User:Mark Widmer/sandbox: Difference between revisions
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The Hill radius is ''not'' simply the distance at which the gravitational forces exerted on the satellite by the star and by the planet are equal, but is in fact generally larger than this distance by an additional factor of <math> \left( \frac{M}{9m} \right) ^{1/6} </math>. This works out to roughly a factor of 6 in the case of Earth and the Sun. | The Hill radius is ''not'' simply the distance at which the gravitational forces exerted on the satellite by the star and by the planet are equal, but is in fact generally larger than this distance by an additional factor of <math> \left( \frac{M}{9m} \right) ^{1/6} </math>. This works out to roughly a factor of 6 in the case of Earth and the Sun. | ||
So long as the planet's mass is less than 1/9 of that of the star. If ''m'' > ''M''/9, then the Hill radius will be smaller than the equal-force distance from the planet, but this is rarely the case. Even in the case of Jupiter, ''m'' is about ''M''/1000, well below ''M''/9. | So long as the planet's mass is less than 1/9 of that of the star. If ''m'' > ''M''/9, then the Hill radius will be smaller than the equal-force distance from the planet, but this is rarely the case. Even in the case of Jupiter, ''m'' is about ''M''/1000, well below ''M''/9. | ||
Revision as of 19:05, 3 August 2021
Possible text to add to Hill_sphere page: NEED TO DOUBLE-CHECK this, as it seems counter-intuitive and may be wrong.
https://en.citizendium.org/wiki/Hill_sphere
The Hill radius is not simply the distance at which the gravitational forces exerted on the satellite by the star and by the planet are equal, but is in fact generally larger than this distance by an additional factor of . This works out to roughly a factor of 6 in the case of Earth and the Sun.
So long as the planet's mass is less than 1/9 of that of the star. If m > M/9, then the Hill radius will be smaller than the equal-force distance from the planet, but this is rarely the case. Even in the case of Jupiter, m is about M/1000, well below M/9.