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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. |
#2
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Satelite eccentricity
"Frank" wrote in message oups.com... 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. reasoning snipped 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 the acceleration is (to the first order) normal to the velocity, But it hasn't. Why not? What is wrong with this chain of reaqsoning? The tendency to 'circularise' the orbit is greater at some times than others - hence the orbit is tended to circular more for half the time and less for half the time. Any help greatly appreciated. |
#3
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Satelite eccentricity
On 18 Jul 2006 09:23:04 -0700, "Frank" wrote:
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. One reason for a circular orbit is that it is a minimum energy orbit. Interactions with other bodies over the long run will tend to cause the system to settle down in the minimum energy configuration. |
#4
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Satelite eccentricity
"Frank" wrote in message oups.com... 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. Isn't it the case that if the rotational period is less than the orbital, the bulge will be carried forward of the satellite as you say next? (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. Hence the nearer one dominates. If the bulge is ahead that would accelerate the satellite, as Earth does to the Moon, hence by your argument tending to reduce the eccentricity. 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. I think the general argument seems right but if the rotation is faster, the bulge leads rather than trails. I'm not a professional though so treat this as a hint, not an answer. George |
#5
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Satelite eccentricity
Frank wrote: 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. It's because the only sattelites that produce tidal effects are those that are close enough to the primary, to produce non-negliable atmospheric effects in the primary also. So the accumulated friction breaking over bllions of year produces nearly circular oribits, Second, every satelite causes a tidal bulge on its primary, more No they don't. Since the GPS constellation are sattelites of Earth and produce no tidal effect on Earth. |
#6
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Satelite eccentricity
Frank wrote: wrote: Frank wrote: It's because the only sattelites that produce tidal effects are those that are close enough to the primary, to produce non-negliable atmospheric effects in the primary also. So the accumulated friction breaking over bllions of year produces nearly circular oribits, But all satelites produce a tidal effect. Just as I produce a gravitational attraction on you. Whether something produces a gravitional attraction and a negligable gravitional attraction are two different issues, which is why I put in the statement ' about billions of years and friction forces, It might not be a LARGE tidal effect. (The tidal bulge is proportional -- among other things -- to the mass of the satelite. So the acceleration on the satelite is proportional to its mass. ) Not when you have a CONSTELLATION of sattelites, since GPS is not A sattelite. Second, every satelite causes a tidal bulge on its primary, more No they don't. Since the GPS constellation are sattelites of Earth and produce no tidal effect on Earth. |
#7
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Satelite eccentricity
In article ,
"George Dishman" writes: Isn't it the case that if the rotational period is less than the orbital, the [tidal] bulge will be carried forward of the satellite as you say next? .... Hence the nearer one dominates. If the bulge is ahead that would accelerate the satellite, as Earth does to the Moon, hence by your argument tending to reduce the eccentricity. This looks correct to me, though I'm no expert. As far as I can tell, the force on the satellite is proportional to its mass; hence _acceleration_ of the satellite is independent of satellite mass, though it depends strongly on distance from the primary. -- Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA (Please email your reply if you want to be sure I see it; include a valid Reply-To address to receive an acknowledgement. Commercial email may be sent to your ISP.) |
#8
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Satelite eccentricity
In article , I agreed with George
Dishman, who wrote (in article ): If the [nearer tidal] bulge is ahead that would accelerate the satellite, as Earth does to the Moon, hence by your argument tending to reduce the eccentricity. On thinking about this some more, I'm confused. Yes, the nearer tidal bulge accelerates the satellite, but the acceleration is greatest at perigee. Acceleration at perigee tends to raise the _apogee_ and thus increase the eccentricity. There's probably something wrong with the way I'm thinking about this problem, but I don't see what it is. -- Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA (Please email your reply if you want to be sure I see it; include a valid Reply-To address to receive an acknowledgement. Commercial email may be sent to your ISP.) |
#9
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Satelite eccentricity
"Steve Willner" wrote in message ... In article , I agreed with George Dishman, who wrote (in article ): If the [nearer tidal] bulge is ahead that would accelerate the satellite, as Earth does to the Moon, hence by your argument tending to reduce the eccentricity. On thinking about this some more, I'm confused. Yes, the nearer tidal bulge accelerates the satellite, but the acceleration is greatest at perigee. Acceleration at perigee tends to raise the _apogee_ and thus increase the eccentricity. There's probably something wrong with the way I'm thinking about this problem, but I don't see what it is. I see the problem, thanks for correcting that Steve. I was wondering if we could measure the rate of change of the Moon's eccentricity by LLR and found this: http://dda.harvard.edu/brouwer_award...6_Williams.pdf which discusses eccentricity rate on page 25. The value of 1.3*10^-11 per year appears to indicate the eccentricity increases due to Earth tides though at a very low rate. George |
#10
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Satelite eccentricity
I can't believe we are confused by something as critical to understanding how planetary systems form as this is. I'm at least as confused as you are. One little suggestion, but I suspect that it's too little to make a difference except when a moon is massive and in a highly-elliptical orbit: At apoapsis, the moon is moving more slowly than the surface of the planet, so the bulge leads. At periapsis, the moon could be moving faster than the surface of the planet, and the bulge would trail. -- Jeff, in Minneapolis |
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