How they find weights of planets?

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Discussion Overview

The discussion revolves around the methods used to determine the weights (masses) of planets, touching on historical and theoretical aspects of gravitational laws, particularly Newton's law of universal gravitation and its derivation from earlier works, such as those of Galileo and Kepler. The conversation also explores the implications of gravitational potential in the context of orbital mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants reference Newton's law of gravitation (Fg=GMm/r²) and question its empirical or derived nature, particularly in relation to Kepler's laws.
  • One participant expresses uncertainty about Galileo's contributions to the understanding of gravitational force and its proportionality to mass.
  • Another participant seeks clarification on how to calculate orbits based on the gravitational force law.
  • A participant discusses their experience with the textbook "Classical Mechanics" by Goldstein, specifically regarding the gravitational potential and its implications for bounded orbits.
  • There is mention of the effective potential and its role in determining the energy states of a particle in a gravitational field.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and knowledge regarding the historical development of gravitational theory and its mathematical implications. There is no consensus on the derivation of Newton's laws or the interpretation of gravitational potential in relation to orbits.

Contextual Notes

Some assumptions about the foundational principles of gravitational theory and the mathematical steps involved in deriving orbits remain unresolved. The discussion reflects a range of familiarity with classical mechanics concepts.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of classical mechanics, astronomy, and the historical development of physics concepts, particularly those exploring gravitational theory and orbital dynamics.

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The calculation of the mass depends on the fact that Fg=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
 
Last edited by a moderator:
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.
 
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.
 
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?
 
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.
 

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