Physics: An astronaut is traveling in a space vehicle moving at 0.490c relative to the earth. the astronaut measures her pulse rate at 66.0 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. (due to vehicle s path there will be no doppler shift in the ) what pulse rate does the earth-based observer measure? beats/min(b) what would be the pulse rate

I think 5 or so check and tell me...

An astronaut is traveling in a space vehicle moving

roderickhinton

10.01.2022

To solve the exercise it is necessary to use the reciprocal Lorenz factor of the special theory of relativity with the pulse rate.

$\Xi = Pulse_{astronaut} * \alpha$

Where,

$\Xi =$ Pulse rate measured by earth observed

$\alpha =$ Reciprocal Lorenz Factor

$\alpha = \sqrt{1-\frac{v^2}{c^2}}$

Here v is the velocity and c the light speed.

PART A) For the given values we can replace it at the previous equation,

$\Xi = Pulse_{astronaut} *\sqrt{1-\frac{v^2}{c^2}}$

$\Xi = 66beats/min * \sqrt{1-\frac{(0.49c)^2}{c^2}}$

$\Xi = 57.5beats/min$

PART B ) If the speed of vehicle is 0.94c:

$\Xi = Pulse_{astronaut} *\sqrt{1-\frac{v^2}{c^2}}$

$\Xi = 66beats/min * \sqrt{1-\frac{(0.94c)^2}{c^2}}$

$\Xi = 22.5beats/min$

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