() 1 dr 2mE 2GMM2 1 1 + r2 %3D p² d0 (2 2.

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The equations of motion of the orbits of the planets due to their gravitational force with the sun are given as follows (in polar coordinates): [attached to the figure]. With M solar mass, m planetary mass, E energy of the planetary incident, l angular momentum system, and G is the universal gravitational constant. Find the solution of the above differential equation and express it in r as a function θ, r = r(θ). This solution depicts an elliptical curve (conical wedge) as the shape the orbits of the planets around the sun.
2
() -
1 dr
2mE
2GMM² 1
+
r2
1
r2 d0
(2
Transcribed Image Text:2 () - 1 dr 2mE 2GMM² 1 + r2 1 r2 d0 (2
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