Originally posted by sonhouseI think the Wikipedia page has a mistake.
http://en.wikipedia.org/wiki/Hill_sphere
in a phyorg forum about gravity. Interesting stuff.
In the example to the right, the Hill sphere extends between the Lagrangian points L1 and L2, which lie along the line of centers of the two bodies. The region of influence of the second body is shortest in that direction, and so it acts as the limiting factor for the size of the Hill sphere. Beyond that distance, a third object in orbit around the second (e.g. Jupiter) would spend at least part of its orbit outside the Hill sphere, and would be progressively perturbed by the tidal forces of the central body (e.g. the Sun), eventually ending up orbiting the latter.
I think that an object that went outside the Lagrangian points would switch orbits immediately, not after being 'progressively perturbed by the tidal forces'.
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Originally posted by twhiteheadGoing just outside the lagrangians wouldn't cause it to just jump into a new orbit, it would happen more stately than that, I imagine a long set of orbital moves before it assumed its new position.
I think the Wikipedia page has a mistake.
[quote]In the example to the right, the Hill sphere extends between the Lagrangian points L1 and L2, which lie along the line of centers of the two bodies. The region of influence of the second body is shortest in that direction, and so it acts as the limiting factor for the size of the Hill sphere. Beyond that d ...[text shortened]... would switch orbits immediately, not after being 'progressively perturbed by the tidal forces'.
One thing I saw on the list, the Earth's hill sphere extends out 1.5 million km which means the moon, which has an ever expanding orbit going outwards at about 2 cm per year, will be the Earth's moon for at least 30 billion years, far after the sun has bloated out to fry the Earth and moon in its outer corona.
Originally posted by sonhouseA stationary object nearly at the lagrangian between earth and sun but a tiny bit closer to the sun, would move towards the sun. An object orbiting the earth that passes just beyond the lagrangian, would be moving away from the earth just before that point. The force on it would be away from the earth. There is no way it would be pulled back towards the earth for another orbit.
Going just outside the lagrangians wouldn't cause it to just jump into a new orbit, it would happen more stately than that, I imagine a long set of orbital moves before it assumed its new position.
So yes, it would definitely jump to a new orbit around the sun.
Originally posted by twhiteheadI wouldn't use the term "Jump", I would use a term more like 'Drift'. Jump implies a big acceleration and there would certainly not be that.
A stationary object nearly at the lagrangian between earth and sun but a tiny bit closer to the sun, would move towards the sun. An object orbiting the earth that passes just beyond the lagrangian, would be moving away from the earth just before that point. The force on it would be away from the earth. There is no way it would be pulled back towards the earth for another orbit.
So yes, it would definitely jump to a new orbit around the sun.
Originally posted by sonhouseIt would be going around earth for half and orbit, go past the lagrangian and switch to an orbit around the sun. The switch would take place at some exact point in space where earths hill sphere and suns hill sphere meet. There would be very little acceleration but the change of orbit would be instantaneous. At one moment it would be curving around the earth and technically in earth orbit, then next moment it would be curving towards the sun and technically in orbit around the sun.
I wouldn't use the term "Jump", I would use a term more like 'Drift'. Jump implies a big acceleration and there would certainly not be that.
If you think of the hill spheres as being cones with a marble rolling around the inside of earths cone (which is a smaller cone than the sun's) then imagine the marble going fast enough that it gets over the lip between the two cones.