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AMATEUR RADIO BY JAMES MORRIS, VK2GVA A look at satellites & their orbits Amateurs are in the privileged position of having access to experimental satellites which provide a range of techni­cal & operational challenges. This month’s article discusses some of the basics of satellite orbits. The laws of planetary motion were first described by Kepler and Newton in the 17th century and they also apply to the motion of satellites around the Earth. Kepler’s first law states that the orbit of a satellite is an ellipse (Fig.1a). The satellite’s closest point of approach is called the perigee, while the apogee is the orbital point furthest from the Earth. The shape of the ellipse is determined by the semi-major axis (a) and the eccen­tricity (e). When the eccentricity is zero, the shape of the orbit is circular. Kepler’s second law states that equal areas are swept out in equal times by the satellite’s radius to the Earth, so that the satellite’s velocity as seen from the Earth will vary, being maximum at the perigee (Fig.1b). For circular orbits, the veloc­ity of the satellite is constant. Kepler’s third law describes the way in which there is a fixed relationship between a satellite’s height and its orbital period, with smaller orbits containing faster moving satellites – see Fig.1c. Kepler’s laws, in conjunction with Newton’s laws, can be used to fully describe the orbit of a satellite around the Earth, resulting in a mathematical model with six constant terms. These constants are called orbital or Kepler­ ian elements. The inclination of an orbit is the angle between the orbi­tal and equatorial planes (Fig.2a). When a satellite moves in the same direction as 72  Silicon Chip the Earth’s rotation, it is said to be in a prograde orbit. Satellites which follow retrograde orbits move in the opposing direction (Fig.2b). The most commonly used orbit is geostationary, where the satellite moves at the same speed as the Earth’s rotation, and has an inclination of 0 degrees. A geostationary satellite appears at a fixed location in the sky, so that it can provide a continuous communications link between ground stations within its “footprint”. The use of satel­lites in geostationary orbit for global communications was envis­ aged by the scientist Arthur C. Clarke in 1945. His calculations, based on Kepler’s laws, showed that geostationary satellites would orbit the equator at a height of approximately 35,786km. This unique orbit is known as the Clarke belt, and contains many satellites which are “parked” in “slots” above the equator. The Optus series of satellites are located in the assigned slots: 156°, 160° and 164° east. Recently, there have been proposals made by amateur groups to establish geostationary communications links with the develop­ment of the Phase IV series amateur satellites. This new genera­tion of Hamsats could provide some very interesting possibilities for long distance voice, packet and image communication. Polar orbiting satellites pass over the north and south polar regions (Fig.2b). The NOAA weather satellites follow polar orbits which are also sun-syn- chronous, passing over the same points at the same local times each day. This allows the same areas of the Earth to be imaged under reasonably consistent lighting conditions. The footprint of a sun synchronous polar orbit satellite overlaps itself during successive passes. SARSATS (search and rescue satellites), which often share a common space platform with weather satellites, utilise this footprint overlapping to obtain accurate readings for the position of ELT (emergency locator transmitter) and EPIRB (emergency position indicating radio beacon) devices. A rather specialised orbit is used by the Russian Molniya satellites, which are inclined at approximately 64°. Their orbits are optimised to provide telecommunications for areas located at high northern latitudes, as geostationary satellites cannot be seen from locations above 81° north or south. Moln­iyan orbits are also highly eccentric, and remain within view of targeted regions for many hours; a specific appli­ c ation of Kepler’s second law. Low Earth orbits Low Earth orbit satellites (LEOS) follow fast, almost circular orbits and are relatively inexpensive to implement (approximately 1/20th the cost of geostationary). LEOS orbits are used extensively by small satellites which gather atmospheric and other scientific data. Many amateur satellites make use of near-polar low Earth orbits with an inclination of greater than 80°. Amateur LEOS are able to rapidly upload and download information around the world, making them ideal vehicles for packet BBS (bulletin board