# Velocity of a spacecraft at relativistic speed

1. Mar 20, 2017

### Huston

1. The problem statement, all variables and given/known data
The closest star system is about 4.3 light years away from Earth. A spacetug is able to move a cargo ship at a constant force of g=9.8N/kg times the mass of the cargo ship for many years. Starting from rest, speed up the cargo ship until you're halfway to the nearest stars, then pull back with the same force to slow the ship down to rest. Determine the maximum speed attained and how many Earth years the trip there takes.

2. Relevant equations
I'm not sure. I really just need help starting it. We haven't really gone over relativity, and my teacher is giving this project as a challenge. I'm not sure if it's easier than I'm making it, but our book doesn't really have much pertinent information on the subject except that we need to use the relativistic position update equation to solve it. We haven't done any relativity problems in class and I'd just love a push in the right direction!

3. The attempt at a solution

2. Mar 20, 2017

### Comeback City

You got yourself a tough teacher if he isn't gonna teach you relativity before giving you relativity problems. Ever hear of the relativistic rocket? There should be many threads about it here on PF.

Btw, it's not easier than you are making it to be, unless I'm missing something myself

3. Mar 20, 2017

### FactChecker

It may depend on who is doing all the measurements of time, mass, force, distance and velocity. If they are all done by the stationary observer, there may not be a problem. It does specify Earth years and is careful to define the force so that mass does not matter. If some of the values are as measured by the traveler, it is more complicated.

4. Mar 20, 2017

### Huston

It is looking for measurements from a stationary observer I believe.

5. Mar 20, 2017

### Huston

I'll go look at the relativistic rocket! I appreciate the help! It's definitely not the easiest class I've ever taken. There's a lot of learning on my own. I had some physics in high school, but this is my intro to physics as a major in University. It seems like this program is going to be intense. It'll be good for me in the long run though.

6. Mar 21, 2017

### Buzz Bloom

Hi Huston:

The following is a discussion of the "relativistic rocket" that looks easier to understand that the PF threads.

Hope this helps.

Regards,
Buzz