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Satelite eccentricity



 
 
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  #1  
Old July 18th 06, 05:23 PM posted to sci.astro
Frank[_1_]
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Posts: 6
Default 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  
Old July 20th 06, 12:51 AM posted to sci.astro
OG
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Posts: 780
Default 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  
Old July 20th 06, 06:13 AM posted to sci.astro
William Hamblen
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Posts: 343
Default 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  
Old July 20th 06, 06:27 PM posted to sci.astro
George Dishman[_1_]
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Posts: 2,509
Default 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  
Old July 20th 06, 07:17 PM posted to sci.astro
[email protected]
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Posts: 240
Default 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.

  #7  
Old July 24th 06, 09:35 PM posted to sci.astro
Steve Willner
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Posts: 1,172
Default 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  
Old July 26th 06, 09:50 PM posted to sci.astro
Steve Willner
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Posts: 1,172
Default 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  
Old July 29th 06, 11:03 AM posted to sci.astro
George Dishman[_1_]
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Posts: 2,509
Default 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  
Old July 29th 06, 05:24 PM posted to sci.astro
Jeff Root
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Posts: 242
Default 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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