Friday, July 18, 2008

Answer: Planet Formation
New Problem: Spinning Fish Tank

Planet Formation

The dust cloud has a great deal of potential energy due to the particles' mutual gravitational attraction. As the cloud collapses, all this potential energy is converted to heat (random kinetic energy of the particles). Find the (negative) gravitational potential of the planet by integrating
-GMm/r from 0 to R, where M = 4/3*pi*r3*density, m = 4*pi*r2*dr*density. You'll find the total heat released was proportional to M2/R. Plugging in some reasonable values for Earth, the temperature comes to 105K. Clearly, the planet cannot be this hot (random thermal motions would keep it from condensing that much), so the planet must cool as it forms.

Spinning Fish Tank

You take a fish tank and spin it (at constant angular frequency). What shape does the surface of the water settle down to? Who cares?

2 comments:

Nikita said...

Well, if you constantly spin it then it'll become a vortex, like a whirlpool.

The lost souls care.

Markkimarkkonnen said...

sorry, no vortex. answer is posted.