Satellite Orbits.

Transcription

1 atellite Orbits It was announced few days ago that a 6-ton NAA weather no-longer functioning satellite that was launched in 1991 would crash into arth some time between Thursday, 22 eptember 2011 and aturday, 24 eptember It eventually crashed early on aturday somewhere over the Pacific Ocean. NAA stated that they would know of the approximate time and location of its crash only about 2 hours before its crash. The orbit of this satellite is known, so why was NAA not able to know when and where it will crash exactly? The answer is that the rate at which the orbit of that satellite or any other object decays (drops) is a function of the atmospheric drag, which in turn is related to the aerodynamics of that satellite or object. A non-operational satellite or some piece of space junk may not be symmetric so its drag coefficient changes as it tumbles around. o, the rate at which it drops will vary significantly on what attitude is its travel. This makes it impossible to know when and where it will eventually slow down significantly to change its orbit and crash. Locating a atellite from an arth tation (Look Angles) It is very important for someone who works in the field of satellites to be able to locate a satellite in the sky in order to point an antenna at it and possibly be able to track it as it moves in the sky if it is not a GO satellite. The standard format for determining the location of a satellite in the sky is called the determination of the look angles. These look angles determine the position that the observer of a satellite has to point his antenna to be able to receive/transmit to the satellite. The look angles are two angles called: Azimuth (AZ): This is the angle measured in the plane parallel to the horizon measure from the polar north (the top-most point on arth) going clockwise. o, this angle has a value between 0 and 360 such that North is 0, ast is 90, outh is 180, and West is 270. levation (L): This is the angle measured in the plane perpendicular to the horizon measure from the horizon going up towards to the vertical line to the horizon. o, this angle has a value between 90 and +90 such that the horizontal direction is 0, Vertically upwards +90, vertically downwards is 90.

2 In addition to these angles, it is usually useful to know the distance from the earth station (or observer) to the satellite for some important computations related to signal attenuation for example. Distance (d): This is the distance from the observer or arth station to the satellite. This distance is equal to the satellite altitude (height of satellite above arth s surface) if the observer is standing exactly under the satellite (the satellite appears exactly above the observer) and is greater than the satellite altitude if the satellite is not exactly above the observer. In the process of computing the Azimuth, levation, and Distance to the satellite, two angles that are not important by themselves but are important for the computation of these quantities must be evaluated. arth s Central Angle (γ): This is the angle at the center of arth between the location of the arth station and the location of the satellite (or what we call subsatellite point). o, imagine that you are at the center of arth and you point one hand towards the arth station and the other towards the satellite. This angle is the angle between your two hands and is limited between 0 and 180. This angle is 0 if the satellite is exactly on top of the arth station (the arth station is at the sub-satellite point), is equal to 180 when the satellite is exactly on the opposite side of the arth station. The intermediate angle (α): This is the angle between the North or outh direction and the sub-satellite point. This angle is always between 0 and 180. The Azimuth is computed from this angle. The above angles and quantities are shown in the following figure:

3 The parameters needed to find the Azimuth, levation, and Distance to the satellite are the following: L = Latitude of arth station (Degrees) [North angles are Positive and outh are Negative] le = longitude of arth station (Degrees) [ast angles are Positive and West are Negative] L = Latitude of ub-atellite point (Deg.) [North angles are Positive and outh are Negative] ls = longitude of ub-atellite point (Deg.) [ast angles are Positive and West are Negative] r = Radius of atellite (km) = atellite altitude (a s ) + Radius of arth (r s ) The resulting quantities from the following measurements are L = levation angle (Degrees) AZ = Azimuth angle from North (Degrees) d = Distance between atellite and arth tation (km) First, we have to find the arth central angle (γ) using the following relation ( L ) ( L ) ( ls le) ( L ) ( L ) γ = + 1 cos cos cos cos sin sin This allows us to compute the distance to the satellite (d) given by d r r = r 1+ 2 cos r r 2 ( γ ) When the distance to the satellite is found, we can find the elevation angle (L) which is either positive or negative depending on the location of the satellite with respect to the arth station If If r > d + r r L =+ ( γ ) d 1 cos sin atellite is visible r < d + r r L = ( γ ) d 1 cos sin atellite is NOT visible Important Note: The L angle in the above derivation must be positive (> 0 ) for the satellite to be visible. This is practically inaccurate because for low angles (0 5 ), the satellite is so low near the horizon that the received signal from that satellite (or the received signal by the satellite from arth) is highly attenuated. In fact, it is usually considered that the minimum angle for a satellite to be visible is 5 for signals in the C band (4 to 8 GHz), 10 for signals in the Ku band (11 14 GHz), and 20 for signals in the Ka band (26 40 GHz). Below these angles, the received signals are unusable.

