# Homework Help: Special Relativity - Dynamics -- Traveling in Space

1. Dec 8, 2015

### Barry Melby

1. The problem statement, all variables and given/known data

Assume that 437 days is a reasonable limit for how long a human can endure constant-velocity space travel. Proxima Centauri, the star closest to our Sun, is 4.24 light years away from Earth.

If you wanted to fly to Proxima Centauri within the 437-day limit in a rocket of mass 2.00×10^6 kg , how much energy would be required to accelerate the rocket to the necessary speed in the Earth reference frame? For this rough estimate, ignore the energy required to stop, and disregard the hundreds of days required at each end of the journey for acceleration.

2. Relevant equations
K = (1-y)mc^2

3. The attempt at a solution

I've tried to attempt this solution, but it seems impossible as you would have to travel faster than the speed of light to get there in 437 days. Where am I going wrong?

2. Dec 8, 2015

### nrqed

Are you taking into account time dilation? he 437 days will be time elapsed aboard the ship, not as measured from Earth (that will be much larger).

3. Dec 8, 2015

### Barry Melby

how would i go about time dilation in this case?

4. Dec 8, 2015

### nrqed

Time on Earth = $\gamma$ times time on the spaceship. This equation contains two unknowns: gamma(which depends on the speed) and the time delay on Earth. So you need a second equation containing these two unknowns and then you can solve.

5. Dec 8, 2015

### Barry Melby

i can't find $\gamma$

6. Dec 8, 2015

### Ray Vickson

Finding $\gamma$ is easy enough if you know the travel velocity $v$. Remember the formula for $\gamma$?

Last edited: Dec 8, 2015