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Imagine a space probe has been placed in a circular orbit about a distant planet. The probe emits a continuous radio signal with a wavelength of 8 m. You measure the signal from earth, and find it to have a wavelength that varies regularly between 7.99943 m and 8.00057 m, with a period of 4.5 hours. Assuming that you are in the plane of the probe's orbit, and that you are not moving, calculate the mass of the planet.

This is what I have done...

By substituting into different equations, I end up with the equation:

a = λ / 2pi

Using Kepler's 3rd Law:

P^2 = a^3 / mt

I end up with :

mt= (λ / 2pi)^3(1 / P)^2

However, I do not know why I am given 3 different values for wavelength, should this be applied in to the answer or not?

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# Kepler's 3rd Law and the Doppler Effect

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