action, there is an equal and opposite reaction. This law explains how a satellite gets into orbit. Newton’s Law of Universal Gravitation Any two objects in the universe attract each other with a force directly proportional to the product of their masses, and inversely proportional to the square of the distance between them. Mathematically, this law is expressed as follows: F = G*(m 1*m2)/d2 where F is the force acting between the bodies G is the universal constant of gravitation m is the mass of a body, and d is the distance between the bodies Simply stated, the more massive the objects, or the closer they are together, the greater the gravitational pull between them. ORBITAL PARAMETERS To better understand the operational application of satellites, you should become familiar with the fundamental terms and relationships associated with satellite orbits. ORBITAL INSERTION To illustrate how a satellite is placed into orbit, refer to Figure 4-3. Imagine someone standing atop a tall mountain and throwing a ball horizontally. Not considering atmospheric friction, the Earth’s rotation, or any other force except gravity, the path of the ball will curve downward due to gravity and it will strike the Earth (Path A). Now, if that person fires a gun horizontally, the bullet will obviously go farther than the ball, but it will still be pulled down to the Earth (Path B). However, if a projectile is fired horizontally at a very high speed, approximately 17,500 miles per hour, the curvature of its path due to gravity will match the curvature of the Earth below it. The projectile will then continue to "fall" around the Earth just as fast as the Earth curves away from the projectile, and become an Earth-orbiting satellite (Path C).
4-8 Figure 4-3. Orbital insertion. For an object to achieve orbit, sufficient energy must be provided so that the path does not intersect the surface of the Earth. However, the object cannot be given too much energy or it will escape the effects of the Earth’s gravity. The following three conditions are required to place an object in orbit: • The object must be put above most of the Earth’s atmosphere (approximately 60 miles high) to negate the effects of atmospheric friction • The object must be imparted with a speed of approximately 17,500 miles per hour within about 200 miles of the Earth’s surface • The object’s speed must be in a direction parallel to the surface of the Earth. POSSIBLE SATELLITE ORBITS Suppose that an object is boosted to an altitude of approximately 200 miles above the Earth’s surface, then turned so that it is horizontal to the Earth, and finally provided with a forward horizontal motion. The object will enter into an orbit the size and shape of which depends on the exact direction and speed of the object at "burnout" (when thrusting terminates). If the object is moving horizontally to the earth, the possible types of orbits it can enter are depicted in Figure 4-4.
4-9 Figure 4-4. Possible satellite orbits. If the object’s burnout velocity is slightly greater than that required for a perfect circular orbit, the resulting orbit will be elliptical with the center of the Earth at one focus. The point farthest from the center of the Earth will be the point of burnout. If the burnout velocity is substantially below the circular-orbit velocity requirement, the object will strike the Earth’s surface. If the burnout velocity is just slightly below the circular-orbit velocity, the object may barely clear the Earth’s surface, but atmospheric drag would soon cause it to slow down below the required orbital velocity and it will strike the Earth. If the burnout velocity is exactly the circular-orbit velocity requirement, a circular orbit results (in practical situations, this is nearly impossible to achieve). Burnout velocities equal to or greater than the escape velocity from the Earth’s gravitational field result in parabolic or hyperbolic orbital paths. At these velocities, satellites will escape the gravitational pull of the Earth and never return. ORBITAL TERMS AND ELEMENTS When an object’s burnout velocity results in an elliptical orbit, a point on the orbit farthest from the center of the Earth is referred to as apogee (apogee – “away”). The point closest to the center of the Earth will be halfway around the orbit and is called perigee (see Figure 4-5). Apogee and perigee are always 1/2 revolution apart. For a circular orbit, apogee and perigee altitude are equal.
