Conservation of Energy with an Ellipse

AI Thread Summary
Mechanical energy is conserved in an elliptical orbit due to gravity being a conservative force, which means that any change in kinetic energy (K.E.) is balanced by a change in gravitational potential energy (U_g). This conservation applies to the entire system of both bodies involved in the orbit. The discussion raises a question about whether the conservation principle remains valid when accounting for the motion of the larger planet, suggesting that the relationship may still hold despite added complexity. Ultimately, the conservation of mechanical energy in elliptical orbits is fundamentally linked to the nature of gravitational forces. Understanding these principles is crucial for analyzing orbital mechanics.
SprucerMoose
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Gday,

This may be a trivial questiom, but I just cannot figure it out.

Why is mechanical energy conserved with an elliptical orbit? I understand that the mechanical energy of the system, i.e. both bodies, is conserved, but how is this isolated to the satellite's mechanical energy being conserved?
 
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Hang on, I think I figured it out.

Is it simply because gravity is a conservative force, thus any change in K.E. = change in Ug, therefore mech energy conserved?

Does this get more complicated if we consider the little motion of the larger planet, or does this simple relationship still hold?
 
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