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I am working on an imaginary world -- call it science fiction if you like -- in which the speed of light is much slower but nothing else is changed. Yes, I know that this is impossible. The speed of light I have chosen is that the distance to the moon is one light year, which means c=12.7 m/sec.

The specific question that interests me is the Apollo moon mission. Since momentum is unchanged, then the astronauts will still be able to go to the moon in four days and return in four days more, as far as their own clock is concerned. The question is, what is the Earth clock doing?

I'm assuming the angular momentum of objects on the surface of the Earth is unchanged from that in our world. So the Earth is rotating at .99962 c and a day is still 24 of our hours. Yes, I know that this is impossible. What interests me is that since the rotation is so fast the clocks on the Earth will be dilated by a factor of 36.45. The velocity of the astronauts relative to the Earth is not constant, so it seems that it would be necessary to integrate the the time dilation of the astronauts relative to the center of the Earth over the entire trip, which is doable but not all that easy. Is there a shortcut for the calculation of the relative time dilations of the two paths: surface of the Earth, and trip to the moon?

The surface of the Moon would be rotating at a mere 0.3c, so once on the moon then the astronauts would lose almost all of their time dilation and have a wait of two or three weeks for the orbiting spacecraft to complete one orbit. As far as the orbiting astronaut is concerned the moon orbit takes two hours.

Anyway, I hope that this crazy problem interests someone who understands these things better than I and can point me in the right direction.

The specific question that interests me is the Apollo moon mission. Since momentum is unchanged, then the astronauts will still be able to go to the moon in four days and return in four days more, as far as their own clock is concerned. The question is, what is the Earth clock doing?

I'm assuming the angular momentum of objects on the surface of the Earth is unchanged from that in our world. So the Earth is rotating at .99962 c and a day is still 24 of our hours. Yes, I know that this is impossible. What interests me is that since the rotation is so fast the clocks on the Earth will be dilated by a factor of 36.45. The velocity of the astronauts relative to the Earth is not constant, so it seems that it would be necessary to integrate the the time dilation of the astronauts relative to the center of the Earth over the entire trip, which is doable but not all that easy. Is there a shortcut for the calculation of the relative time dilations of the two paths: surface of the Earth, and trip to the moon?

The surface of the Moon would be rotating at a mere 0.3c, so once on the moon then the astronauts would lose almost all of their time dilation and have a wait of two or three weeks for the orbiting spacecraft to complete one orbit. As far as the orbiting astronaut is concerned the moon orbit takes two hours.

Anyway, I hope that this crazy problem interests someone who understands these things better than I and can point me in the right direction.

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