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## Homework Statement

*Imagine you are observing a spacecraft moving in a circular orbit of radius 128,000 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?*

## Homework Equations

[tex] M= \displaystyle{\frac{rv^2}{G}}; \space

where \space G= 6.67\times10^{-11} \space m^3 kg^{-1} s^{-2},

\space r \space is \space km, \space and \space v \ is \space

km/s

[/tex]

## The Attempt at a Solution

Well, as we have a change in wavelength 2.99964 m and 3.00036 m respectively, the original signal should equal 3.00000m. With the formula from my textbook ( "Astronomy" 6th edition by Chaisson and McMillan, page 63), [tex] \frac{apparent\space \lambda}{true \space \lambda} -1 = speed \space in \space c[/tex] Then I multiply it by c and convert meters to kilometers and get[tex] \approx 36 km/s. [/tex]

I input r and G as [tex] G= 6.67\times10^{-11} \space m^3 kg^{-1} s^{-2}, \space r= 128, 000 km. [/tex]

So: [tex] M= \displaystyle{\frac{(128000km)*(36 km/s)^2}{6.67\times 10^{-11}\space m^3 kg^{-1} s^{-2}}} = 2.48\times10^{18} kg. [/tex]

When I input this answer into the website in which we do our homework by, it gives me a lousy red X. I'm sure I messed up, because I was expecting a planet approximately in the 10^20-28 kg range.

Regardless, I've been stuck on this for a bit. Help is much appreciated.

Sincerely,

Nikos