How they find weights of planets?

[decibel]

? (lol)

 

[Phobos]

answer from an astronomer's FAQ website...
http://itss.raytheon.com/cafe/qadir/q2910.html

 

[StephenPrivitera]

The calculation of the mass depends on the fact that F_g=GMm/r². Where did Newton come up with this equation? Is this law empirical or derived? Is it derived from the fact that F=ma and planets travel in ellipses?
Newton never knew the masses of the planets. So he couldn't have done anything like Kepler and taken tons of data and invented his law.
EDIT:
This site used Kepler's Laws to derives Newton's
http://www.physics.ubc.ca/~outreach/phys420/p420_95/tracy/universal.html

 

[StephenPrivitera]

Originally posted by Ambitwistor
Given Galileo's work, Newton knew that the gravitational force on a body had to be proportional to its mass.

I guess I am not aware of Galileo's work.

 

[StephenPrivitera]

Originally posted by Ambitwistor

He then calculated the orbits that would result from such a force law

Do you happen to know how to do this? I can't seem to figure it out for myself.

 

[StephenPrivitera]

I picked up Classical Mechanics by Goldstein in my library. I skipped straight to chapter 3 which is on the two-body problem (although I had to flip back to chapter one to figure out what a Lagrangian is).
I'm having trouble with some things.
The graph of the gravitational potential U=-GMm/r looks like a hyperbola to me. If E<0, then certainly the particle is bounded in that it will not reach infinity. But what does this say about the shape of the orbit? Also, the fact that E<0 does not put a lower bound on r (except of course r>0). What about the graph indicates that the U of the particle will oscillate?

 

[StephenPrivitera]

Ah, that's great news. I had been wondering that for a while. Goldstein draws pictures of this effective potential and uses its shape to show that the object is bound at certain energies. Let me dig through Goldstein some more and I'll let you know if (when) I need more help.