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If you could fly and survive in space, how much force would you need to move Earth at 1 meter per second?

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    $\begingroup$ Speed is not proportional to force. Acceleration is proportional to force. What have your tried to solve this problem? $\endgroup$ – DanielSank Jul 4 '15 at 22:31
  • $\begingroup$ Your question makes sense if you replace "force" with "impulse". And that impulse is simply the mass of the Earth times $1 {\rm m\,s^{-1}}$. According to the estimates of this paper, the impulse is rather more than that imparted to Earth by the Chicxulub Impactor, which wiped the non avian dinosaurs out. $\endgroup$ – WetSavannaAnimal Jul 5 '15 at 1:38
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Whatever force you like. Since force just determines the rate change of velocity, you can use a massive force for a trillionth of a second or a tiny force for a long time period.

However, if changed the velocity of the Earth (relative to the Sun) of 1 m/s, you'll would cause an impulse – change in momentum – on the Earth of $5.972×10^{24}$ kilogram-meters and waste $1.779×10^{29}$ joules of energy. This, regardless of the force.

To really understand how much energy that is, imagine half of Earth's mass being just TNT blowing up. Yeah, that's how much $4.252×10^{19}$ tons of TNT is.

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Your question makes sense if you replace "force" by "impulse". And that impulse is simply the mass of the Earth times $1 {\rm m\,s^{-1}}$. Moreover, you need to make the qualification: how much impulse is needed to change the Earth's motion state so that it is moving at $1 {\rm m\,s^{-1}}$ relative to its motion state now.

According to the estimates of this paper, the impulse is rather more than that imparted to Earth by the Chicxulub Impactor, which wiped the non avian dinosaurs out.

Your question also makes sense if you replace "force" by "kinetic energy". You might like to work this out too, and compare it with the kinetic energy of the Chicxulub Impactor.

If I were a Tyrannosaurus Rex, I should be very afraid of you.

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Force is just a product of mass and acceleration and to calculate the force required to move the earth is quite easy. Though incredibly difficult to produce. IF we take the mass of earth as 5.9736 x 10^24 kg. And the acceleration 1 meter per second per second. And that is where you are wrong when you said 1 meter per second which is the unit for speed or velocity. Anyways, the force required will be given my a simple product of mass and acceleration, i.e F=m.a. That gives 5.9736 x 10^24 N.

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