Orbits of Planets are Circles!

  • Thanu Padmanabhan
Part of the Lecture Notes in Physics book series (LNP, volume 895)


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.


Angular Momentum Velocity Space Real Space Elliptical Orbit Central Force 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thanu Padmanabhan
    • 1
  1. 1.Inter-University Centre for Astronomy and AstrophysicsPuneIndia

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