Spacecraft Question: How Fast to Travel for 2 Days on Earth?

[CollectiveRocker]

How fast must a spaceship be traveling relative for one day on the spacecraft to equal 2 days on Earth? I'm pretty sure that t(0) = 172,800 seconds, and t = 86,000 seconds. Do I just need to use ∆t = t – t(0), simplify that to t = γt(0), and then since γ = 1+ (1/2)(v^2)/(c^2); take the resulting equation and just resolve for v?

 

[Olaf.of.Ísland]

If I remember correctly, you will want to use the relativistic equation for gamma and not the approximation for speeds much lower than the speed of light. So,
gamma = 1/(sqrt(1-(v^2/c^2))) Otherwise, using the aproximation will yeild a speed faster than the speed of light which is not possible.

 

[CollectiveRocker]

I'm ending up with v = sqrt{(((t(0)^2)(c^2))/(∆t^2))-c^2} Can someone please check my math?

 

[Olaf.of.Ísland]

Close, it may be easier to notice that gamma = (earth time) / (spaceship time)

So, gamma = 2 in your case. Should be easy from here . . .

 

[CollectiveRocker]

How does gamma equal Earth time/ spaceship time or 2? Is this just though simplification?

 

[CollectiveRocker]

So I can just set gamma equal to 2, and solve for v!

 

[Olaf.of.Ísland]

Yes, that should do the trick.

 

[CollectiveRocker]

Thanks a bunch Olaf.

 

[CollectiveRocker]

If gamma =2, then 2 = 1/(1+(v^2)/(c^2)), thus leaving you with a negative value when you simplify for v.