The Earth orbits around the Sun because it has angular momentum. If we stopped the Earth in orbit and then let it fall straight towards the Sun, how long would it take to reach the Sun in seconds?

Details and assumptions

The mass of the sun is 2*10^30 Kg.
The mass of the earth is 6*10^24 Kg.
The earth is 149,600,000 Km from the Sun.
You may treat the Earth and Sun as point masses.

closed as off-topic by John Rennie, Kyle Kanos, Abhimanyu Pallavi Sudhir, Waffle's Crazy Peanut, jinawee Dec 26 '13 at 18:28

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  • 2
    $\begingroup$ This seems to be a homework question. $\endgroup$ – fibonatic Dec 26 '13 at 14:04

This is a very standard mechanics problem whose solution can be found anywhere in the web. If you have no idea how to solve the problem, then the following thoughts might help you to be able to do the maths. If not, please ask for further hints.

You can apply Kepler's third law! Think about the motion of the Earth as falling into the Sun and getting back to the initial position afterwards. So, your orbit is just a line. Now it's your turn: Determine the semimajor axis of this orbit. Then, compute the orbital period by using Kepler's law. From this you can easily get the free fall time.

Hopefully, this helps you.


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