======================================================================== Visual Satellite Observing F A Q Chapter-05 What Are The Mechanics Of A Satellite In Orbit? ======================================================================== ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ + This FAQ chapter is "under construction". Some of the + + sections may be unwritten as yet. Other sections may + + contain out-of-date, unreviewed, or "starter" material. + + Yet other sections may be works in progress, partially + + written and reviewed. + ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ + In this chapter, the following sections are considered + + to be completed (written and reviewed): + + None + ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ---- 5.0 Astrodynamics, TLE Files and Prediction Models School children everywhere read books or are shown films depicting satellites as going endlessly around the Earth in perfect ellipses or circles. In the complex near-Earth space environment many factors exist that prevent this idealized concept of perfect ellipses from materializing. These factors make the prediction of a satellite's visible passage a fairly complicated matter, a task best handled by a computer. In this chapter, basic astrodynamics, orbit-changing natural forces, and orbital predictions by computer are discussed. ---- 5.1 The Study of Orbits: Celestial Mechanics and Astrodynamics The study of the orbital motion of planets, comets, moons or other natural objects is known as "celestial mechanics." The study of the orbital motion of artificial satellites is known as "astrodynamics." In reality, astrodynamics is an adaptation of celestial mechanics to the special problems of spacecraft motion. The computational methods used by software to predict a satellite's position rely on celestial mechanics for the basic calculations, followed by adjustments with astrodynamical methods and factors. ---- 5.1.1 The Six Fundamental Orbital Elements Before a satellite's position can be predicted, the orbit must be described. An ellipse in three-dimensional space can take on all sorts of variations: it can be skinny or very round; it can be small or large; it can be pointed "up" or "down" or "sideways" or take on any number of "tilts." To uniquely define the size, shape and orientation of an orbit, celestial mechanics tell us that a minimum of five variables must be known. The sixth variable describes on what part of the orbit the satellite is. ---- 5.1.1.1 Semi-Major Axis Draw a line the "long way" inside an ellipse so the line bisects it. The semi-major axis is equal to one half of the length of the line. The semi-major axis defines the size of the ellipse. ---- 5.1.1.2 Eccentricity No, this does not refer to the personality of the satellite observer. Symbolized as "e," it is the degree of "ovalness" of the ellipse. To be an ellipse, an orbit must have an "e" of zero or greater but less than one. Skinny ellipses have eccentricities close to one while roundish ellipses have an "e" near to zero. A circle is actually an ellipse with an eccentricity of zero. ---- 5.1.1.3 Inclination Inclination, "i," is the "tilt" of the ellipse with respect to the earth's equator. "i" is zero degrees if the orbit is always over the equator. An orbit which passes over the north and south poles has an "i" of 90 degrees. ---- 5.1.1.4 Argument of Perigee Before the Argument of Perigee can be defined, the word "perigee" needs to be defined first. "Perigee" has nothing to do with costly bottled water, but has everything to do with the point of the orbit that is closest to the center of the earth. Argument of Perigee (abbrev.: AOP) measures the angle from the south-to-north equator crossing (the "ascending node") to the point of perigee. The angle is measured from west to east along the plane of the orbit. The symbol for AOP is "w" (lowercase omega). The purpose of AOP is not so much to determine where the perigee is; it really serves to decribe which way the orbital ellipse's major axis is "pointing." Think of grabbing the major axis like a handle and turning the ellipse around the center of the earth while maintaining the same inclination and maintaining the same equator crossing point. How far you turn the handle past the ascending node in degrees is the AOP. ---- 5.1.1.5 Right Ascension of the Ascending Node This one's not as hard as it looks. The ascending node is the point where the satellite crosses the plane of the earth's equator from south to north. It might be tempting to think that this point could be defined by extending a line of longitude out into space. Unfortunately, the earth's own orbital motion means that every day the extended longitude line points to a different spot among the stars. The point of the vernal equinox (the sun's ascending