# Equations on a road trip

1. Jun 25, 2009

### Vebjorn

Hi! Im going on a 10 h road trip further north in Norway tomorrow, does anyone here have some fun equations i can solve? I mean, simple equations. I calculated the gravitational pull between the moon and the earth (Quite a big number i must say) Those kind of things, the equation to calculate the earth's rotation speed? Anything that can keep me busy! I also appreciate some complicated equations as well, but not too complicated as i am 15 years old and internet is a bit of a problem in the car!

- Vebjorn

2. Jun 25, 2009

### protonchain

Find the velocity of the Earth's orbit around the sun (simple enough, probably simplest).

If you like velocities, then calculate the same thing for the moon's orbit around the Earth.

Find the equation that relates gravitational acceleration (g - 9.81 m/s^2 on Earth) to mass and radius.

Find an approximate value for the mass of the Earth using the moon's orbit parameters (little more involved).

Repeat the same for the sun's mass and the Earth's orbit parameters.

3. Jun 26, 2009

### Vebjorn

Thank you! I leave in about 10 minutes! :)

4. Jul 1, 2009

### Wallace

Try this cute problem. Given the equation

$$a^n + b^n = c^n$$

is it possible to have a solution if a, b and c are all integers for any n>2? I have this neat proof that no solutions exist, but there isn't enough space left in this post to write it down.

5. Jul 6, 2009

### Vebjorn

Hm, I'm not sure i got the question and im not sure what integers means. Maybe thats why :P I'll look it up.

6. Jul 6, 2009

### Wallace

Sorry, my previous post was a bad joke. This puzzle is known as Fermat's last thereom, and it remained unsolved for many centuries. It was solved a few years ago but I think the consensus is that the current best solution is not very elegant, and a better one is still sought. Look up the history of the problem (google, wiki....) as it is a classic bit of mathematics history.

7. Jul 7, 2009