# Homework Help: Mass of a planet given wavelength of an orbiting craft?

1. Oct 4, 2009

### burnout_128

Problem:
Suppose a spacecraft is in a circular orbit about a distant planet. The spacecraft emits a continuous radio signal with a wavelength of 6 m. You observe the signal's wavelength to vary between 5:99969 m and 6:00031 m; the period of variation (i.e., the full period of the signal) is 5 hours. Calculate the mass of the planet. Assume that you are located in the plane of the spacecraft's orbit. It may help to know that the circumference of a circle with radius a is 2$$\pi$$a, and to recall that speed equals distance divided by time.

I'm pretty sure I have to use the Doppler effect in some way because I'm given wavelengths but I am unsure how to use it. Can anyone help?

2. Oct 4, 2009

### Vanadium 50

Staff Emeritus
You know the velocity of the orbit.
You know the period of the orbit.
You therefore know the radius of the oribit.
You therefore know the centripetal force, and therefore the gravitational force.

3. Oct 4, 2009

### burnout_128

By using this formula: (change in wavelength / true wavelength) x speed of light
= ( (6.00031-5.99969) / 6) x 300000
= 31 km/s <--Is this the orbital velocity?
What other formulas are needed? M = rv2/G ?

4. Oct 5, 2009

### gabbagabbahey

What makes you think the true wavelength is 6m (I'm not saying you are incorrect, I'm just saying you should provide a justification for this, since it is not a given quantity.)?

And isn't the "change in wavelength" the maximum (or minimum) minus the true wavelength (not max minus min)? Remember, when the craft is moving directly towards/away from you, you expect to observe the minimum/maximum wavelength.

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