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Let’s say a rocket which is at rest relatively to an asteroid. The rocket engine start and the rocket is launched toward the asteroid’s neighborhood. When the rocket engine is working, the rocket accelerates. Few minutes later, the rocket engine turns off and the rocket is now travelling at 0.5c, let’s say.

1) My first question is : the rocket engine is used to propulse the rocket forward, the motion of the rocket is due to the reaction of the ejection of the fluid from within the rocket engine. When the rocket reaches 0.5c, the rocket’s reference frame becomes galilean and an observer at rest in the rocket would considers that the rocket is motionless and that it’s the asteroid which is moving. However, the asteroid is more massive than the rocket, so its kinetic energy is higher than the rocket’s one, since they have relatively to each other the same speed. Where does the energy of the asteroid come from?

2) My second question is : GR tells us that energy has gravitational effects and that the “amount” of energy is proportional to the gravitational force (even if there is no gravitational force in GR). So, I would say that the asteroid has more effective gravitational effects when it’s moving rather than when it’s at rest. Is it correct? Does this explain the difference between the GR’s calculation and the newtonian calculation of light bending, the fact to consider not only mass but energy too?

It makes so much time that I wonder about these questions. There are the result of my misunderstanding of the subject and I would like to clear that up for once. Thanks for your help.

Zeit