# Physics Problem - Time Dilation?

You leave on a mission to a distant star. Your craft accelerates at a 0.65 g for 30 days. From your point of view, you spend the next 1000 days moving at this speed.

What is the difference between the period of this steady travel from your point of view and from the point of view of an earth observer?

I need to know how to SOLVE this. DO NOT GIVE ME THE ANSWER, PLEASE GIVE ME A FORMULA!! I know there are many professors out there who scold people who want answers, so what I want is to know how to solve this. THANK YOU.

Also, the problem does not state 0.65 c, the problem states 0.65 "g". I don't know if it's talking about gravity, or some other variable I have yet to learn about.

### 2 Answers

- billrussell42Lv 75 months agoBest answer
v = v₀ + at

t = 30 day x 24 hr/day x 3600 sec/hr = 2592000 s

0.65g = 0.65 x 9.8 m/s² = 6.37 m/s²

v = at = 6.37 x 2592000 = 1.65e7 m/s, which is relativistic, but I think (?) that the equation is still valid, just that as mass increases, the force needed to maintain that acceleration increases.

time dilation

t' = t/γ

γ = 1/√(1–(V²/c²))

γ = 1/√(1–(1.65e7/3e8)²) = 1.0015

time slows down for the traveler

so the 1000 days is seen to an external observer as 1000 x 1.0015 = 1001.5 days

Thank you so much for this!