Recent content by antythingyani

The 1-e^2 terms cancel and then again we will be left with a/r isn't it?!?

we can express r as a function of semimajor axis (a) and the true anomaly (theta). In that case maybe finding a way to turn dt into dtheta would be handy... or trying to express theta as a function of t.

Two bodies with masses m2 and m1, m2=a.m1 and m2>m1 orbit each other in circular orbits. if the barycenter moves at a speed v with respect to an inertial reference frame, What should be the relative speed of the bodies so that m1’s orbit in this inertial frame will have cusps?

The question is basically : derive the average of (a/r)^3 taking time as an independent variable. (where a is the semi major axis and r is the distance in an elliptical keplerian orbit.

Summary:: Averaging (a power of) semimajor axis to position ratio wrt to time - celestial mechanics I evaluated it this far, but i don't know how to change the dt to d theta ... the final solution is supposedly (1-e^2)^-(3/2) . Any help will be appreciated. [Image re-inserted with correct...

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