# Spaceships in Special Relativity

## Homework Statement

There are two shuttles that depart simultaneously from a spacestation floating in deep space. At regular intervals (1.5hrs as measured by clocks on the shuttles), they send light signals to the spacestation.

1. Shuttle Alpha travels at a constant relativistic velocity. Two successive signals from it are received at the spacestation 2.0hrs apart according to clocks on the station. When will the next signal be received?
A. More than 2.0hrs later
B. Exactly 2.0hrs later
C. Less than 2.0hrs later
D. There is not enough information

2. Shuttle Epsilon travels in a straight line with a speed that increases at a constant rate. The two shuttles pass each other just as Alpha is sending its 4th signal to the station. Which of the following is correct?
A. Shuttle Epsilon is also sending its 4th signal
B. Shuttle Epsilon has already sent its 4th signal
C. Shuttle Epsilon has not yet sent its 4th signal
D. There is not enough information

## Homework Equations

I don't even know what equations are relevant here. There is only one number given (1.5 hours as measured by clocks on the shuttles). On the formula sheet I will be given, I have the metric equation, Lorentz transformations, and the integral ∫√(1-v(t)^2) over the interval from tA to tB to find Δt'AB.

## The Attempt at a Solution

For the first one, i answered A. More than 2.0hrs later. I'm assuming that Shuttle Alpha is traveling at a constant velocity AWAY from the spacestation, so by the time it sends another light signal, that light will have a larger distance to travel to reach the spacestation. Does that seem valid?

The second one is what I'm having problems with. I feel like I have to know the acceleration of the shuttle or something. At first, I figured it had already sent its 4th signal since by the time it passes Alpha, it's going way faster than Alpha, thus Epsilon's clock is ticking more slowly. But then I realize that means in the beginning of its trip, Epsilon's clock was ticking faster. Then I talk myself into circles.