How do you calculate the kinetic and potential energies of the Earth at the perihelion and aphelion?(adsbygoogle = window.adsbygoogle || []).push({});

Given that the Earth's orbit is nearly circular

GMm/R^2 = m(v^2)/R where M = sun's mass, m = Earth's R = orbital radius

so

v = √(GM/R)

The kinetic energy, E, would be

E = (1/2)m(v^2) = (1/2)GMm/R

The Earth's potential energy, U, would be

U = -GMm/R

However, the change in E between the perihelion and aphelion would be

(1/2)GMm/[(1/R) - (1/r)] where R and r are the respective orbital radii;

while the change in U would be

-GMm/[(1/R) - (1/r)] .

Given conservation of energy, the last two terms can not both be right.

This brings me back to the original question.

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# Earth's Orbit

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