4-10 Figure 4-5. Orbital parameters. Orbital Elements Six parameters, often referred to as the "orbital element set," establish the size, shape, and orientation of an orbit in space as well as the location of a satellite in its orbit. These parameters, some of which are depicted in Figure 4-6, are as follows: • Semi-major axis • Eccentricity • Inclination • Right ascension of the ascending node • Argument of perigee • Time
4-11 Figure 4-6. Orbital elements. The semi-major axis is simply o ne-half the diameter of an ellipse. The length of the semi-major axis is used to define the size of an orbit. From this, the orbital period (the time it takes a satellite to complete one orbital revolution) can be calculated. Eccentricity defines the shape of an ellipse. For all ellipses, the value of eccentricity lies between zero and one. The larger the value, the more elliptical the orbit. Circular orbits have an eccentricity equal to zero. A satellite orbit with an eccentricity equal to or greater than one will escape the Earth’s gravitational field (parabolic or hyperbolic orbit). The semi-major axis and the eccentricity of the orbit are determined before launch to design the orbit for that particular satellite’s mission. Inclination is used to orient the orbital plane with respect to the Earth. It is the angular measurement made at the ascending node (the point at which a satellite crosses the equatorial plane going from south to north) from the equatorial plane to the orbital plane (see Figure 4-6). Inclination orients the orbital plane to the equatorial plane, and determines the northernmost and
4-12 southernmost latitudes covered by the satellite’s ground track. Inclination also defines another manner in which orbits are described: • Prograde: inclination > 0° but < 90° • Retrograde: inclination > 90° but < 180° • Polar: inclination equal to 90° • Equatorial: inclination equal to 0 ° or 180° The final element used to define the size and shape of the orbit and the orbital plane is Right Ascension of the Ascending Node. This is the angular measurement in the equatorial plane from the Vernal Equinox (that point determined by a line extending from the center of the Sun through the center of the Earth to the celestial equator at the start of spring) eastward to the ascending node. The remaining two orbital elements are used to position the orbital plane. The Argument of Perigee orients the orbit within the orbital plane. It is the angular measurement from the ascending node along the orbital path to the point of perigee. Once the perigee point has been determined, the point of apogee is 180° away. Finally, to determine where a satellite is in its orbit at a specific time, Epoch Time or True Anomaly is used. Epoch Time is an arbitrary time used as a starting point. Normally, the time when a satellite is at the ascending node is used as epoch time. True Anomaly is the angular measurement from the point of perigee along the orbital path to the location of the satellite at the epoch time. Although period is not categorized as an orbital element, it is very useful in satellite operations. Typically, the period of a satellite is the time it takes to travel from one ascending node point to the following ascending node point (referred to as the "nodal period"). The minimum period a satellite can have and still be in a stable, non-decaying orbit is approximately 87.5 minutes. If there is any less time, the object will eventually reenter the Earth’s atmosphere. REFERENCE SYSTEMS Since observational data for a satellite may be derived by any one of a wide variety of types and locations of sensors, an understanding of the common reference systems used is essential. Each reference system is designed for a particular use, fulfilling at least one of the following purposes: • to locate a specific object in space
4-13 • to discriminate between two or more objects in space • to describe motion of an object in space. Reference systems may be classified into two basic types, either inertial or non-inertial. An inertial reference system is one in which direction does not change with time. It is used in locating the position of a satellite to establish the orbital plane and the satellite’s orbit within that plane. A non-inertial reference system does change direction with time. The four reference systems typically used in space operations are summarized in Table 4-1 below: Table 4-1. Summary of Common Reference Systems COORDINATE SYSTEM ORIGIN USED TO LOCATE Geographic (Non-Inertial) Earth Center Earth Radius Tracking Station Topocentric (Non-Inertial) Tracking Station Slant Range Locate satellite Ref: Tracking Station Geocentric (Inertial) Earth Center Geocentric Radius Locate satellite in space Orbit (Inertial) Earth Center Celestial Radius Locate satellite in its orbit LAUNCH AND ORBITAL MANEUVERING Many factors enter into the mission planning and subsequent design of a satellite. One of the most restrictive facets of this planning is the launch environment (i.e., booster, launch site, launch "window"). LAUNCH AZIMUTH AND INCLINATION Launch azimuth is the direction from the launch site in which a booster is launched. The relationship between the location of the launch site and the launch azimuth to the resulting inclination of a satellite’s initial orbit is very specific. The minimum orbital inclination of a satellite is equal to the latitude of the launch site, and is achieved with a launch azimuth of due East. For launches with any azimuth other than due East, the orbital inclination will always be greater than the latitude of the launch site. Practically speaking, a satellite launched on an azimuth between 0° and 180 ° will have an inclination between 0° and 90 °, or a prograde orbit. Satellites launched on azimuths between 180° and 360° will have inclinations between 90° and 180°, or a retrograde orbit.
