Finding the eccentricity of Earth's orbit

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SUMMARY

It is possible to calculate the eccentricity of Earth's orbit using Kepler's laws of planetary motion and the formula for eccentricity. Given the semi-major axis (a) and the period of Earth's orbit (T), one can derive the eccentricity (e) using the relationship e = √(1 - (b²/a²)), where b is the semi-minor axis. The gravitational constant and the mass of the sun are also essential in determining the orbital parameters, confirming that the eccentricity can indeed be calculated with the provided data.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with orbital mechanics and parameters
  • Knowledge of the gravitational constant (G)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Research the derivation of Kepler's laws of planetary motion
  • Study the formula for calculating orbital eccentricity
  • Explore the relationship between semi-major and semi-minor axes
  • Learn about the gravitational constant and its role in orbital dynamics
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Astronomy students, physicists, and anyone interested in celestial mechanics and the mathematical modeling of planetary orbits.

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Given the mass of the sun, the gravitational constant, the period of Earth's orbit, and the semi-major axis of Earth's orbit, is it possible to find the eccentricity of the orbit? If yes, how?
 
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Kindly post your own thoughts on the matter, as per the Physics Forums Guidelines, which you agreed to.
 
I'm really not sure if it can be done. If it can I don't know how. I guess that maybe it can't be done, since there appears to be no way to find to foci.

This is not actually a homework question by the way.
 

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