How many times should all the people in the Northern-Hemisphere should jump simultaneously into the air to alter the Earth's orbit by 1 m?
It depends on how high they jump!
Seriously, no amount of jumping will alter the Earth's orbit. If everyone in the Northern hemisphere jumps up at the same time, they exert a downwards force on the Earth for a small amount of time (an impulse). This 'pushes' the Earth down, a very very little bit. However, as soon as they leave the Earth, they are exerting a force on the Earth that is not balanced by the ground pushing up, and, as long as they come down again, the impulse will be equal in size, but opposite in direction to the one they use to push off. Hence the Earth will not move.
If they jump up and down quickly enough, they could heat up the Northern hemisphere to a higher temperature than the South, which would produce a tiny radiation pressure that would give the Earth a minute 'downwards' impulse.
Michael Inkson, Physics Undergrad, Cambridge University, UK
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