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Assume there are no other forces acting and the rocket+fuel described do not weigh anything. Also, by rocket I mean engine/thruster, not space shuttle.

Suppose you have a planet, say of mass 1,000,000,000kg and you push it with a rocket which exerts a force of 1N. This will accelerate the planet by 1 x 10^-9 m/s².

Then, suppose you have a feather of mass 0.005kg and push it with the same rocket which exerts a force of 1N, accelerating it by 200 m/s².

It follows that the feather will traverse a distance of 1m much faster than the planet and thus spend much less rocket fuel to do so. So, the energy used to propel the planet must be much more than the energy used to propel the feather.

But, work done = force × distance, 1 × 1 = 1J for both the planet and the feather. I think I have misunderstood something. How is this possible?

Assume there are no other forces acting and the rocket+fuel described do not weigh anything. Also, by rocket I mean engine/thruster, not space shuttle.

Suppose you have a planet, say of mass 1,000,000,000 kg and you push it with a rocket which exerts a force of 1 N. This will accelerate the planet by $10^{-9}\, m/s^2$.

Then, suppose you have a feather of mass 0.005 kg and push it with the same rocket which exerts a force of 1 N, accelerating it by $200\, m/s^2$.

It follows that the feather will traverse a distance of 1 m much faster than the planet and thus spend much less rocket fuel to do so. So, the energy used to propel the planet must be much more than the energy used to propel the feather.

But, work done = force × distance, $1 \times 1 = 1\, J$ for both the planet and the feather. I think I have misunderstood something. How is this possible?

Assume there are no other forces acting and the rocket+fuel described do not weigh anything. Also, by rocket I mean engine/thruster, not space shuttle.

Suppose you have a planet, say of mass 1,000,000,000kg and you push it with a rocket which exerts a force of 1N. This will accelerate the planet by 1 x 10^-9 m/s^2.

Then, suppose you have a feather of mass 0.005kg and push it with the same rocket which exerts a force of 1N, accelerating it by 200 m/s^2.

It follows that the feather will traverse a distance of 1m much faster than the planet and thus spend much less rocket fuel to do so. So, the energy used to propel the planet must be much more than the energy used to propel the feather.

But, work done = force x distance, 1 x 1 = 1J for both the planet and the feather. I think I have misunderstood something. How is this possible?

Assume there are no other forces acting and the rocket+fuel described do not weigh anything. Also, by rocket I mean engine/thruster, not space shuttle.

Suppose you have a planet, say of mass 1,000,000,000kg and you push it with a rocket which exerts a force of 1N. This will accelerate the planet by 1 x 10^-9 m/s².

Then, suppose you have a feather of mass 0.005kg and push it with the same rocket which exerts a force of 1N, accelerating it by 200 m/s².

It follows that the feather will traverse a distance of 1m much faster than the planet and thus spend much less rocket fuel to do so. So, the energy used to propel the planet must be much more than the energy used to propel the feather.

But, work done = force × distance, 1 × 1 = 1J for both the planet and the feather. I think I have misunderstood something. How is this possible?