node viewed from the center of the earth) points to a fixed point in space. So the ascending node of the satellite is measured eastward, along the equator, from the vernal equinox point. The angle is called "Right Ascension." So the angle from the vernal equinox to the satellite's ascending node is the Right Ascension of the Ascending Node (abbrev.: RAAN). The symbol for RAAN is an uppercase Omega (an upside-down U with little splayed feet). ---- 5.1.1.6 Time of Perigee Passage Although the time of perigee passage is one of the six classical orbital elements, it is not used for satellite work. The problem with time of perigee passage is that it becomes difficult to measure for circular or near-circular orbits. A circular orbit has no perigee (or, if you like, you can think of the entire orbit as being a continuous perigee). ---- 5.1.2 Adjusting the Theoretical Orbit If space near earth were a perfect vacuum and if there were no other gravitational forces exerted by other celestial bodies such as the sun and moon, the theoretical elliptical orbit as uniquely described by the six classical orbital elements would suffice. The elements would never have to be revised. Inertia would keep the satellite in the exact same orbit revolution after revolution, forever. Such an orbit is called a "Keplerian" orbit, after the astronomer Johannes Kepler. A satellite in space near earth does not enjoy these theoretical conditions. There are a number of forces that influence a satellite, all of which conspire to nudge it out of its theoretical path. In order to reasonably predict the position of a satellite, the classical orbital elements must be adjusted over time to account for these influences. In 1808 Lagrange proposed his "method of variation of parameters." He devised a technique to permit the variation of the Keplerian elements to vary as a function of time. Furthermore, his method called for the new orbit, which included the effects of the variations, to be coincident at one point to the original orbit. Lagrangian orbits are called "osculating" orbits. The importance of the osculating orbit method is that it provides a vehicle for continuously adjusting orbits to account for so-called "perturbations." A perturbation is any force that causes a satellite to deviate from its Keplerian path. ---- 5.1.2.1 The Earth Is Lumpy The earth is not spherical. Rotation causes a flattening of the poles, and transforms the earth's shape from a sphere to a spheroid. The flattening is on the order of 1 part in 298. In addition, there are "hills and dales" in the earth's figure where it is higher or lower than the theoretical spheroid. These "geoid heights" vary from roughly 80 meters above to 100 meters below the 1:298 spheroid line. Our planet is not of uniform density either. The Apollo lunar missions added "mascons" to our lexicon, with mascon meaning "mass concentration." These are essentially lumps in the earth's crust or mantle. These irregularities in the earth's figure and density mean that a satellite will feel small off-center gravitational tugs as it passes over different parts of the planet. For example, if there is a mass concentration to the east of the satellite when it is travelling from south to north, the mass concentration will exert a small gravitational force that will tug the satellite a little bit to the east. ---- 5.1.2.2 Ascending Node Precession The earth's equatorial bulge causes the plane of the orbit to shift to the east or west. This change in the Right Ascension of the Ascending Node can be approximated by the formula -3 1.6239 x 10 Omega dot = ---------------- n cos i 2 2 [ a (1 - e ) ] where: Omega dot = rate of change of RAAN n = number of orbits per day a = semi-major axis e = eccentricity i = inclination The change in the ascending node varies with inclination, the semi-major axis, the eccentricity and the number of orbits per day. Note the "cos i" term. Since the cosine of 90 degrees is zero, a polar orbit does not vary in RAAN (but there will be a small change in RAAN due to other perturbations). A low inclination orbit has the greatest change in RAAN per day. ---- 5.1.2.3 Perigee Precession The location of the perigee shifts along the plane of the orbit due to the earth's irregular shape. This means that, for example, a polar orbit's perigee will move from above the north pole, southward to over the south pole and back again. The rate of the perigee precession is given by -4 8.1196 x 10 2 omega dot = ---------------- n ( 5 cos i - 1 ) 2 2 [ a (1 - e ) ] where: omega dot = rate of change in AOP n = number of orbits per day a = semi-major axis e = eccentricity i = inclination 2 If you look at the (5 cos i - 1) term, it becomes zero at an inclination of 63.44 degrees and also at 116.57 degrees. An orbit at either of these inclinations