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## Homework Statement

The Apollo astronauts returned from the moon under the Earth's gravitational force and reached speeds almost 25,000 mi/h WRT Earth. Assuming (incorrectly) they had this speed for the entire trip from the moon to Earth, what was the time difference for the trip between their clocks and clocks on Earth?

Given:

Velocity of Apollow WRT Earth: 25,000 mi/h

Assumed (I'm not sure if I'm actually supposed to use or assume this):

Distance from Earth to the moon: 238, 857 mi

## Homework Equations

I believe I have solved for t (Earth's frame), but I'm having a problem solving for t' (Apollo's frame). If I'm doing the time dilation factor right, it would be either 1 or the square root of a negative number, so I'm not sure what to do with that.

## The Attempt at a Solution

Earth's Frame:

t=L/v=238,857 mi/ 25000 mi/h=9.55428 h

Apollo's Frame:

t'=t/ɣ=9.55428 h*√(1-(25,000/c)²)=this doesn't work