Timeline for Is there a maximum distance from a planet that a moon can orbit?
Current License: CC BY-SA 4.0
11 events
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| Mar 20 at 17:00 | history | edited | Michael Seifert | CC BY-SA 4.0 |
Added direct comparison to Moon's orbital radius
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| S Jun 21, 2019 at 11:01 | history | suggested | Euro Micelli | CC BY-SA 4.0 |
Clarification on the last sentence. It would give the wrong impression if quoted out of context
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| Jun 21, 2019 at 4:28 | review | Suggested edits | |||
| S Jun 21, 2019 at 11:01 | |||||
| Jun 20, 2019 at 13:47 | comment | added | Michael Seifert | @DavidHammen: True, but the radius of the Hill "sphere" is also only approximately given by $a\sqrt[3]{\frac m {3M}}$; in fact, the exact expressions for the bounds of the Hill "sphere" are the roots of the same fifth-order polynomial that gives the distances to L1 and L2; see the derivation in the Wiki article. And yes, it's not actually a sphere in the geometric sense (hence the scare quotes on "sphere" in my second sentence), though I suppose you could argue that it's a "sphere" in the sense of a "sphere of influence." | |
| Jun 20, 2019 at 13:04 | comment | added | David Hammen | Michael, note that @uhoh stated "It's not the same thing but it's somewhat related." The distances between the Sun-Earth L1 and L2 points and the Earth are the real solutions to two slightly different fifth order polynomials, neither of which has a closed form expression. The expression $a\sqrt[3]{\frac m {3M}}$ is a close approximation of these distances. Two additional comments: (1) The so-called Hill sphere isn't really a sphere, and (2) An orbit with a radius that is more than half the Hill sphere radius is most likely unstable. | |
| Jun 20, 2019 at 12:36 | history | edited | Michael Seifert | CC BY-SA 4.0 |
added 543 characters in body
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| Jun 20, 2019 at 11:52 | history | edited | Michael Seifert | CC BY-SA 4.0 |
deleted 1 character in body
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| Jun 20, 2019 at 9:17 | comment | added | uhoh |
Nice answer! +1 I think that I would say "For the Sun-Earth system..." rather than the "Earth-Moon system"; the Earth's Hill sphere is defined and exists whether or not The Moon exists, it's an artifact of the Sun-Earth system. You might also mention that the Earth-Moon Lagrange points L1 and L2 are also at about 1.5 million kilometers. It's not the same thing but it's somewhat related.
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| Jun 20, 2019 at 8:27 | comment | added | Oscar Bravo | I love answers where you learn something new! I'd never heard of the Hill Sphere before... Also, it seems to be a common theme in orbital dynamics to forget that everything is moving. The slingshot maneuver makes no sense at all until you realise this. | |
| Jun 19, 2019 at 21:06 | vote | accept | leeman | ||
| Jun 19, 2019 at 20:56 | history | answered | Michael Seifert | CC BY-SA 4.0 |