will have a fixed perigee, meaning that the perigee will remain over a certain line of latitude. Conversely, a low inclination orbit will have the greatest daily change in AOP. ---- 5.1.2.4 It's A Drag Our atmosphere extends tens of thousands of kilometers out into space. With increasing altitude the makeup of the atmosphere transitions from the nitrogen and oxygen mix we breathe into a "plasmasphere" consisting primarily of ionized hydrogen atoms. At the height of the lowest satellite orbits the atmosphere is extremely thin and rarefied, but the incessant collision of a satellite with what few air molecules there are serves to gradually slow the satellite and thus perturb it into a different orbit. A discussion of the physical structure of the earth's upper atmosphere, plasmasphere and magnetosphere is beyond the scope of this FAQ. Discussion will be limited to the observed effects of the atmosphere on satellite behavior. ---- 5.1.2.4.1 Neutral Drag In low earth orbits, say 1000 km above the earth's surface and lower, the atmosphere primarily consists of a mixture of hydrogen, helium and oxygen atoms. These atoms are not ionized and therefore carry no electrical charge. The drag force exerted on the satellite is entirely due to kinetic "collisions" with the satellite. Because there is no electric charge involved, this type of drag is known as "neutral drag." Neutral drag is what your hand feels when you put it outside of your car window at 100 km per hour, and it is the same force that slows down the satellite and nudges it into a different orbit. Traditionally the "standard" drag equation has been used as a simple model for neutral drag: 1 A 2 drag force = --- C p --- (V ) 2 d M where: C = drag coefficient d A = projected surface area facing the "wind" M = satellite mass p = rho (air density) V = velocity of satellite This equation expresses what we know from everyday experience. It says that lightweight objects feel more drag than heavy objects (i.e., dropping a feather and a stone through the air) and that drag increases with the square of the velocity. Applied to a satellite, neutral drag serves to perturb the satellite out of its classical Keplerian orbit into a smaller and lower orbit. The effect is similar to dragging your feet a little bit when using a playground swing: with each pass through the sand at the bottom each succeeding swing is a little less high than the one before it. The continual erosion of a satellite's semi-major axis is termed "orbital decay." Neutral drag is the primary component in orbital decay. It is important to note that the neutral drag equation cited above is extremely difficult to use in practice. The two main difficulties are the air density and the coefficient of drag. Air density changes with the solar cycle; with every solar flare or geomagnetic event; with the seasons; from day to night; and there are short-term random "gusts" on the order of a few minutes. The coefficient of drag is also difficult to ascertain for very high supersonic speeds in very low air densities. ---- 5.1.2.4.2 Charged Drag and Thermal Drag Thousands of kilometers above the earth the atmosphere becomes the "plasmasphere." It consists primarily of ionized hydrogen, oxygen, and helium. Studies of the Lageos satellite found that the metal surface of the satellite is electrically charged and draws charged molecules to it. This electrical interaction causes "charged drag." Thermal drag occurs when the sunlit side of the satellite emits infrared radiation while the shadowed side of the satellite, being cooler, emits far less radiation. Because half of the satellite is emitting radiation, while the other half is not, relatively speaking, there is a tiny net thrust away from the illuminating source, i.e., away from the sun. This thrust is called "thermal drag" (even though it really is a thrust, the opposite of drag). Charged and thermal drag is much smaller in magnitude than neutral drag. ---- 5.1.2.5 Lunar and Solar Perturbations Satellites in eccentric orbits with very high apogees are particularly susceptible to being perturbed by the gravity of the moon, the sun, or both. These perturbations can gradually increase eccentricity, which causes perigee height to lower. The lower perigee cause more drag; the whole cycle repeats and the satellite reenters the atmosphere. A good example is Oscar 13 (USSPACECOM #19216). Launched in 1988, it sported a high apogee of 38,000 km and a perigee of 720 km. Oscar 13 decayed in late 1996, all 38,000 kilometers of orbit having been eaten up by luni-solar perturbations and drag. Another form of solar perturbation is radiation pressure. Satellites that are very light (low mass) and have large surface areas suffer from being pushed around by the force of sunlight. Radiation pressure is essentially the