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Linuxkid
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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
M= \displaystyle{\frac{rv^2}{G}}; \space<br /> <br /> where \space G= 6.67\times10^{-11} \space m^3 kg^{-1} s^{-2},<br /> <br /> \space r \space is \space km, \space and \space v \ is \space<br /> km/s <br />
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), \frac{apparent\space \lambda}{true \space \lambda} -1 = speed \space in \space c Then I multiply it by c and convert meters to kilometers and get\approx 36 km/s.
I input r and G as G= 6.67\times10^{-11} \space m^3 kg^{-1} s^{-2}, \space r= 128, 000 km.
So: 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.
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.
Nikos