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If a relativistic rocket is pushed by a laser sail, in the frame of reference from which the laser is being fired, the ship is gaining mass and needs more and more energy to accelerate it any further, approaching infinite energy requirements.

In the relativistic rocket's frame of reference, it gains no mass. If it were propelled by an internal fuel source, the rocket would only ever need the same amount of fuel to continue accelerating at the same rate it always has been.

Does this mean that a relativistic rocket requires less fuel if carried onboard than if propelled by external means, such as a laser sail?

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    $\begingroup$ Two mistakes, if you take acceleration a as change of velocity per second it needs more and more energy for the same a. Second since the laser beam gets more and more doppler shifted it gives less energy. $\endgroup$
    – trula
    Commented Feb 18, 2022 at 18:19
  • $\begingroup$ OK. I know the rocket's acceleration is going to slow in our frame of reference no matter what, because of relativity, but the rocket is still accelerating at the same rate in it's frame of reference. Doesn't that mean the laser encounters more resistance than the rocket's own engines would? $\endgroup$
    – Ben Warner
    Commented Feb 18, 2022 at 20:09

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In the internally powered relativistic rocket's frame of reference there is no increase of relativistic mass. So the acceleration stays good.

In the externally powered relativistic rocket's frame of reference there is no increase of relativistic mass. So the acceleration stays good.

In the launchpad frame the internally powered relativistic rocket gains relativistic mass. So the acceleration suffers.

In the launchpad frame the externally powered relativistic rocket gains relativistic mass. So the acceleration suffers.

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