Relativity - time in different reference frames

[Feodalherren]

Homework Statement

An astronaut is traveling in a space vehicle moving at
0.500c relative to the Earth. The astronaut measures her
pulse rate at 75.0 beats per minute. Signals generated by
the astronaut’s pulse are radioed to the Earth when the
vehicle is moving in a direction perpendicular to the line
that connects the vehicle with an observer on the Earth.
(a) What pulse rate does the Earth-based observer measure?

Homework Equations

The Attempt at a Solution

$t_{astronaut}=\gamma t_{earth}$

$\gamma = 1.154701$

Then $\Delta t_{earth} = 51.962 s$

$\frac{75beats}{51.962s} = 1.443beats/s \frac{60s}{min} = 86.66 bpm$

should be 64.9 bpm.

$1_{}$

 

[rpthomps]

 

[Feodalherren]

But they are saying beats PER minute not minutes per beat. It's totally counter intuitive the way that they are doing it. What a joke question.

 

[rpthomps]

The beats are like a clock, with a period 0.8 s. This is the proper time on the spaceship. An observer outside the ship notices, due to time dilation, that the period is longer. This translates into less beats per minute.

 

[Feodalherren]

I thought the proper time was always the stationary one?

 

[rpthomps]

The idea of "stationary" doesn't work well with relativity. It could be easily argued that the ship is stationary and the Earth is moving with respect to it. Therefore, the definition of proper time is that the clock in question has not moved in a particular reference frame. For the astronaut, her "clock" is her pulse. Her pulse travels with her and is therefore "stationary" with respect to the ship. This is proper time. For the observers on Earth, her "clock" is moving. It was to the left in one instance and now it is moved to the right a little. This, is measured time.

 

[Feodalherren]

Gah this is so confusing. Everything was great until Einstein came along and ruined it.

Alas, my struggle continues. Thank you for the help Sir!

 

[rpthomps]

You're welcome.