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There would be no orbit. You have to have a body to orbit around and without a star or other planet to orbit around, it would just move in a straight line.
No, a moon is a natuaral satellite and would always be in orbit around a planet. If it did'nt orbit the planet it would fall into the planet.
Well lets say the person got a good push on a platform, then it would take around 90-110 mins.
They orbit as stars would in any other halo. It is gravity that causes everything to orbit and "spin around" Stars can also orbit around other stars called a binary orbit.
The orbit would increase in size (the planet would orbit farther from the sun).
The moon has no known satellites. Anything in orbit around it would be in a fairly unstable orbit, and would not remain there.
Your question isn't very clear. The moon revolves around the earth so it essentially has the same orbit around the sun.
That would the "orbit".
A lunar eclipse
Jupiter has 63 confirmed moons in orbit around it. No planets are in orbit around it, since they would then be classed as moons. The planets in orbit either side of Jupiter are Mars and Saturn.
It would orbit around one of the other planets, orbit around the sun, or become part of the Asteroid or Kiper Belt.
Depending on the direction in which your speed was pointed, and at what stage of the launch it was faster, any of these could happen: -- you would get to orbit sooner -- you would settle into a smaller, more circular orbit -- you would settle into a larger, more eccentric orbit -- you would not orbit at all, but escape the Earth completely and never return