4-14 Most U.S. launches take place from one of two complexes: Kennedy Space Center, Cape Canaveral, Florida, or Vandenberg Air Force Base in California. If a satellite is launched with the Space Shuttle from Kennedy Space Center (which is located at a latitude of 28.5° North) on a due East azimuth, its orbital inclination will be 28.5° and the limits of its ground track will be between 28.5° North and 28.5° South latitude. Therefore, the limits of the ground track equal the launch inclination. Launch Site Limitations Many safety factors must be considered when launching from a particular site. Of course, one of the safety considerations is not to launch over populated areas. Consequently, there are limitations to the launch azimuths from each site. Because of safety considerations, the maximum practical inclination from a Kennedy Space Center launch is 57°. However, after an initial orbit is established, the inclination of an orbit can be changed by out-of-plane maneuvers (described later in this section), but this is costly in terms of on-orbit propellant. To obtain an orbit with an inclination greater than 57°, U.S. satellites are launched from Vandenberg AFB, CA. A significant advantage of launching from Vandenberg is the capability to economically achieve polar orbits, with ground tracks covering all latitudes from the North Pole to the South Pole. Another limitation induced by the location of a launch site is the affect of the Earth’s rotational velocity. The speed of the Earth changes with latitude, ranging from zero mph at the poles to about 1037 mph at the equator. Since the Earth rotates from West to East, all points on its surface have an eastward velocity, with the greatest eastward velocity occurring at the equator. The farther a launch site is from the equator, the less the Earth’s rotational velocity imparts energy to the booster. This results in requiring more fuel to get a satellite into orbit, or a tradeoff with the satellite’s payload weight to conserve on-orbit fuel. Launching from an equatorial site offers a significant advantage, and is an important consideration since many satellites operate in low-inclination orbits. Launch Window Satellite launches take place within a specified time interval referred to as the "launch window." Some of the factors affecting the launch window are: • Launch and orbit lighting conditions • Sun angles • Payload orbit requirements • Satellite system phasing
4-15 • Tracking and communications requirements • Collision avoidance with other space objects. During the winter months, the available launch window for lighting conditions alone can be as little as 3 hours per day. When combined with other factors, launch windows become very constrained. ORBITAL MANEUVERING It is rare that a satellite is launched directly into its final orbit. A satellite will typically need to change its orbit at least once to be able to perform its mission. For example, the Space Shuttle may deploy a communications satellite designed for placement in a geosynchronous orbit. The Shuttle itself cannot reach geosynchronous altitude, so a small booster attached to the satellite has to be pointed in the proper direction at the right time and place, and thrusted for a precise length of time. Then, once it gets to geosynchronous altitude, it will have to thrust again to stay in its desired orbit. Mission Considerations After a satellite has been on orbit for a period of time, it is often necessary to change its orbit by thrusting. Firing a spacecraft’s thrusters results in a Delta "V"−a change in the satellite’s velocity. The amount of fuel used during a burn depends on the desired velocity change and the mass of the satellite. Since the amount of fuel carried is limited, fuel consumption is one of the primary considerations in satellite mission planning, and is critical to mission life. On orbit, a satellite can thrust in any direction. Thrusting along the flight path, forward or backward, is the most common. Forward thrusting increases a satellite’s velocity and is known as a "prograde burn." With prograde burns, the orbital path of the satellite will be raised at all points except the burn point. Thrusting opposite to the direction of the orbit, which slows a satellite down, is called a "retrograde burn." For retrograde burns, the orbit will be lowered at all points except the burn point. Maneuvers Most maneuvers may be performed any place in the orbit; however, there are certain points that minimize energy requirements for a particular type of maneuver: • The most economical method for obtaining a change in orbital period is by applying thrust at perigee or apogee
4-16 • The most economical place to perform an inclination change is at either the ascending or descending node
• The most economical place to perform a change in right ascension of the ascending node is at either of the tw o midway points between the ascending and descending nodes
• The change in inclination or right ascension is easiest if it is performed at apogee
• The most economical place to perform a maneuver to change perigee height is at apogee.
