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Satelite eccentricity
An article in the current Scientific American says that most regular
satelites in th solar system have orbits that are nearly equatorial and nearly circular. "Equatorial" I can understand "circular" puzzles me. Please tell me what is wrong with my reasoning. First, an acceleration at perigee (in the direction of motion) will not affect the distance at perigee but will increase the distance at apogee. An acceleration at apogee, on the other hand, will increase the distance at perigee. Second, every satelite causes a tidal bulge on its primary, more noticable on water, but still existant on land. The tidal bulge is greatest on the spot which the satelite was directly above SHORTLY BEFORE. (Also, there is another bulge on the opposite side of the planet.) This bulge provides an acceleration eastward to the satelite since the satelite (if it's not named "Phobos") has a sidereal period greater than its primary's rotational period. The net accelleration is the difference be tween the acceleration provided by the bulge directly underneath and that provide by the bulge on the opposite side of the planet. The size of the bulge is inversely proportional to the cube of the distance from the satelite to teh planet, and the net acceleration is proportional to the SIXTH power of the distance. So, if the distnace at apogee is 1% greater than the distance a perigee, the acceleration at perigee must be 6% greater. The increase of distance at apogee must be (more than) 6 times teh increase at perigee.This leads to the conclusion that any eccentricty should increase over time. But it hasn't. Why not? What is wrong with this chain of reaqsoning? Any help greatly appreciated. |
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