Is the ratio of the two times in the right direction?

[jesuslovesu]

Homework Statement

Sun and Earth are 8.3 lightminutes apart, as measured in their rest frame. What is the speed of a spacecraft that makes the trip in 5.0 min according to its onboard clocks?

Homework Equations

The Attempt at a Solution

I'm not really sure how to proceed. I figured out that 8.3 lightmins = 1.5 x 10^11 m. I was thinking that since the ship traveled in a time span of 5 minutes that gamma = 1.66 (8.3/5) but apparently that was incorrect.

Is the ratio of the two times in the right direction? I don't see any other way to find the velocity

 

[learningphysics]

I'm confused by this equation you gave...

gamma = 1.66 (8.3/5)

this isn't right. remember 8.3lightminutes is a distance as you calculated...

What is the time the trip takes according to an observer at rest? The distance divided by that time is the velocity you need... you'll have both a gamma and a v in your equation... but you can rewrite gamma in terms of v... then you can solve the equation for v.

 

[jesuslovesu]

t = x / v = 8.3 lightmins / v

What equation should I be using so far I've tried x' = gamma(x - vt) and t' = gamma(t -vx/c^2) but I haven't been able to come up with anything useable with them yet.

I would think the former, but I tried that and I actually got c for the answer.

 

[learningphysics]

t = x / v = 8.3 lightmins / v

Yes, so t = 1.5*10^11/v

That's the time seen by an observer at rest... an observer inside the ship sees 5 min = 300s.

So use the time dilation relationship to relate 1.5*10^11/v and 300

 

[learningphysics]

Time dilation: $$\Delta{t} = \gamma\Delta{t_0}$$

where $$\Delta{t_0}$$ is the proper time (time elapsed in the ship)