**Your answer seems reasonable.**

Find out if you're right!

← Space oddity radio
·
Level 5
(265 points)

I'm in a spaceship very far away from earth but traveling straight towards earth with a speed v. It's boring out here, so I decide to try and tune in to some of my favorite earthly radio stations. I remember that my favorite station has a frequency of 100.3 MHz and so tune my radio to **exactly** this frequency. Amazingly, I hear the radio station just like I do on earth! How fast is my spaceship going **in m/s**? (Hint: it's not that fast...I think I should check whether my engines are on).

**Details and assumptions**

- Photons of electromagnetic radiation have an intrinsic kinetic energy related to their frequency by \(E=hf\) where \(h\) is Planck's constant.
- The gravitational interaction between photons and earth can be treated via usual Newtonian gravity and \(E=mc^2\) to convert between energy and mass.
- The total energy of the photons is conserved.
- The earth can be treated as a sphere of radius 6370 km and mass \(6 \times 10^{24}~kg\). You can ignore rotation of the earth.
- The speed of light is \(3 \times 10^8~m/s\).
- Assume the earth is at rest.

Find out if you're right!

Sign up to access problem solutions

That seems reasonable. Find out if you're right!

Are you feeling smart or lucky? Find out if your answer is correct.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...