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View Full Version : Geocentric orbit and a banana peel



Dead_Moroz
2010-Jan-20, 09:55 PM
Just curious: I'm on a (high) Earth orbit eating a banana. Having finished it, I decide to get rid of the peel and throw it in the direction of the Earth. My question is: will the peel ever reach the Earth's atmosphere to burn in it, or it'll only have a more eccentric orbit than I have now and will be orbiting the Earth forever before the Sun turns into a red giant and will burn both the peel and the Earth?

grant hutchison
2010-Jan-20, 10:02 PM
The latter: the velocity generated by your throw will be small relative to your orbital velocity, so it will modify the shape of the orbit a little. If you start off in circular orbit, the peel will end up with a lower perigee and higher apogee. (This particular orbital problem was a plot element in Arthur C Clarke's short story, Jupiter V; except it involved throwing an astronaut off Amalthea towards Jupiter.)
The only way to get the banana peel all the way to the Earth would be to throw it backwards, completely cancelling your orbital velocity, so that it would then fall radially towards Earth.
Or, I suppose, you could fire it straight towards the Earth with some hypervelocity that would render your cross-wise orbital velocity trivial.

Grant Hutchison

Dead_Moroz
2010-Jan-20, 10:12 PM
Thanks, that's the kind of answer I wanted to get :) So, I'd better take the banana peel with myself in order not to multiply garbage around the Earth.

antoniseb
2010-Jan-20, 10:24 PM
The latter: the velocity generated by your throw will be small relative to your orbital velocity, so it will modify the shape of the orbit a little. ...
Extending the idea a little, You might think that the dead hulk of Pioneer 10 is free of the Sun, and therefore free to explore the whole universe (slowly), but in fact it is in a very slightly different orbit around the galaxy than is the Sun, and will likely come back in our general direction in 200 million years.

Van Rijn
2010-Jan-21, 12:38 AM
or it'll only have a more eccentric orbit than I have now and will be orbiting the Earth forever before the Sun turns into a red giant and will burn both the peel and the Earth?

Just a couple comments on short term versus long term:

In the short term it will only be in a slightly more eccentric orbit. In the long term, though, a banana peel isn't exactly the toughest thing around, so isn't going to last that long. If it were a bit more substantial, though, and depending on its original orbit, it might eventually be perturbed away from the Earth into a heliocentric orbit or it might eventually even come back to Earth.

korjik
2010-Jan-21, 01:47 AM
Depends on your definition of a high orbit. Under 1000km and it will prolly reenter due to air drag. The numbers would have to be run to find out how long it would be up there

Dead_Moroz
2010-Jan-21, 02:58 PM
I stressed the 'high' orbit, as I wanted to remove the resistance of atmosphere as a factor, which will ultimately slow the peel's velocity, so that the latter would drop. A peel is a metaphor, of course, I was just curious how an object would behave in such a case.
In the example with the Pioneer, the 'Earth' from the banana peel situation is the Galactic core (the center of gravity)?