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Moon orbit - max distance (Read 1123 times)
wil
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Moon orbit - max distance
10/18/18 at 13:32:04
 
The Hill sphere for the Earth is about 1.5 mln km.
 
But when I try to set only two times bigger distance to the Moon: 2x400 = 800 only, then the Moon escapes from the Earth immediately.
 
This is something wrong in the GS, or the Hill sphere is a nonsense?
 
This is about 1/3 of the Hill's distance possible for stable lunar orbit, thus about: 500 = 0.5 mln km only, maybe 550 !
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Tony
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Re: Moon orbit - max distance
Reply #1 - 10/18/18 at 15:29:55
 
Hill Sphere is sometimes mistakenly interpreted as the volume with which an object can orbit. It is not.
In prograde orbits, objects can orbit out to about 1/3 of a Hill Sphere. In retrograde orbits, they can exceed 1/2 Hill Sphere. Anything past this and the Sun will strip them away.
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wil
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Re: Moon orbit - max distance
Reply #2 - 10/18/18 at 16:14:01
 
Ok.
Thus what is the real maximum distance in the case of the Moon, or in general: in any three-body scenario?
 
Hill by 2, 3, maybe e?
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frankuitaalst
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Re: Moon orbit - max distance
Reply #3 - 10/28/18 at 05:32:37
 
I've made a little sim :  
in the sun -earth system : created 100 massless bodies , between 500.000 and 750.000 km , thus between 1/3 and 1/2 Hill . I gave them 0 eccentricity .
See Sim in annex.  
 
It is worthwile to see :  
* eccentricity of all the bodies rises ,  
* some bodies (about 10% ) escape the system . It is interesting to notice the escape goes over the L1 OR the L2 point  ( the line L2 L1 is directed towards the sun . So 1/2 Hill is partially stable .  
* and further :  when we zoom out in the sim one can observe the escaped bodies will occupy the L4 and L5 clouds .
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frankuitaalst
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Re: Moon orbit - max distance
Reply #4 - 10/28/18 at 11:21:35
 
The sim above gives us additional info about the stability of the Earth - Moon system in what concerns the Hill sphere .  
I gathered the output of the above sim ( Sma and eccentricity of all of the 100 minor bodies ) in a data file and represented the data  in a chart .  
The chart represents :  
 
X-axis : the Sma of each body ( 0 to 0.01 AU = 0 to 1.500.000 km )  
Y-axis : the eccentricity of each body ( 0 to 1 ) .  
 
The sim was ran untill no more  bodies escaped . This period covers 196 frames in the animation.  
 
One can (briefly ) see the sim starts with all bodies lined up at Ecc=0 and Sma = 1/300 AU and 1/200 AU ) = (1/3 and 1/2 Hill) .  
 
The eccentricies soon rise , also some Sma get bigger .  
After some time some bodies escape at Ecc around 0.8-0.6) while puping up their Sma , and escape to the right of the chart , escaping Earth's gravity field.  
This happens several times .  
 
After some time the system seems to "stabilize" , resulting in  dynamical behaviour , but without escaping bodies .  
At the end it seems bodies even at 1/2 Hill ( = 0.005 Sma) , but at appropriate eccentricities , do not have the "intention " to escape .  
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MoonStabilty_HillSim_.gif
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