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Moons orbit around the sun (Read 6246 times)
frankuitaalst
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Moons orbit around the sun
04/25/09 at 04:45:13
 
Kevin draws my attention on the following :  
"According to some people the moon orbits the Sun and not the Earth:  
http://www.math.nus.edu.sg/aslaksen/teaching/convex.html "
I think this has been discussed earlier here , but I can't find it right now.  
In a fixed xy frame to the sun in the center the orbit of the moon looks like this :  
On this scale the moons orbit can be described as a polygon with no backwards movement.  
( a wave like motion superimposed on the Earths path) .  
As the orbital period of the moon isn't in an integer ration of the Earths orbital period the polygon is not closed , resulting in the Saros cycle .  
The animation covers 50 years .
I can imagine that some moons of the gas giants indeed show a retrograde motion with curls .    
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MoonOrbit50y.gif
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Tony
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Re: Moons orbit around the sun
Reply #1 - 04/25/09 at 14:24:38
 
It's discussed here:
http://www.bautforum.com/space-astronomy-questions-answers/25604-shape-moon-orbi t-around-sun.html
I posted some Gravity Simulator images in the 10th post.
 
But I don't see why this would disqualify the moon as orbiting Earth.  It actually orbits both.  If the Earth instantly vanished, the moon would continue around the sun in a very similar orbit.  If the sun suddently vanished, the moon would continue to orbit the Earth almost as if nothing happened.
 
This can not be said of some of Jupiter's inner moons.  For example, for part of its orbit around Jupiter, Europa exceeds solar escape velocity, so if Jupiter suddenly vanished, Europa would continue on its hyperbolic solar orbit to infinity.  One way of looking at it is that during each orbit, Jupiter captures Europa from an interstellar trajectory, then ejects it back onto an interstellar trajectory.
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kheider
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Re: Moons orbit around the sun
Reply #2 - 04/26/09 at 10:27:29
 
Quote from Tony on 04/25/09 at 14:24:38:
This can not be said of some of Jupiter's inner moons.  For example, for part of its orbit around Jupiter, Europa exceeds solar escape velocity, so if Jupiter suddenly vanished, Europa would continue on its hyperbolic solar orbit to infinity.  One way of looking at it is that during each orbit, Jupiter captures Europa from an interstellar trajectory, then ejects it back onto an interstellar trajectory.

Thanks for the 411 guys.  Do you know the peak orbital velocities for Io and Europa?  I believe the escape velocity from the Sun@Jupiter is 18.5 km/s.  I believe the average orbital velocity for Io is 17.334 km/s and Europa is 13.740 km/s.
-- Kevin
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frankuitaalst
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Re: Moons orbit around the sun
Reply #3 - 04/26/09 at 12:12:16
 
The orbital velocity of Jupiter which is about 13 km/s should also be taken into account.  
So Europa has a range of net orbital velocity relative to the sun of 0 to 26 km/s.  
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Tony
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Re: Moons orbit around the sun
Reply #4 - 04/26/09 at 12:28:04
 
This shows what happens to Europa at different parts of its orbit when Jupiter's mass is set to 0.
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frankuitaalst
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Re: Moons orbit around the sun
Reply #5 - 04/26/09 at 12:39:44
 
Nice plot !  
I wondered how you did this , but at second glance I think you calculated the net velocity at different places of the orbit and checked for escape velocity . Is this correct ?
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Tony
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Re: Moons orbit around the sun
Reply #6 - 04/26/09 at 13:19:11
 
Quote from frankuitaalst on 04/26/09 at 12:39:44:
Nice plot !
I wondered how you did this , but at second glance I think you calculated the net velocity at different places of the orbit and checked for escape velocity . Is this correct ?

I made a simulation with 360 massless particles evenly distributed along Europa's orbit, 1 per degree.  I then ran the simulation and recorded which ones struck the sun, and which ones escaped.  The particles are numbered in order when you use the linear distribution feature.  Then I restarted the simulation, took a screenshot before the simulation evolved, opened the screenshot in PhotoStudio, and colored the particles I identified.
 
But an analytic method like you describe would work too.
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