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10:21
@MooseBoys I think that may be the other way round. from the spheres reference frame the journey takes 1/70th the time but it's getting hit with the fine mist of gas 70x faster so instead of 7 minutes the sphere would be hit with enough energy to vaporize it within about 6 seconds.
@Vashu I think my reply to Mooseboys applies. Also, I don't think blackbody radiation is enough, it would imply that you could pump the entire output of an 10MW hydroelectric dam into a vacum-insulated 2-foot ,1 ton sphere of tungsten and have it not melt. with time dilation it would have to do so 70x as fast.

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