In-Plane Maneuvers
When a satellite needs to change its altitude, period, or eccen tricity, additional energy is required. This energy requirement is true whether or not the element's value is being increased or decreased. The type of tran sfer used to meet this energy requirement depends on the satellite's mission, and the amount of fuel available.
The most energy efficient in-plane ma neuver is known as the Hohmann Transfer (see Figure 4-7). The Hohmann Transfer is a two-impulse maneuver between two co- planar orbits.
Courtesy of Damon, Thomas D. (2001) Introduction to Space: The Science of Spaceflight, Third Edition. Krieger Publishing Company. Figure 4-7. Hohmann transfer.
In accomplishing a Hohmann Transfer, two applications of thrust are required. Each thrust changes the speed of the satellite and places it in a new orbit. If an increase in altitude is
4-17 desired, the point of departure becomes the perigee of the tran sfer orbit and the point of injection into the higher circular orbit becomes the apogee of the transfer orbit. The use of the Hohmann Transfer minimizes the velocity change required, with the advantage of using minimum fuel. The disadvantage of the H ohmann Transfer is th at it takes longer than most other transfers. The Hohmann Transfer is used extensively with interplanetary satellites, because it does not require a large maneuver engine or fuel tanks.
Another way to accomplish an altitude change is referred to as the Fast Transfer (see Figure 4-8). This transfer is most useful when time is a critical factor. In the Fast Transfer, the transfer orbit crosses the final orbit at an angle. The burn is performed in two increments but requires substantially more fuel than the Hohmann Transfer. It is, however, the quickest way to get to the final required orbit. The Fast Transfer is typically used by surveillance satellites to reposition over new target areas.
Courtesy of Damon, Thomas D. (2001) Introduction to Space: The Science of Spaceflight, Third Edition. Krieger Publishing Company. Figure 4-8. Fast transfer.
Out-of-Plane Maneuvers
To change inclination or right ascension, an out-of-plane maneuver is required. The inclination maneuver changes only inclination and maintains right ascension. This plane change requires one burn at either the ascending node or descending node of the original orbit. The amount of inclination change depends on the length of the burn.
The right ascension maneuver changes only right ascension without changing inclination. This plane change requires one burn anywhere in the original orbit except at the ascending or
4-18 descending nodes. The maximum effect is achieved when the burn is performed midway between the nodes. ORBIT TYPES AND APPLICATIONS The laws of nature force the orbits of all satellites to lie in planes that pass through the center of the Earth. A satellite’s ground track is formed by the intersection of the surface of the Earth and a line between the Earth’s center and the satellite. As the satellite moves in its orbit, this intersection traces out a path on the ground below it. GROUND TRACK If the Earth did not rotate, a satellite would retrace the same ground on each revolution (see Figure 4-9). Notice that the maximum latitude North and South of the equator over which the satellite passes is equal to the satellite’s inclination. Figure 4-9. Example of ground track (non-rotating Earth). The orbital plane of a satellite remains fixed in space as the Earth rotates under it. The effect of this rotation is to displace the ground track westward on each successive revolution of the satellite by the number of degrees the Earth turns during one orbital period (see Figure 4-
4-19 10). This is referred to as nodal regression. The resulting ground tracks provide operators with an indication of the position of their satellite in accomplishing its mission.
