Spaceships in Special Relativity

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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.

 

[anathema]

Thank you for your post. I would like to offer my thoughts on your questions.

For the first question, your answer of "A. More than 2.0hrs later" is correct. This is because of time dilation, which is a consequence of special relativity. As Shuttle Alpha is traveling at a constant relativistic velocity, time is passing slower for the shuttle compared to the spacestation. This means that when the next signal is sent, the time on the shuttle will have passed more than 2.0 hours, but the time on the spacestation will have only passed 2.0 hours.

For the second question, you are correct in considering the acceleration of Shuttle Epsilon. As it is traveling at a constant rate of acceleration, its speed will increase at a constant rate. This means that it will take some time for Epsilon to catch up to Alpha and pass it. Therefore, the correct answer is "C. Shuttle Epsilon has not yet sent its 4th signal" as it will take some time for Epsilon to reach that point in its journey.

In terms of equations, you can use the time dilation equation t' = t√(1-v^2/c^2) to calculate the time passed on the shuttle compared to the spacestation, where t' is the time passed on the shuttle, t is the time passed on the spacestation, v is the velocity of the shuttle, and c is the speed of light. For the second question, you can use the equations of motion to calculate the time it will take for Epsilon to pass Alpha.

I hope this helps clarify your understanding of these concepts. Don't hesitate to ask if you have any further questions.