Satellite Orbits
Satellites can be categorized in two ways. The first deals with their altitude above the earth's surface. There are LEOs, MEOs, and GEOs. These
Figure 6.1. Simplified functional block diagram of a satellite communications transponder. This is the conventional translating RF repeater or ''bent-pipe''satellite configuration.
Figure 6.1. Simplified functional block diagram of a satellite communications transponder. This is the conventional translating RF repeater or ''bent-pipe''satellite configuration.
abbreviations stand for low earth orbit, medium earth orbit, and geostationary earth orbit, respectively.
Satellites can also be characterized by their orbits:
• Equatorial
The figure a satellite defines in orbit is an ellipse. Of course, a circle is a particular class of ellipse. The Molniya, so popular with the Russians, is a highly inclined elliptical orbit.
The discussion in this chapter will dwell almost entirely on geostationary satellites. A geostationary satellite has a circular orbit and is classified as equatorial. Its orbital period is one sidereal day (23 h, 56 min, 4.091 s) or nominally 24 hours. Its inclination is 0°, which means that the satellite is always directly over the equator. A geostationary satellite appears stationary over any location on earth, that is within optical view.
Geostationary satellites are conventionally located with respect to the equator (0° latitude) and a subsatellite point, which is given in degrees longitude at the earth's surface. The satellite's range at this point, and only at this point, is 35,784 km (22,235 statue miles) above the earth's surface (sea level). Table 6.1 gives details and parameters of the geostationary satellite.
Table 6.1 also outlines several of the advantages and disadvantages of a geostationary satellite. Most of these points are self-explanatory. For satellites not at geosynchronous altitude and not over the equator, there is the appearance of movement. The movement with relation to a point on earth will require some form of automatic tracking by the earth station antenna to always keep it pointed at the satellite. If a satellite system is to have full earth coverage using a constellation of geostationary satellites, a minimum of three satellites would be required, separated by 120°. As an earth station moves
TABLE 6.1 The Geostationary Satellite Orbit
For the special case
Altitude
Period
Orbit inclination
Velocity
Coverage
Number of satellites
Subsatellite point Area of no coverage Advantages
Disadvantages of a synchronous orbit—satellite in prograde circular orbit over the equator: 19,322 nautical miles, 22,235 statute miles, 35,784 km 23 h, 56 min, 4.091 s (one sidereal day) 0°
6879 statute miles/h
42.5% of earth's surface (0° elevation)
Three for global coverage with some areas of overlap (120° apart) On the equator
Above 81 ° north and south latitude Simpler ground station tracking No handover problem Nearly constant range Very small Doppler shift Transmission delay Range loss (free-space loss) No polar coverage
Source: Reference 1.
northward or southward from the equator, the elevation angle to a geostationary satellite decreases (see Section 6.2.3). Elevation angles below 5° are generally undesirable, as will be discussed subsequently. This is the rationale in Table 6.1 for ''area of no coverage.'' Handover refers to the action taken by a satellite earth terminal antenna when a nongeostationary (often misnamed ''orbiting satellite'') disappears below the horizon (or below 5° elevation angle) and its antenna slews to a companion satellite of the system that is just appearing above the opposite horizon. It should be pointed out here that geostationary satellites do have small residual relative motions. Over its subsatellite point, a geostationary satellite carries a small apparent orbit in the form of a figure eight because of higher space harmonics of the earth's gravitation and tidal forces from the sun and moon. The satellite also tends to drift off station because of the gravitational attraction of the sun and moon as well as solar winds. Without correction, the inclination plane drifts roughly 0.86° per year (Ref. 1, Section 13.4).
6.2.2 Elevation Angle
The elevation angle or ''look angle'' of a satellite terminal antenna is the angle measured from the horizontal to the point on the center of the main beam of the antenna when the antenna is pointed directly at the satellite. This concept is shown in Figure 6.2. Given the elevation angle of a geostationary satellite, we can define the range. We will need the range, d in Figure 6.2, to calculate the free-space loss or spreading loss for the satellite radiolink.