4-20 Figure 4-10. -Example of ground track (rotating Earth). As mentioned above, a satellite in either a circular or an elliptical orbit will trace out a path over the Earth between the limits of latitude as determined by the inclination angle. A satellite in a circular orbit will spend equal amounts of time North and South of the equator. However, a satellite in an elliptical orbit will remain North or South of the equator for unequal periods of time. Only satellites that are in circular orbits travel along their ground track at a constant velocity. When an orbit is inclined to the equator, the component of satellite velocity in the direction due East or due West varies continuously throughout the orbit. More specifically, a satellite in a nearly circular orbit moves slower in an easterly or westerly direction at the equator and faster when it is at its most northerly or southerly points. The relative speeds of satellites in elliptical orbits vary even more. FIELD OF VIEW The field of view of a satellite is defined as the area of the Earth’s surface that is in view from the satellite at any given time. Satellites in high orbits have greater fields of view than those in lower orbits. For example, a satellite at an altitude of 800 nmi has a circular field of view with a diameter of about 4,100 nmi. A satellite at 200 nmi has a circular field of view with a diameter of about 2,000 nmi.
4-21 TYPES OF ORBITS The various types of orbits are the result of different satellite missions, and the desire for satellites to perform their missions over different areas of the Earth’s surface (i.e., have different ground tracks). Low Earth Orbit A satellite is considered to be in a low earth orbit (LEO) at altitudes between approximately 150 and 800 miles above the Earth’s surface. At an altitude of approximately 150 miles, a satellite’s period will be about 90 minutes. The Space Shuttle and some scientific satellites are typically placed in low inclination, low earth circular orbits. Polar Orbit In contrast to a low inclination orbit and its latitude limitations, a polar orbit passes over the entire surface of the Earth. A polar orbit has an inclination of 90° and is usually circular (see Figure 4-11). Due to the ability to pass over the entire surface of the earth throughout the course of several days, the polar orbit is used extensively by imagery satellites. Figure 4-11. Polar orbit. Geosynchronous Orbit A satellite placed in orbit with an average altitude of approximately 19,300 nautical miles ( nm) will have an average angular velocity exactly equal to that of the Earth’s. Stated more simply, the satellite would have a period approximately equal to one day. This means that it would take as long for the satellite to complete one revolution around the Earth, as it takes for the earth to rotate once about its axis. Such an orbit is called a geosynchronous orbit.
4-22 If a geosynchronous orbit with an inclination of 0° were perfectly circular, the satellite would appear to remain stationary in space above the same point on the Earth’s surface. This is referred to as a geostationary orbit (see Figure 4-12).This orbit is predominantly used by relay satellites to provide a continuous communications capability among ground stations within their very broad field of view. Some surveillance and warning satellites also use the geostationary orbit. The geostationary field of view is constant, covering nearly one-third of the Earth’s surface with latitude limitations of approximately 70° North and South of the equator. Effective satellite communications from a geostationary orbit is not possible at either pole. Figure 4-12. Field of View from a Geostationary Orbit. Elliptical Orbit To obtain satellite communications capability in the northern or southern latitudes, a highly eccentric elliptical orbit, commonly referred to as a Molniya orbit is used (see Figure 4-
