Sleeping Beauties in Theoretical Physics pp 25-42 | Cite as

# Orbits of Planets are Circles!

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## Abstract

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.

## Keywords

Angular Momentum Velocity Space Real Space Elliptical Orbit Central Force
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing Switzerland 2015