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SITUATION: Suppose I am a mad scientist and I have made a machine which has enough mass to push the earth. Now I am controlling the machine with a remote control with which I can change its speed, direction, acceleration, etc. I am on the earth and the machine is in outer space. Now I increase the speed of the machine to such extent that it collides with the earth and pushes it significantly to displace its center of mass.

Now the QUESTION is: The earth and I comprise the system. The machine is controlled by the remote. So since I am interacting with the machine in this way, the machine also belongs to the system where I belong. Hence an internal force is displacing the center of mass of the system.

Isn't this like I am sitting on my chair and I am pushing it forward? Please clarify my mistake.

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  • $\begingroup$ How do you propose to "increase the speed of the machine" or change it's "speed, direction, acceleration"? If you use booster rockets, then it is not a part of your Earth-you system. If you really mechanically push it from Earth, you'll change Earth's velocity accordingly such that the center of mass of Earth-you-machine system is unmoved. $\endgroup$
    – Aritra Das
    Commented Oct 30, 2015 at 18:50
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    $\begingroup$ You should take @AritraDas 's comment more seriously. Clicking a switch or moving a slider cannot, by itself, change the path of a big machine. Clicking the switch can fire a booster rocket, though. $\endgroup$
    – WillO
    Commented Oct 30, 2015 at 19:00
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    $\begingroup$ I think you have pointed out your own mistake: the italicised portion of your question. $\endgroup$
    – Yorik
    Commented Oct 30, 2015 at 19:01
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    $\begingroup$ @Aniket if you're asking what would happen if you could move Earth with magic, this isn't a physics question. If you're asking about moving Earth with rockets on a mecha then it's a physics question. Rockets aren't "imaginary hands" though, so you'll have to choose one or the other. $\endgroup$
    – Asher
    Commented Oct 30, 2015 at 19:56
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    $\begingroup$ By Newton's third law, the machine pushing the earth experiences a equal and opposite force. So the center of mass of the system earth+machine does not move since the net force on it is zero. I'm not sure where your confusion lies. $\endgroup$
    – ACuriousMind ♦
    Commented Nov 2, 2015 at 14:08

3 Answers 3

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By pushing a remote, you are not giving energy to the machine. You are just giving a signal that allows another energy source to start working.

This other energy source - the "imaginary hand" as you say - is a battery on board, fuel on board or similar. The Earth is not a part of this system and does not cause the motion to start. Therefor the impact will change the motion of the Earth. (Requiring a BIG-massed machine to do any significant change, of course)

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  • $\begingroup$ I see. If a field is pulling in the machine, and this field is created by the earth or by something on the earth, then newton's third law says that there is no net force on it at a collision, since the push from the collision equals the pull done in the opposite direction. In your case with a remote it is not a field that pulls in the machine - the remote only triggers another source to start exerting a force on the machine alone $\endgroup$
    – Steeven
    Commented Oct 31, 2015 at 10:35
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as you do not have any support at your Back or any frictional ground , earth will move forward and your big machine will move backwards by conservation of momentum.this also result in loss of energy. even if you use rocket considerable amount of fuel will move backwards again resulting in conservation of momentum. an internal force in both directions cancel to 0.

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You are not exerting any force on the machine, you are only controlling it. So when you are only controlling it, implies that the energy supplied to the machine must be an external agent, you can still, if you were to control it by physically applying a force, you would get an equal and opposite reaction, so there would have been no change in the earth's motion. But since you assume that the you could control earths motion, either the machine or the energy supplied to the machine must be an external agent.

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