- Figure 6.2. Definition of elevation angle (0) or ''look angle''and range (d) to satellite.
6.2.3 Determination of Range and Elevation Angle of a Geostationary Satellite
Geostationary satellites operate at an altitude of about 35,785 km above sea level. Unless an earth station is directly under a satellite, however, the distance d of Figure 6.2 will be greater than 35,785 km. The value of d can be established by use of the law of cosines of plane trigonometry. Consider first that the earth station is on the same longitude as the subsatellite point, taken to be at 0° latitude. The subsatellite point is located where a straight line from the satellite to the center of the earth intersects the earth's surface. See Figure 6.3. From the figure we can now state that
where 0' is latitude. The equatorial radius of the earth is 6378.16 km, the polar radius is 6356.78 km, and the mean radius is 6371.03 km (Ref. 2). To obtain the most accurate value of d, it would be necessary to take into account the departure of the earth from sphericity, but an approximate value of d can be obtained by taking r0, the earth's radius, to be 6378 km and h, the height of the satellite above the earth's surface, to be 35,785 km in equation (6.1). Divide all terms in equation (6.1) by (h q r0)2 or (42,163)2,
which gives
where f = r0/(h + r0) = 0.1513. Once d is known, then all three sides of the triangle in Figure 6.3 are known and the angle $ can be determined by applying the law of cosines again. The applicable equation is
The elevation angle 6 measured from the horizontal at the earth terminal is equal to $ - 90°.
For an earth terminal not on the same meridian as the subsatellite point, we can use the equation (from the spherical law of cosines)
in equation (6.1) in place of cos 6', where is the difference in longitude between the subsatellite point and the earth terminal; cos Z is the angular distance of a great circle path for the special case that one of the end points is at 0° latitude (Figure 6.4). Also, the expression follows from the law of cosines for sides from spherical trigonometry (Ref. 3, Section 44) The azimuth angle a of an earth - space path can be determined by using (Ref. 3, Section 44)
The angle a is shown in Figure 6.4a for an earth terminal located to the east of the subsatellite point. The azimuth angle measured from the north in this case would then be 180° + a. For an earth terminal located to the west of the subsatellite point (Figure 6.4b), the angle from true north is 180° - a.
Example 1. Calculate azimuth and elevation angles and distance from a point 40° N, 105° W for a satellite where the subsatellite point is located at 119° W.
From equation (6.1) we find that d = 37,666 km and the elevation angle 0 = 43.73°; the azimuth angle is 201.2°.
Range, elevation, and azimuth angles may also be determined by nomogram with sufficient accuracy for link analyses (link budget). See Figure 6.5
6.3 INTRODUCTION TO LINK ANALYSIS OR LINK BUDGET 6.3.1 Rationale
To size or dimension a satellite terminal correctly, we will want to calculate the receive signal level (RSL) at the terminal. The methodology is very similar to what we used in Chapters 2, 3, 4, and 5. However, there are certain legal constraints of which we should be aware.
6.3.2 Frequency Bands Available for Satellite Communications
The frequency bands assigned for satellite communications are given in Table 6.2 as corrected by recent Radio Regulations (Ref. 4). Generally, these frequency bands are referred to in band pairs. One of the band pairs, usually of higher frequency than the other, is used for the uplink path (i.e., terminal to satellite), and the other is assigned the downlink path. In this text we will be dealing with the following commonly used frequency band pairs (uncorrected for recent Radio Regulations, but commonly accepted in the industry):
- Figure 6.5. Determination of range to a geostationary satellite, azimuth, and elevation angles. (From Ref. 1, courtesy of COMSAT, Washington, DC.)
INTRODUCTION TO LINK ANALYSIS OR LINK BUDGET 313 TABLE 6.2 Fixed Satellite Service Frequency Allocationsa
Applicable Radio
Uplink (MHz) Region Bandwidth (MHz) Regulation Article
Applicable Radio
Uplink (MHz) Region Bandwidth (MHz) Regulation Article
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