4 The next to last step is to find the intermediate angle (α) which is given as ( ) 1 sin ls le cos L α = sin sin ( γ ) The last step is evaluating the Azimuth which is conditioned on the location of the arth station with respect to the sub-satellite point as follows When L > L If ls > le AZ = α (atellite is North-ast of arth station) If ls < le AZ = 360 α (atellite is North-West of arth station) When L < L If ls > le AZ = 180 α (atellite is outh-ast of arth station) If ls < le AZ = α (atellite is outh-west of arth station) Parameters for etting atellite Orbits We have learned so far that satellite orbits can be classified into: 1. Circular or lliptical: Circular orbits are generally used for commercial communication satellite while elliptic orbits are used for some specialized satellites (many spy satellites have elliptical orbits). One use of elliptic orbits is due to the fact that the satellite slows down when it is near it apogee, which means that the satellite remains visible at a specific arth station for long periods of time in each orbit. 2. LO, MO, or HO Orbits: These descriptions are usually used for circular orbits of different heights. It is clear that a satellite in an elliptical orbit may have its complete orbit in one of these heights, however, an elliptical orbit may partially be in the LO region for part of the orbit and in the MO, or even HO in other parts of the orbit, especially for highly elliptical orbits, so some elliptical orbits may not fit in the classification of LO, MO, or HO if the difference in altitude between the apogee and perigee points is significantly high. However, these classifications are not sufficient to determine the exact orbit of a satellite. That is, there exist an infinite number of orbits that are circular, elliptical, LO, MO, or HO. o, the above are not sufficient to indicate the exact orbit of a satellite. Three more parameters are needed for this task considering only circular orbits. These parameters are 3. The Orbit Inclination: The inclination of an orbit is the angle the plane of the orbit makes with the plane of arth s equator. o, an orbit in the same plane of the equator (called an quatorial orbit) has an inclination of 0, while an orbit that passes over the North and outh poles (called a Polar orbit) has an inclination of

5 90, other orbits that are different from equatorial and polar orbits have inclinations between 0 and 90. The following figure shows orbits with different inclination angles Inclination of Blue = 0, Green = 18, Red = 36, Cyan = 54, Purple = 72, Black = The Inclination Phase: Not all orbits with the same inclination are the same. That is, there are an infinite number of different orbits with the same inclination. For example, two satellite orbits may have the same inclination of 30 but one of them crosses the plane of the equator at the longitudes of 0 and 180, while the other crosses the plane of the equator at the longitudes of 10 and 190. The following figure shows orbits with same inclination angle but with different inclination phases

6 Phase of Blue = 0, Green = 10, Red = 20, Cyan = 30, Purple = 40, Black = 50 All orbits have the same inclination of The atellite Phase in its Orbit: ven for a particular orbit, multiple satellites may have that same orbit but each one of them may be at a different point in that orbit. That is, the different satellites are following each other in the same orbit. The following figure shows different satellites in the same orbits but at different phase of the orbit. Orbital Phase of Blue = 0, Green = 60, Red = 120, Cyan = 180, Purple = 240, Black = 300 All satellites have the same orbit with the same inclination of 60 and the same inclination phase of 0.