Time Dilation and gravity

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).

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

Redbelly98
Staff Emeritus
Homework Helper
Hint: what is the time dilation factor at this speed?

The way I have it set up, the time dilation factor is less than 1, am I doing something wrong?

Redbelly98
Staff Emeritus