opposite of thermal drag. The former is caused by photons "colliding" with the satellite, while the latter is a reaction force caused by the emission of (usually infrared) photons. ---- 5.1.3 Other Definitions ---- 5.1.3.1 Apogee ---- 5.1.3.2 Period ---- 5.2 How do TLE's describe a satellite in orbit? What do all those numbers mean? ---- 5.2.1 Line 0 -- Satellite Name ---- 5.2.2 Line 1 ---- 5.2.2.1 Line Number ---- 5.2.2.2 USSPACECOM Catalog Number ---- 5.2.2.3 International Designator ---- 5.2.2.4 Epoch ---- 5.2.2.5 First time derivative of mean motion ---- 5.2.2.6 Second time derivative of mean motion or n-dot-2 ---- 5.2.2.7 BSTAR drag term ---- 5.2.2.8 Ephemeris Type ---- 5.2.2.9 Element number and Checksum ---- 5.2.3 Line 2 ---- 5.2.3.1 Line Number ---- 5.2.3.2 USSPACECOM Catalog Number ---- 5.2.3.3 Inclination ---- 5.2.3.4 Right Ascension of the Ascending Node ---- 5.2.3.4.1 What is an Ascending Node? ---- 5.2.3.5 Eccentricity ---- 5.2.3.6 Argument of Perigee ---- 5.2.3.7 Mean Anomaly ---- 5.2.3.8 Mean Motion ---- 5.2.3.9 Revolution Number ---- 5.2.3.10 Element number and Checksum ---- 5.3 What are the various prediction models? ---- 5.3.1 SGP4 ---- 5.3.2 SGP ---- 5.4 How do satellites decay? Sooner or later all good things must come to an end. Objects in high orbits merely die with their power supplies; solar cells degrade with time due to radiation exposure and damage due to debris, radioisotopic thermo-electric generators eventually are unable to supply sufficient power. Satellites in low Earth orbit have one last chance to perform - when they sink back into the atmosphere and are consumed in an orgy of fire, somewhere around 120 km high. A re-entry has the added bonus of being visible to daylight observers too, as a chaotic series of intertwined contrails across the sky. Satellite re-entries can be quite spectacular and viewed by large numbers of people as the craft will often be seen over a few hundred to a few thousand kilometres before it finally succumbs. For example Sputnik 2 was witnessed by many people during its descent on 14th April, 1958. In the ten minutes it took to travel from over New York to the Amazon, it descended from 130 km to around 60 km, leaving a trail of `sparks' some 100 km long, the satellite itself a multitude of brilliant colours. ---- 5.4.1 Factors in decay ---- 5.4.2 What decreases with decay -- apogee or perigee? ---- 5.4.3 Can decay be predicted? Unfortunately the lifetime of a satellite is notoriously difficult to predict. As the orbit (specifically the perigee) lowers, atmospheric drag increases. This varies according to atmospheric conditions, the solar cycle, the mass and surface area of the satellite, to name a few factors. It retains all the chaos of weather forecasting with little of the certainty; only in the final hour or two of the satellite's life can useful predictions be made. Even then the craft may skip along the upper atmosphere, like a stone skimming across a pond, due to aerodynamic interactions. Thus re-entry predictions made a couple of months in advance will pinpoint a day of demise with an error of a week or so. The geographical location can certainly not be predicted (though potential areas can be). Predictions of expected re-entries can be obtained from the Goddard SpaceFlight Centre via the OIG BBS. A current synopsis can be found here. Though most re-entries are a hit and miss affair, a few can be viewed with some certainty, where either mission controllers have deemed it necessary to `pilot' a craft back into the atmosphere in order to dispose of it (and not add to the debris in low Earth orbit), or in the case of the shuttle landing, or where one of the ascent stages of a launch vehicle falls to Earth due to it having (intentionally) insufficient orbital velocity. ---- 5.5 Tracking Facilities and Methods ---- 5.5.1 The Space Surveillance Network (United States) The United States Space Command (USSPACECOM) operates a network of tracking and detection stations referred to as the Space Surveillance Network (SSN) to keep track of objects orbiting the earth. This tracking and identification process is simply called "space surveillance". The various facilities of the network report their data to the Space Control Center (SCC) at Cheyenne Mountain Air Force Base in Colorado where the data is reduced to determine orbits. The SSN consists of many ground stations and sensors, some of which are dedicated to space surveillance, some which have another primary purpose but are still owned and operated by USSPACECOM, and others which are sites or sensors with another primary purpose and not owned by USSPACECOM. These three categories are referred to as Dedicated Sensors, Collateral Sensors, and Contributing Sensors. The SSN is sometimes confused with the Air Force Satellite Control Network (AFSCN). The AFSCN is a dedicated system of ground antennas for the command and control of satellites and though the AFSCN produces data which can (and does) produce orbital elements, the AFSCN is not used for space surveillance. ---- 5.5.1.1 Dedicated Sensors Dedicated sensors include optical systems, radio frequency systems, and various radars. There are three optical systems dedicated to space surveillance and detection: * Ground-based Electro-Optical Deep Space Surveillance (GEODSS) system operating at Socorro, New Mexico; Maui, Hawaii; Diego Garcia; and ChoeJong San, South Korea * Maui Optical Tracking and Identification Facility (MOTIF) in Hawaii * Combined Radio frequency/Optical Surveillance System (CROSS) in San Vito, Italy Radar systems include a phased array radar operated by the U.S.A. Air Force at Eglin Air Force Base (AFB), Florida, and the (U.S.A.) Navy Space Surveillance (NAVSPASUR) system, which is a "radar fence" stretching some 4800 km (3000 miles) across the southern United States. These are briefly described in the sections which follow. ---- 5.5.1.2 Collateral Sensors The collateral sensors are all radars whose primary purpose is the detection of missiles and aircraft, which may be attacking the North American continent. They provide data on detection of space objects, as well, and therefore are used in the SSN. There are phased array and tracking radars located at: * Thule AB, Greenland * RAF Fylingdales Moor, United Kingdom * Clear AFB, Alaska, U.S.A. * Cape Cod, Massachusetts, U.S.A. * Robins, Georgia, U.S.A. * Eldorado, Texas, U.S.A. * Beale AFB, California, U.S.A. * Cavalier AFS, North Dakota, U.S.A. * Shemya, Alaska, U.S.A. * Pirinclik, Turkey Additionally, there are a set of radars used primarily for test and evaluation of U.S.A. InterContinental Ballistic Missile (ICBM) and space launches at Antigua, British West Indies; Kaena Point, Hawaii; and Ascension Island in the Atlantic, which provide some space surveillance data. ---- 5.5.1.3 Contributing Sensors These sensors are not under direct control of USSPACECOM but are under agreement to provide, part-time, space surveillance data to the SCC. There are four radars and an electro-optical sensor. The four radars are: the ALCOR and ALTAIR-B radars at Kwajalein Atoll, Marshall Islands; and the Haystack and Milistone radars at Tyngsboro Massachusetts. The electro-optical sensor is a separate 63 inch telescope colocated with the MOTIF and GEODSS at Maui, Hawaii. It is referred to as the Air Force Maui Optical Station or AMOS. ---- 5.5.2 Tracking Methods The optical, radio frequency, and radar sensors of the SSN use similar methods to locate and track a space object. Objects can be seen by detecting visible or infrared light, located by detecting the radio frequencies emitted by active satellites, or by observing radar reflection. Regardless of the method, data collected is called "TEARR" data. TEARR is an acronym for "Time, Elevation, Azimuth, Range and Range Rate." The TEARR data is based on a topocentric coordinate system with the sensor at the center. Raw TEARR data, from multiple observations, is passed to the SCC and reduced to an orbit. The more TEARR data from widely spaced sensors, the more accurate the deduction of the orbit. ---- 5.5.2.1 Visible The GEODSS uses low-light-level TV (along with CCD arrays), computers and large telescopes to detect the visible light reflected off objects orbiting the earth. GEODSS primary purpose is for the detection of objects in deep space, from about 5500 km (3000 NM) to beyond geosynchronous altitude. Since GEODSS detects visible light, it must operate at night in clear weather. Most GEODSS sites consist of two 101.6 cm (40 inch) telescopes which primarily search for faint, slow-moving objects, and a 38.1 cm (15 inch) telescope for wide searches of lower altitudes for objects traveling at higher relative speeds. (The Diego Garcia site has three 101.6 cm telescopes.) The images from the CCD arrays or low-light-level TV are fed directly to computer where the computer extracts the star background. The remaining objects are satellites (or debris) which show up as streaks. The GEODSS instruments then determine the TEARR data and transmit it directly to the SCC. GEODSS provides more than 65% of all deep space object tracking and identification. One of the two 1.2 m (47.2 inch) telescopes of the MOTIF is also used for visible light detection and tracking but is used primarily for imaging. The MOTIF 1.2 m visible sensor must also operate at night, and is hindered by a bright moon. The CROSS at San Vito, Italy is the only system combining visible detection with the capability to detect radio frequencies from active satellites. CROSS replaced the old Baker-Nunn cameras at the site and contributes to a significant improvement in coverage