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in the same plane As shown in Fig 311, it takes 1 to 2 months for the satellite to be fully operational (although not shown in Fig 312, the same conditions apply) Throughout the launch and acquisition phases, a network of ground stations, spread across the earth, is required to perform the tracking, telemetry, and command (TT&C) functions Velocity changes in the same plane change the geometry of the orbit but not its inclination In order to change the inclination, a velocity change is required normal to the orbital plane Changes in inclination can be made at either one of the nodes, without affecting the other orbital parameters Since energy must be expended to make any orbital changes, a geostationary satellite should be launched initially with as low an orbital inclination as possible.

Interpret tan 1 x as the angle (between /2 and /2) whose tangent is x. Let y = tan 1 x. Then, tan y = x Dx (tan y) = 1 dy sec2 y =1 dx 1 1 1 dy = = = dx sec2 y 1 + x2 1 + tan2 y Thus, Dx (tan 1 x) = 1 1 + x2 and 1 dx = tan 1 x + C 1 + x2 (37.3)

The difference is the amount of randomness in the turn around The turn is now 180 10 instead of 30 The reasoning is that since the sensors are 10 on either side of the front, if we turn the robot around and keep it within this limit (10 ) of where it came from (if it is over the line) it will still sense the line and turn back in Another way the same effect can be achieved is by widening the line If you change the number in the statement LineWidth 7 to 20 the boundary would become too wide for the robot s front to be outside the line when it turns the 180 30 There is still a problem The robot seems to spend most of its time around the perimeter straddling the line This is predictable.

It will be shown shortly that the smallest inclination obtainable at initial launch is equal to the latitude of the launch site Thus the farther away from the equator a launch site is, the less useful it is, since the satellite has to carry extra fuel to effect a change in inclination Russia does not have launch sites south of 45 N, which makes the launching of geostationary satellites a much more expensive operation for Russia than for other countries which have launch sites closer to the equator Prograde (direct) orbits (Fig 24) have an easterly component of velocity, so prograde launches gain from the earth s rotational velocity For a given launcher size, a significantly larger payload can be launched in an easterly direction than is possible with a retrograde (westerly) launch In particular, easterly launches are used for the initial launch into the geostationary orbit.

The relationship between inclination, latitude, and azimuth may be seen as follows [this analysis is based on that given in Bate et al (1971)] Figure 313a shows the geometry at the launch site A at latitude l (the.

If the turning around is almost 180 whenever it senses the line with all or just the front sensor, then it will almost always go back to where it came from, and if that happens to be from a long run while straddling the line until it comes to the corner, then it will just turn around and go back to the other corner This is not very effective behavior The robot should cover more of the inside area, especially if it is supposed to be doing some useful work in that area Therefore, even though we have solved the problem of escaping, we have not solved it in a satisfactory manner The algorithm needs further re nement There is also another problem If the robot approaches a corner at exactly 45 to it, then the left and right sensors would trigger together, but not the front one.

Figure 3.11 From launch to station of INTELSAT V (by Atlas-Centaur). (From Satellite Communications Technology, edited by K. Miya, 1981; courtesy of KDD Engineering & Consulting, Inc., Tokyo.)

Inverse Cotangent (Arc Cotangent) y = cot x Interpret cot 1 x [0 < x < ] x = cot 1 y [all y]

STS-7/Anik C2 mission scenario. (From Anik C2 Launch Handbook; courtesy of Telesat,