# Is it possible for a charged, fast-moving object to slow down and enter geo-stationary orbit?

I've had a wild idea which I can not discuss at length in this forum, but it comes down to the following problem:

A sphere of radius R=~10μm and mass m=~10-16Kgr is travelling towards the earth at v = ~10^8m/sec. The sphere carries a charge Q and intersects the earth's magnetic field perpendicularly, at a distance r, such that it enters an elliptic orbit. Given an electron wave function of ~5eV, is there any possible configuration of Q and r that would allow the sphere to end up in a stable geo-stationary orbit?

Would releasing charges at particular points of each rotation make any difference?

Even though I did get a physics BS 13 years ago, I took a different direction and the calculations required are way beyond my current capabilities. If anyone finds the problem interesting, I'll be glad to hear from you.

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## migrated from scicomp.stackexchange.comApr 29 '13 at 23:39

This question came from our site for scientists using computers to solve scientific problems.

@ChristopherAkritidis: Welcome to SciComp! This question is cool, but has no direct computational science component. It's definitely more suitable for physics. Everyone else: if you think the question is more suitable for physics, flag the question or vote to close; up-voting a comment is nice, but flagging notifies mods, and five non-mod close votes will close a question. – Geoff Oxberry Apr 29 '13 at 23:39
Why these particular numbers? Why is this idea one that you "can not discuss at length in this forum?" – Ben Crowell Apr 29 '13 at 23:42
What you need is a good ratio of capacitance to mass. You need to avoid discharge at the same time, limiting the mass you have to move. Practically, this would be a large spherical wire mesh surrounding a micro satellite, large and light to the extent of what could withstand the acceleration. Even then, the movement due to the magnetic field is nothing like you've imagined because the field lines are not oriented in a helpful way and they are probably useless anywhere near GEO. – Alan Rominger Apr 30 '13 at 0:05

Your sphere is traveling at $10^8 \, \mathrm{m/s}$ (33% the speed of light) but Earth's escape velocity is $11200 \, \mathrm{m/s}$. There is absolutely no way the sphere could ever enter any sort of orbit around the Earth, regardless of the interaction between it and the Earth's magnetic field.
$$KE_{relativistic} = \left( \left( \frac{1}{\sqrt {1 - \frac{v^2}{c^2}}} \right) - 1 \right)mc^2 = 8.7 \cdot 10^{16} \, \mathrm{J}$$
@Brandon What did you use for m in the energy calculation? $$KErelativistic = ((\frac{1 }{\sqrt{1 - v^2/c^2}})-1)mc^2 = ((\frac{1 }{\sqrt{1 - 0.09}})-1)*10^{-16}*9*10^{16}J = 0,43J$$ – Christopher Akritidis Apr 30 '13 at 16:41