Orbits of Planets are Circles!
Yes, it is true. And no, it is not the cheap trick of tilting the paper at an angle to see an ellipse as a circle. The real trick is a bit more sophisticated. It turns out that the trajectory of a particle, moving under the attractive inverse square law force, is a circle (or part of a circle) in the velocity space (The high-tech name for the path in velocity space is hodograph). The proof is quite trivial and, in fact, the entire Kepler problem is quite trivial but for the textbooks making it complicated. If you think straight you can solve it in couple of steps, as I will now show.
KeywordsAngular Momentum Velocity Space Real Space Elliptical Orbit Central Force
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