Relativistic motion and understanding it

[Niles]

Homework Statement

E.g.: A spaceship flies past Mars with a speed of 0.985c relative to the surface of the planet. When the spaceship is directly overhead, a signal light on the Martian surface blinks on and then off. An observer on Mars measures that the signal light was on for 80.0ms.

I have to find out, how long time passes when measuring the pulse of light by the pilot of the spaceship?

The Attempt at a Solution

From the observer on Mars, it takes 80 ms. From the pilots inertial frame, it must take a longer time, because of the Lorentz factor.
But how does this add up with the fact, that the pilot won't have aged as much as the observer on Mars when the flight has ended? Because with my calculations, something about ~460 ms is the duration of the pulse. But that is longer time, which is good because of the Lorentz factor, but he will have aged more then? Or is 80 ms to the pilot, and ~460 ms to the observer on Mars?

 

[Niles]

I have a question, related to my first post.

A spacecraft traveling 0.9c has the length 91.5 m seen from the outside (so length in rest is 210m). It has to pass a tunnel 215 metres long - how long does this take?

I just use velocity = distance/time, right? There's no need to use Lorentz here?

 

[Doc Al]

When the spaceship is directly overhead, a signal light on the Martian surface blinks on and then off. An observer on Mars measures that the signal light was on for 80.0ms.

This statement's a bit fishy. How far does the ship travel in 80 ms? How can it remain "directly overhead" as the light blinks on and off?

Hint: You can treat the flashing of the light as being measured by the moving clock of the pilot. How would the observer on Mars view that moving clock? Work backwards.

A spacecraft traveling 0.9c has the length 91.5 m seen from the outside (so length in rest is 210m). It has to pass a tunnel 215 metres long - how long does this take?

I just use velocity = distance/time, right? There's no need to use Lorentz here?

It depends on what is meant by "pass through" the tunnel. When does the passing begin and end? (Any needed Lorentz factor is already computed for you.)

 

[Niles]

1) A very good and helpful way of looking at it. Thanks.

2) The text in my book is as follows: "The aircrafts will be in a line that is 91.5 m long and traveling at 90% the speed of light relative to a stationary observer. For how long a time period will the line of aircrafts be inside of the asteroid, which is 215 metres?"

 

[Doc Al]

That time for the aircraft ( spacecraft , I hope!) to be inside the asteroid begins when it's nose first enters and ends when its tail leaves.

 

[Niles]

Oh yeah, it really does say spacecraft .. funny, I hadn't noticed

So total distance is 215 m + 91.5 m - and from there I use v = dis/tim?

 

[Doc Al]

So total distance is 215 m + 91.5 m - and from there I use v = dis/tim?

That's right--that's all there is to it. As seen by the "stationary observer", the spacecraft travels that distance in passing through the asteroid.