Calculation of a planet's mass via wavelengths

AI Thread Summary
To calculate the mass of a distant planet based on a spacecraft's emitted radio signal, the variation in wavelength due to the Doppler effect must be analyzed. The spacecraft's continuous signal, with a wavelength shift between 5.99969m and 6.00031m over a 5-hour period, indicates a velocity change that can be linked to the planet's gravitational influence. Utilizing Kepler's third law and Newton's law of gravitation will provide the necessary framework for this calculation. The relationship between the frequency shift and velocity is crucial for determining the mass accurately. Understanding these principles will lead to the correct calculation of the planet's mass.
Poppinkrey
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I got to find an answer or a push to the right tracks on this question.

Suppose a spacecraft is in a circular orbit about a distant planet. the spacecraft emits a continuous radio signal with a wavelength of 6m. The signal's wavelength varies between 5.99969m and 6.00031m; the period of variation (full period of wavelength) is 5 hours. What is the mass of the planet? Assume that you are located in plane of the spacecraft 's orbit and knowing that circumference is 2piea (a = radius) and that speed = distance / time.

Thanks in advance!
 
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I believe this requires kepler's 3rd law (where the common focus is in the distant planet).
 
Poppinkrey said:
I believe this requires kepler's 3rd law

That's a good idea. You can also use Newton's law of gravitation. Now you have to include the given frequencies. Do you know a relationship between velocity and frequency shift?
 

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