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If you are standing on earth's surface, in what direction (and at what speed) should you throw a 1Kg uniform sphere of radius 0.1 meters in order to put it into lower earth orbit? Assume that there is air, but it is not moving relative to the earth

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  • $\begingroup$ Go to: sciencemadness.org/talk/… and download the orbit.pdf for a better understanding of the mechanics of the influence of Newtonian throws on orbits. $\endgroup$ – Gert Mar 2 '16 at 0:09
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    $\begingroup$ Actually, the idea of putting a (very large) spin on the sphere (and maybe some ridges for stitching patterns) and putting it into a very low earth orbit is not out of the question. I don't see the word "stable" anywhere in the question. It's possible this has been calculated somewhere - it's worth a check. This question deserves something more quantitative than a "it can't work because it won't work" response. $\endgroup$ – uhoh Mar 2 '16 at 1:09
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If we ignore air resistance for a moment, then all orbits in an inverse square force like gravity are closed. this means that if you throw something hard enough it will complete one orbit then return to its starting point i.e. your hand.

So if you throw the object downwards it obviously hits the Earth, and if you throw it straight upwards it goes up then down and hits the Earth. For all the angles in between the object will go into orbit, though it will be an exceedingly low orbit since once an orbit it will pass through the point where you released it.

If you want to put the object into a roughly circular orbit you can't do this just by throwing it. Satellites are launched using a rocket trajectory like this:

Satellite launch

(image from the NASA site)

And this requires a continuous boost from the rocket. You can't replicate this with a throw.

Adding air now means that if you throw the object hard enough to get it out of the atmosphere it will simply burn up, just as satllites burn up when the reenter the atmosphere.

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  • $\begingroup$ If you throw the object fast enough it will leave the RSOI of the Earth. $\endgroup$ – ThePlanMan Mar 2 '16 at 9:18
  • $\begingroup$ @ThePlanMan: well yes, if you throw it at greater than escape velocity then (ignoring air resistance) its orbit will be hyperbolic. $\endgroup$ – John Rennie Mar 2 '16 at 9:31
  • $\begingroup$ Challenge: calculate the velocity required (including atmospheric drag) for parabolic orbit. I've just nerd snipped myself xkcd.com/356 $\endgroup$ – ThePlanMan Mar 2 '16 at 10:17