The two thrust modes, high thrust and low thrust, do approach each other in character as the delta V being imposed approaches zero. 3.2 EFFECTS OF T/W ON DELTA V AND TRIP TIMES For a low thrust case with a constantly thrusting spiral flight path, the delta V, from energy considerations, turns out to be the absolute value of the difference in circular orbit velocity between the beginning circular orbit and the final circular orbit. This is independent of the thrust level so long as it is down in the very low thrust region. Thus, the delta V required for geosynchronous transfer with a 10-3 thrust level is the same as it is with a 10_4 or 10-5 or 10_^g thrust level. Trip times, however, are inversely proportional to the thrust. Trip time can be approximated by delta V divided by the acceleration (T/W). This gives the thrusting time which is very close to the total flight time. As the thrust level decreases and flight time increases this approximation becomes more and more accurate. Toward the end of the transfer there is often a short coasting phase but this is never more than a few hours from Earth orbit operations. A plot of altitude reached vs delta V and/or flight time is given in Figure VI-D-3-2. Delta V for a geosynchronous transfer from a 250 NM initial parking orbit with zero plane change is 15,000 fps. Trip time for a vehicle with-001 T/W, which is probably an upper limit for moving a large station, is approximately 5 1/2 days. As a comparison the same transfer with a high (impulsive thrust level requires a delta V of 12,700 fps and a transfer time approx. .25 days (see Table VI-D-3-1). 3.3 GUIDANCE AND NAVIGATION (G&N) REQUIREMENTS Guidance and navigation requirements can be greatly simplified by going to very low thrust operations. Things happen so slowly that real time calculations and tracking can be carried out on the ground during the thrusting operation. A simple efficient guidance is by thrusting horizontally to the ground in the plane of the orbit. While the most optimum thrust is along the velocity vector, for low thrust the velocity vector stays very horizontal and the efficiency losses of a horizontal thrust are entirely negligible. The advantage of horizontal thrust is in simplicity of implementation. The pointing accuracies required are very low (5 to 10 degs) during everything but the very final orbit corrections. Navigation would be by tracking and computer calculations on the ground. Time elements are so slow, with flight times of at least on the order of a week, that integrations on the ground can be very easily carried out even on something as unsophisticated as a small desk computer. Guidance would then simply be by transmitting an enable/disable command to the thrusters.
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