systems), which have been used for primary international communications during disasters. The excellent MAJOR AXIS, A ORBIT SATELLITE EARTH PERIGEE APOGEE SEMI-MINOR AXIS, b MINOR AXIS, B world-wide coverage and low cost of LEOS also provides a strong commercial potential. Currently, there are a number of proposals for global personal communications on the corporate drawing boards. A disadvantage of LEOS is the amount of tracking required at the ground, as they tend to move rather quickly. This is partially offset by the fact that the satellites are closer to the Earth, with the associated increase in signal strengths. Lower gain antennas may be used, which often have broader direc­tional characteristics and less critical aiming requirements. Orbital perturbations The Earth has a slight bulge at the equator and a flatten­ing of the poles; its true shape is as an oblate spheroid. This complicates the determination of satellite motion, as Kepler’s laws assume the Earth to be perfectly spherical. The Earth’s mass is not evenly distributed, producing minor variations in the gravitational forces acting on its satellites. The difference in gravity experienced at two points in an orbit produces a ‘gravity gradient’ or slope. A satellite will be more attracted to one of these points, and accelerate towards it. Geostationary satellites are attracted towards the positions of 75° E or 105° W, and require regular ‘station keeping’ to prevent their inevitable slide towards what are commonly referred to as satellite graveyards (orbital points situated between gravitational ‘bulges’). A recent example of this effect occurred in 1992, when two ARABSAT series spacecraft suddenly ran out of station keeping fuel. They began to drift along the Clarke belt towards 75° E and although still otherwise operational, were eventual­ly powered down to prevent interference to other satellites. The gravitational fields of the sun and moon significantly affect geostationary satellites, by inclining their orbits away from the equator. The LEOS are less affected, due to the in­creased effect of the Earth’s gravitational field at close range. Again, station keeping is required to correct the orbit of satel­lites affected, by the firing of onboard thrusters in the op­posite direction of the drift. At heights of below approximately 1000km, satellites are affected by atmospheric drag, which serves to reduce the eccen­tricity and apogee height of their orbits. Atmospheric drag can be a particular problem for low Earth orbiting satellites. Attitude The orientation of a satellite in its orbit with respect to the Earth is its attitude, which is maintained through attitude control. This differs from station keeping in that the shape of the orbit is not of prime concern. Attitude control is used for local stabilisation. To simplify the stabilisation of satellites in low orbits, the gravitational field of the Earth is utilised. After launch, the spacecraft gradually aligns itself vertically with the Earth, so that the antennas are pointing in the desired direction. During this time, amateurs monitoring the satellite’s beacon may notice periodic fading as the satellite ‘oscillates’ around the stable attitude. This effectively modulates the beacon, an effect used to help determine the status of the satellite in the initial orbit stage. SEMI-MAJOR AXIS, a 2 a b a ECCENTRICITY OF ORBIT, e = 2 PERIGEE HEIGHT = a(1 - e) 6378km APOGEE HEIGHT = a(1 + e) 6378km (a) SATELLITE NEAR PERIGEE V2 A2 T2 A1 PERIGEE T1 APOGEE V1 SATELLITE NEAR APOGEE EARTH ORBIT (b) PERIOD ~= 105 MINUTES HEIGHT = 1000km r V ~= 26000km/h EARTH r= 6378km LOW ORBIT HIGH ORBIT HEIGHT = 35786km VELOCITY ~= 11000km PERIOD = 24 HOURS (c) Fig:1: this diagram illustrates Kepler’s Laws of planetary motion which also describe the orbits of satellites around the Earth. Note that at apogee the satellite is travelling at its slowest speed. Geostationary satellites, which generally carry telecom­ munications and broadcasting, are too far from the Earth for gravitational torque stabilisation to be efficient. These satel­lites are stabilised by two basic methods. An entire satellite may be set spinning, in the manner of a gyroscope. The antennas must then either have circular symmetrical radiation patterns, or be placed upon a non spinning (despun) platform. Alternatively, internal stabilisers may be used, in the form of momentum wheels, which provide the necessary overall stabilising torque. Satellites which use this August 1993  73 N The point directly underneath the satORBITAL PLANE ellite at the Earth’s SATELLITE surface is called the sub satellite point (SSP). Radio frequenEQUATORIAL cies received at the PLANE EARTH i°  ground appear to