4-23 13). The Molniya orbit has an apogee nearly equivalent to the geosynchronous altitude and an inclination of approximately 63° to 64°. A satellite in this type of highly eccentric elliptical orbit slows down at apogee in the Northern Hemisphere (providing longer duration over its greatest field of view) and whips through perigee (smallest field of view) in the Southern Hemisphere. This provides communications in the Northern Hemisphere for nearly 75 percent of the satellite’s orbital period. If the apogee/perigee points were shifted 180°, this orbit would cover the Southern Hemisphere. Figure 4-13. Molniya orbit. Semi-Synchronous Orbit An average orbit with an altitude of approximately 10,800 nmi results in a period of about 12 hours and is referred to as a semi-synchronous orbit. The purpose of placing satellites in this type of orbit is to allow a user to receive signals from more than one satellite at any time. Navigation and certain kinds of area communications (Molniya) satellites use the semi- synchronous orbit. Sun-synchronous Orbit The sun-synchronous orbit takes advantage of the precession of the orbital plane caused by the Earth not being a perfect sphere. All sun-synchronous orbits are highly inclined (normally with inclinations between 95° and 105 °) retrograde orbits that precess eastward around the Earth’s polar axis at the rate on one revolution per year. Since the Earth-Sun line also revolves eastward at the rate of one revolution per year, the orbital plane will maintain a
4-24 constant orientation relative to the Earth-Sun line (see Figure 4-14). If the satellite’s orbital period is then synchronized with the rotation of the Earth, it will pass over the same point on the Earth’s surface at the same local time at a regular interval. Figure 4-14. Sun-synchronous orbit. A sun-synchronous satellite ensures that a constant sun angle and uniform lighting exists for the same field of view from revolution to revolution. For certain mission requirements, a noon/midnight sun-synchronous orbit can be selected that would provide good photography for about one-half of every revolution. Most meteorological and earth resources LEO satellites are placed in sun-synchronous orbits, imaging the entire Earth on a regular schedule. ORBITAL PERTURBATIONS AND DECAY There are other forces besides the Earth’s gravity (referred to as perturbations) which act on an orbiting satellite. Although much smaller, these other forces are of sufficient magnitude to cause orbital decay, and result in significant changes in a satellite’s ground track over time if not recognized and corrected for periodically. Changes in a satellite’s ground track can result in reduced mission effectiveness. To neutralize the effects of natural perturbations, a satellite may perform "station-keeping" thruster burns.
4-25 ORBITAL PERTURBATIONS The Earth is not a perfect sphere. The North Pole region is more pointed than the flatter South Pole region, and a bulge exists at the equator. This bulge, referred to as the Earth’s oblateness, causes the equator to be slightly elliptical. Earth’s Asymmetry These asymmetrical conditions have an influence on the orbital parameters of satellites in low-and-medium- altitude orbits. One effect of the Earth’s asymmetry is positive, in that the nodal regression of an orbit can be timed to make an orbit sun-synchronous without using precious fuel to maneuver for that purpose. Atmospheric Drag The Earth’s atmosphere does not suddenly end, it gradually tapers off into interplanetary space. Generally speaking, atmospheric drag circularizes and decreases the apogee of a low earth orbit. Any drag caused by air resistance can normally be disregarded above 300 nmi. Occasionally, however, a period of extreme solar activity may occur that will heat the atmosphere and cause it to expand. Third Body Effects Newton’s Law of Universal Gravitation indicates that there is a force of attraction (gravity) between all objects and bodies in the universe. The gravitational pull of "third bodies" such as the Moon and the Sun can affect the orbits of geosynchronous and deep space satellites. Radiation As discussed previously, the Sun is continually expelling matter in the form of ionized gas. The particles in this gas (mostly electrons and protons) that penetrate interplanetary space move with high velocities. These particles, commonly referred to as the solar wind, exert a pressure on satellites, particularly those with large area-to-mass ratios. This pressure induces a restraining force on satellites, and is only present on the daylight (or, windward) side of the Earth. This causes irregular perturbations of a satellite’s orbit. Electrons and protons can become trapped when encountering the Earth’s magnetic field. They oscillate back and forth along the lines of magnetic force, and since the magnetic field completely encircles the Earth, the trapped particles completely encircle the Earth. This region of trapped particles, mentioned earlier in Chapter 3, is known as the Van Allen Radiation Belt.
