Kepler's Third Law: Eliptical Orbits & Planet Masses

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SUMMARY

Kepler's Third Law describes the relationship between the orbital period of a planet and its distance from the sun, emphasizing that orbits are elliptical rather than circular. The discussion clarifies that while traditional education often simplifies this law by ignoring planetary mass, the accurate formulation incorporates mass, transitioning from a proportionality statement to an equality through Newton's law of universal gravitation. The equation used for calculations is 4π²r³/GM, where r is the radius of the orbit and M is the mass of the central object.

PREREQUISITES
  • Understanding of Kepler's Laws of Planetary Motion
  • Familiarity with Newton's Law of Universal Gravitation
  • Basic knowledge of elliptical geometry
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of Kepler's Third Law with elliptical orbits
  • Learn how to apply Newton's Law of Universal Gravitation in orbital mechanics
  • Explore the implications of mass in celestial mechanics
  • Practice solving problems using the equation 4π²r³/GM
USEFUL FOR

Astronomy students, physics enthusiasts, educators teaching orbital mechanics, and anyone interested in the mathematical foundations of planetary motion.

dilan
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I don't know but in school I learned it in a different way. I mean in school the Kepler's third law was thought as if all the orbits were circular. But according to the definition its all elleptical, and in the school equation we won't add the planets mass, but here
http://en.wikipedia.org/wiki/Kepler's_third_law

The planet mass is also added.
So I am not sure what kind of equation I should use to solve sums?

Thanks
 
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Two points:
(a) A circle is special kind of ellipse; I'm sure you instructor approximated the orbits as circular just to keep the calculations easier.
(b) The masses are added in turning Kepler's 3rd law from a statement of proportionality to an equality; it goes beyond Kepler's original law by adding Newton's model of universal gravity.​

I don't know what you mean by "solve sums".
 
Hi

Doc Al said:
Two points:
(a) A circle is special kind of ellipse; I'm sure you instructor approximated the orbits as circular just to keep the calculations easier.
(b) The masses are added in turning Kepler's 3rd law from a statement of proportionality to an equality; it goes beyond Kepler's original law by adding Newton's model of universal gravity.​

I don't know what you mean by "solve sums".

Hi
Thanks a lot for replying. We finished orbital motion just 3 days ago and he gave us a work sheet with problems to solve. I think your correct, he approximated the orbits as circular to keep thinngs simple. The equation that I am using is
4pi^2r^3/GM

r- radius of orbit
M - mass of the center object

Thanks
 

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