Imagine you are observing a spacecraft moving in a circular orbit of radius 55,0

Question

Imagine you are observing a spacecraft moving in a circular orbit of radius 55,000 km around a distant planet. You happen to be located in the plane of the spacecraft's orbit. You find that the spacecraft's radio signal varies periodically in wavelength between 2.99964 m and 3.00036 m. Assuming that the radio is broadcasting normally, at a constant wavelength, what is the mass of the planet? . kg I have been really struggling with this, please help me and show me how to calculate the correct answer? Thanks

Explanation / Answer

First, we get the velocity in orbit using the doppler.
Round c to 3*105 km/s
Note that the average signal is 3.000000 m

v orbit = c * (3.00036 -3)/3 .. doppler shift
v orbit = 36 km/s
a = v^2/r
a = (36km/s)^2/55000km
a = 23.56 m/s^2

a =GM/r^2
M = a r^2/G
M = 23.56 m/s^2 *(55000000 m)^2/ 6.67x10^-11

M = 10686.6566*10^23 kg
M = 1.068 x 10^27 kg

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