4-26 The belt has an inner and outer portion. The inner Van Allen belt starts at an altitude of approximately 250 to 750 miles, depending on the latitude. It extends to about 6,200 miles where it begins to overlap the outer belt. This inner belt extends from 45° North latitude to about 45° South latitude. The outer Van Allen belt begins around 6,200 miles and extends to an altitude that varies from 37,000 to 52,000 miles. The upper boundary is dependent on the activity of the Sun. Electromagnetic Forces The Earth’s magnetic field extends far into space. As a satellite orbits the Earth, it is traveling through this magnetic field. The electronic components of a satellite also produce a magnetic field that consequently reacts with the Earth’s magnetic field. Additionally, the ions and electrons in the Earth’s magnetic field collide with the satellite, causing a negative charge on the satellite’s surface. The negative charge is larger on the day-side of an orbit than on the night side. The interaction of these induced fields with the Earth’s magnetic field causes a magnetic drag to act on a satellite. This drag can cause charging or torquing of a satellite. ORBITAL DECAY AND DEORBIT For satellites that pass close to the Earth (low orbit or highly elliptical orbits), we can arrange for the satellite to re-enter, or let it re-enter by itself. Deliberate re-entry of a satellite with the purpose of recovering the vehicle intact is deorbiting. We usually do this to recover something of value: people, experiments, film, or the vehicle itself. The natural process of spacecraft (or any debris: rocket body, payload, or piece) eventually re-entering Earth’s atmosphere is decay. In some situations the satellites are in such stable orbits that natural perturbations won’t do the disposal job for us. In these situations, we plan to remove the satellite from the desirable orbit. To return a satellite to Earth (or low Earth orbit), it would take just as much energy as it did to place it in orbit. Obviously it is impractical to return old satellites to Earth from a high orbit. We usually just boost the satellite into a slightly higher orbit to get it out of the way, and there it will sit for thousands of years to come. SUMMARY The overall purpose of understanding the principles of orbital mechanics is to recognize the elements that affect the design and planning of a satellite’s mission. Many mission planning factors and constraints, such as on-orbit fuel, satellite weight, and launch site considerations, were mentioned in this chapter. However, one factor essential to the planning of a satellite’s mission remains to be discussed, and that is the selection of a satellite booster, or launch vehicle.
5-1 CHAPTER 5 LAUNCH AND RECOVERY SYSTEMS INTRODUCTION This chapter provides an overview of the systems and operations associated with the launch and recovery of spacecraft. The discussion includes a description of the U.S. launch and orbit transfer vehicles used to place payloads into orbit, an overview of launch and recovery operations, a description of the three major U.S. launch sites, a summary of the major ground processing activities that contribute to a successful launch and recovery, and a look at some future launch systems. It should be noted that the information contained in this chapter represents only a snapshot of the current U.S. launch vehicle inventory. As you might expect when dealing with a dynamic industry, this inventory will change as technologies emerge, evolve, and are replaced or removed. BACKGROUND During the early years of the space program, both the National Aeronautics and Space Administration (NASA) and the Department of Defense ( DoD) developed launch vehicles to satisfy their own specific requirements. Consequently, there has been a wide variety of launch vehicles used to support the space program. DoD developed the Atlas, Delta, and Titan series of launch vehicles from ballistic missile technology. Meanwhile, NASA developed the Scout and Saturn. Used to send Apollo crews to the Moon, both are now out of production. All these launch vehicles, which can only be used once, are called expendable launch vehicles (ELVs) and each has a different capability to put satellites in orbit. From the least to the most capable in terms of lift, they are Pegasus, Taurus, Delta, Atlas, and Titan. The Pegasus is a recent addition to the inventory of expendable launchers and is aircraft-launched. The Taurus is a ground-launched, mobile vehicle. Currently, there is no one vehicle that can launch all satellites into all the orbits required for the various missions. NASA and DoD select the vehicle best suited for their particular mission based on the size, weight, and desired orbit of the payload. In 1972, President Nixon approved NASA’s plan to create a reusable launch vehicle called the Space Shuttle, and directed that it become the primary U.S. launch vehicle, replacing all ELVs except the Scout. This made both NASA and DoD dependent on a single launch vehicle for access to space but, in theory, the resulting high launch rate for the Shuttle would significantly reduce the cost per flight. The Shuttle was first launched in 1981, and was declared operational in 1982. The phase-out of ELVs began. However, in 1984, concerned about having “assured access to space,” DoD successfully argued that it needed a “complimentary” ELV as a backup to the Shuttle and initiated what became known as the “Titan IV Program.” Production lines for the Delta and Atlas launch vehicles were closed down in anticipation that only the Shuttle and Titan IVs would be used by the end of the 1980s.