in the eastern hemisphere. CROSS must operate a night, in a dark sky, and its capabilities are classified. ---- 5.5.2.2 Infrared The second of the two 1.2 m telescopes of MOTIF is operated in the infrared (IR). It is operated primarily to image in the infrared and provide IR signature information, but is also used to determine TEARR data. The two 1.2 m MOTIF telescopes are on a single mount and are operated together. The visible sensor is operated only at night but the IR sensor is used during daylight for IR imaging and tracking. There is an additional 1.6m (63 inch) telescope on Maui which is being fitted with IR instruments and will be used for space object identification and will be able to image during daylight. ---- 5.5.2.3 Radar The phased array radar in Florida is used to track both deep space and near earth objects simultaneously. As many as 10,000 observations per day are made and produce TEARR data as well as radar cross-section data. The NAVSPASUR system consists of three high-power transmitters and six receivers strung across the southern United States. The transmitter stations send a continuous signal, restricted to a narrow north-south spread, but a wide east-west spread. The three transmitters combine to form a "fan" of radar energy extending many tens of thousands of kilometers into space. As a satellite passes through this "fan" or "fence", it reflects the signal back to the ground receivers. The ground stations then process the received data into TEARR data. ---- 5.5.3 The Products When sensors of the SSN acquire an object, its TEARR data is forwarded to the SCC. The data is reduced and orbital elements are produced. The SCC compares the observations with the predicted location of all cataloged objects. Either a match is made and the TEARR data is used to refine the orbit of the known object, or the data may indicate a previously uncataloged object. One of the concerns is the decay and reentry of a satellite. The SCC produces an RA (reentry assessment), formerly called a TIP (tracking and impact prediction) to predict when and where a larger decaying object will reenter. The RA is only available to authorized military users. Cataloged objects are tabulated into lists of classified and unclassified orbital elements. These lists are posted to a USSPACECOM computer bulletin board for which access allowed for about 100 authorized agencies. Unclassified elements are then released by NASA. ---- 5.5.3.1 Two-Line Element Lists Lists containing the standard two-line elements (TLE's) for unclassified objects are released to NASA's Goddard Space- flight Center (GSFC) and the Jet Propulsion Laboratory (JPL) via memorandum of agreement with USSPACECOM. These element lists are made available from the GSFC and the JPL via the World Wide Web or FTP. Two-line elements for classified objects are released to the GSFC and JPL on a special case basis but never released to the public. ---- 5.5.3.2 SPACEWARN Bulletin Though not a product of the SSN, the SPACEWARN Bulletin is published by the NASA National Space Science Center/World Data Center for Rockets and Satellites. It provides information on space launches, and updates on space probes and satellites but may contain data on decays. The bulletin is available on the World Wide Web or anonymous FTP: ftp://nssdca.gsfc.nasa.gov/active.spx/spx.AAA where AAA is the issue number. ---- 5.5.3.3 Weekly Decay Message The USSPACECOM 1st Command and Control Squadron publishes a weekly tabulation of the objects expected to decay within the next 60 days. This Weekly Decay Message is distributed via military message traffic and also made available to the authorized users of the USSPACECOM BBS. The GSFC receives this list and republishes it as the 60-Day Forecast Report on their Orbital Information Group (OIG) BBS. ======================================================================== This FAQ was written by members of the SeeSat-L mailing list, which is devoted to visual satellite observation. Members of this group also maintain a World Wide Web site. The home page can be found at the URL: http://www.satobs.org/ The information on the VSOHP web site is much more dynamic than that found in this FAQ. For example, the VSOHP site contains current satellite visibility and decay predictions, as well as information about current and upcoming Space Shuttle missions and Mir dockings. The VSOHP site also contains many images, equations, and data/program files that could not be included in this FAQ while maintaining its plain text form. This FAQ and the VSOHP web site are maintained asynchronously, but an effort is made to synchronize information contents as much as possible. The material in this FAQ chapter was last updated in February 1998. ========================================================================