Another time dilation/travel question

[kehler]

Homework Statement

Vladimir Titov and Musa Maranov spent just under 366 days in the Mir Space Station during 1987 and 1988. Work out how many seconds they had time traveled into the future of Earth time.

Homework Equations

The orbit was circular at a height above the ground of 390km, the radius and the mass of the Earth are 6378km and 6x10^24kg. G=6.7 x 10^-11

The Attempt at a Solution

I found the velocity using the formula v=squareroot(GM/r)=7706.96m/s
The time elapsed on Earth is 366days=31622400 seconds
So the time elapsed for the travellers is
Tt=Tearth/gamma
=31622399.99
Is this correct? The time difference seems extremely small :S. Do I need to take anything else into account?

 

[bdforbes]

Are you sure it's 366 days in Earth time? Maybe it's 366 days for the cosmonauts.

 

[tiny-tim]

Vladimir Titov and Musa Maranov spent just under 366 days in the Mir Space Station during 1987 and 1988. Work out how many seconds they had time traveled into the future of Earth time.
…
The orbit was circular at a height above the ground of 390km, the radius and the mass of the Earth are 6378km and 6x10^24kg. G=6.7 x 10^-11
…
I found the velocity using the formula v=squareroot(GM/r)=7706.96m/s
The time elapsed on Earth is 366days=31622400 seconds
So the time elapsed for the travellers is
Tt=Tearth/gamma
=31622399.99
Is this correct? The time difference seems extremely small :S. Do I need to take anything else into account?

Hi kehler!

(To two significant figures, I think the correct answer is 31622400.00 )

You haven't specified what gamma you were using.

Hint: you can use the approximation √(1 - x²) = 1 - x²/2.

It's only the x²/2 part that you're interested in!

 

[kehler]

I used the approximation you stated, tiny tim. If I had used the regular formula for gamma it would have been too small to have made any difference.
I think it means 366 days Earth time, bdforbes, cos the years are specified right after that.

 

[HallsofIvy]

In any case, the problem is badly phrased. They wouldn't "travel into the future" in any sense. The question is really asking the difference in time elapsed for the cosmonauts as compared to time on the earth.

 

[kehler]

I guess it means to the astronauts it would seem like they have traveled into the future because of the time difference.
But I agree that it's rather poorly worded.

 

[gabbagabbahey]

I guess it means to the astronauts it would seem like they have traveled into the future because of the time difference.
But I agree that it's rather poorly worded.

There's also the small fact that the frame of reference of the astronaut's is a non-inertial frame. They aren't traveling at a constant velocity, just a constant speed.

 

[Vanadium 50]

They aren't traveling at a constant velocity, just a constant speed.

Yes, but as only the square of the velocity appears in the expression for gamma, this doesn't make a difference.