Let's say we have a space ship with a 1kg mass, and 1J stored in a battery or something. I am going to explore two things we can do with this setup to propel the craft. The first one is simply shooting the mass itself out the back.(adsbygoogle = window.adsbygoogle || []).push({});

If we shoot the mass out the back by using that 1J of energy, our craft would gain 1J in the opposite direction, right?

What if we converted our 1kg mass to light energy, and shot that out the back with a laser, though? For simplicity, let's say we only shoot a single photon containing all our energy. From energy-mass equivalence, the total energy of the photon would be [itex]c^{2}+1[/itex] joules.

This is where I get confused. I'm not sure if the total energy the ship would gain in the opposite direction of the photon should be [itex]c^{2}+1[/itex] joules or just 1 joule. I'm thinking it could be the former because we are sending [itex]c^{2}+1[/itex] joules in the opposite direction. I'm also, however, thinking it could be the latter because the relativistic mass of the photon would be [itex]\frac{c^{2}+1}{c^{2}}[/itex], and because the total energy gained should match up with the first case scenario where we just shoot the 1kg mass out.

Can someone help? Thanks!

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# Photon thruster

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