vary from high to low i° = INCLINATION during the satellite’s pass overhead, due to the effect of Doppler (a) shift (Doppler shift is a phenomenon N associated with the POLAR ORBIT behaviour of waves HEIGHT ~= 1000km pro­p­a gated from a mov­ing transmitter). The nominal freORBIT quency of a particular beacon or transponder (transponders are HEIGHT 35786km EQUATOR devices which, upon receiving signals, 5F 8 180 o 164 o automatically issue 160 o responses) is given 156 o for the TCA, when the Doppler shift is B2P 113 o zero. (b) In the case of satFig.2a illustrates the inclination of a satellite orbit, ellite AO-21, with a while Fig.2b shows the geostationary orbits of the Optus satellites at around 160°E, the Intelsat 5F8 nominal downlink satellite at 180°E & the Palapa B2P satellite at 113°E. of 145.987MHz (FM voice), the received method are called three-axis or body frequency may vary from approximatestabilised. ly 145.990MHz at AOS to 145.984MHz To correct for errors in spacecraft at LOS. The effect of Doppler shift attitude, a variety of techniques are is greater for passes which are more used, such as firing thrusters, accel- directly overhead. erating the momentum wheels, and AO-21 is a LEOS with a near polar employing reaction wheels to absorb orbit of 83° inclination. Apogee and the effects of disrupting forces. perigee heights are 1000km and 958km respectively. The orbital period is Tracking about 105 minutes, and a good pass Tracking a satellite involves locating may last for 20 minutes. The FM voice transponder uses an its position in orbit and determining its motion. This information is referred experimental digital pro­cessing systo the Earth’s motion, so as to provide tem which is used to regenerate weak pointing coordinates (look angles) for or distorted signals. The downlink a station’s antenna system. Times at frequency, as mentioned, is approxiwhich the satellite will be visible to mately 145.987MHz. the station are calculated, and the A beacon on 145.822MHz (CW) is feasibility of communications with quite useful for tracking, even with the satellite during these times are an FM receiver. Due to the relatively evaluated. wide­band nature of the FM signal, it is The time at which a satellite appears not necessary to use an expensive mulover the radio hori­zon, and beacons timode rig to tune in. Try 145.990MHz or other transmissions are received, as a starting frequency on which to is known as the acquisition of signal monitor the satellite. (AOS). The time of closest approach Some handheld transceivers can (TCA) and loss of signal (LOS) then be tuned in 5kHz and 12.5kHz steps, describe the completion of the pass. giving a series of three frequencies 74  Silicon Chip (145.990MHz, 145.9875MHz and 145.985MHz) to track Doppler shift. Receive antenna requirements for this satellite are mini­mal and a ¼-wave ground plane should give good results. The uplink frequency for this transponder is 435.016MHz, making it “mode B” in hamsat terminology. The uplink requirements are a little more involved. Power levels in the range of 25W are con­sidered the minimum useful level, although AO-21 has been worked with a dual band hand-held (WA5ZIB/KB8KVY). By using a predictive tracking program, it would be possi­ble to determine the best time to listen out for the satellite, although it is also possible to just tune in and wait. After the first pass, add 105 minutes to the AOS to give an indication of when the next pass might be (given that the satellite will be in view at the next pass). For those with a computer, a tracking program is essential for detailed orbital analysis and more advanced satellite experimentation. These programs require a set of up-to-date Keplerian ele­ ments for each satellite being studied, which are available from bulletin boards in a standard format. Further information Amateur satellite information is avail­­able from AMSAT Aus­tralia. Their HF net meets on Sundays at 1000z (UTC). Net frequencies are 7.064MHz and 3.685MHz, depending on conditions. AMSAT Austra­lia is at GPO Box 2141, Adel­aide 5001. Public domain satellite track­ing programs and NASA-issued Kep­ler­ian elements are available from the Satcom Australia BBS on (02) 905 0849. References (1). The Inclined Orbit Satellite Tracking Guidebook, M. Long & J. Keating, MLE Inc, 1993 (available from AvComm Pty Ltd, PO Box 225, Bal­gow­ lah, NSW 2093). (2). Satellite Communications Systems, G. Maral & M. Bousquet, John Wiley & Sons, 1986. (3). Satellite Communications, T. Pratt & C. Bostian, John Wiley & Sons, 1986. (4). Advanced Electronic Communications Systems, W. Tomasi, Prentice Hall, 1987. (5). Satellite Communications, D. SC Roddy, Prentice Hall, 1989.