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Imagine that I have a powerful and big thruster enought to move a planet, for example the Earth.
Earth's mass is 5.97237×10^24 kg, gravity is 9.807 m/s and escape velocity 11.186 km/s
My thruster has 100x10^24 Newtons equal to 16,74 times the mass of the Earth

My question is how to calculate the acceleration of Earth while it's pushed by a thruster:
I don't know how to calculate that but I have some ideas:

  • Earth's mass / Thruster's power = 16,74 m/s/s.
  • (Earth's mass / Thruster's power) - Earth's gravity = 6,933 m/s/s. I am not sure of that because I am moving the centre of mass also, so I am moving the gravity centre also.
  • Or some other calculation.

EDIT: I edit my question because I haven't enought repto make comments.
@sammy gerbil, so basically it's Earth's mass / Thruster's power, that is the raw force and then I have to subtract the force of the Earth's Mass * Gravity of the sun and moon?

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$F=ma$ where $F$ is the resultant force on the Earth and $m$ is the mass of the Earth. In addition to the force from the thruster, $F$ includes the gravitational force from the Sun, Moon and other planets.

$a$ the total acceleration of the Earth. Since the Earth is moving in a circle around the Sun, it is already accelerating towards the Sun.

Escape velocity has nothing to do with this problem. Neither does Earth's gravity. The Earth is not escaping from itself.


No, $a=F/m$ not $a=m/F$.

The gravity force from the Sun, Moon etc is proportional to the product of masses divided by the square of the distance between them. See Newton's Law of Universal Gravitation.

If you are not intending your simulation to be realistic (a rocket thruster moving the Earth is probably not reaslistic), you might as well ignore all other forces and use only the thruster force for $F$.

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