Q about relativistic mass increase, starship

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SUMMARY

The discussion focuses on the implications of relativistic mass increase for a starship propelled by antimatter, specifically through positron-electron reactions. It establishes that while the ship's mass increases at relativistic speeds, the energy released from the annihilation of mass into energy can offset this increase, allowing for effective propulsion. The key takeaway is that the ratio of the ship's mass to the energy produced does not remain constant, contradicting initial assumptions about mass-energy equivalence in high-speed travel. For detailed calculations, refer to the provided resource on special relativity and rocket dynamics.

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A warning is often given that if one wants to have a spaceship traveling at relativistic speeds (usually to get to another star), the ship's mass increases, making acceleration more difficult. But if it where an antimatter propelled ship, with mass being turned into energy, then wouldn't the mass increase be offset by the increased energy released?

In other words, say you have a best case scenario: it's a positron-electron reaction, producing all gamma rays, which by then we know how to redirect and use, almost 100%, for forward propulsion. So all propellant mass is being turned into energy, almost all of which is being spent on forward propulsion. Isn't the propellant mass increasing, along with the whole ship's mass, and so the ratio of ship's mass to energy being released in the "combustion chamber" always the same?
 
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No. The easiest way to see this is to not even use the concept of "relativistic mass". For detailed calculations, see for instance

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
 
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