# B How to calculate the Doppler Shift Frequency

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1. May 30, 2017

### mpolo

I would like to know the formula for calculating the Doppler shifted frequency received by someone on Earth that is received from a space ship traveling at 85 percent the speed of light away from Earth. Please show example of the formula being used. Lets say the spacecraft sent a radio signal from the ship at 100 MHZ what would the received frequency of that signal be on earth?

2. May 30, 2017

### PeroK

Have you tried googling for "relativistic Doppler shift"?

3. May 30, 2017

### mpolo

Yes I have looked but I would like to see someone actually do it with real numbers and a bit of explanation I am curious as to how the time dilation works in the scheme of things. In other words what would it look like if I were in a space ship traveling at 99% the speed of light towards a group of stars. Would the light of the stars be blue shifted? If so, by how much?

Last edited: May 30, 2017
4. May 30, 2017

### PeroK

The equation is:

$f_o = f_s \sqrt{\frac{1+v}{1-v}}$

Where $f_o=$ is the observed frequency, $f_s$ the frequency of the source and $v$ is the speed expressed as a fraction of the speed of light. E.g. $v = -0.85$ or $v = 0.99$ in the two examples you wanted. If $v$ is positive then motion of the source is towards the observer and if $v$ is negative then motion of the source is away from the observer.

You could put that formula into a calculator or spreadsheet and plug away!

5. May 30, 2017

### mpolo

Oh Man, Thanks this is perfect thanks so much! This is exactly what I was looking for! Going to have fun putting this is to a program and trying different values.

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