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Message started by wil on 10/18/18 at 13:32:04

Title: Moon orbit - max distance
Post by wil on 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 !

Title: Re: Moon orbit - max distance
Post by Tony on 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.

Title: Re: Moon orbit - max distance
Post by wil on 10/18/18 at 16:14:01

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?

Title: Re: Moon orbit - max distance
Post by frankuitaalst on 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 .

Title: Re: Moon orbit - max distance
Post by frankuitaalst on 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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