The elliptical orbits and inverse-square law forces.

[d-richard]

Greetings,
I read a chapter in the book College Physics by Vuille and Serway explaining the laws of planetary motion in terms of the universal law of gravitation. The first law stated that planets move in an elliptical orbit and the book's explanation was that all objects bound by an inverse-square law move in ellipses if orbiting, not in circles. Could anyone please explain why inverse-square law forces cause this effect? Thanks.

 

[A.T.]

in ellipses if orbiting, not in circles.

Circles are ellipses.

 

[UltrafastPED]

Kepler's Laws of Planetary Motion: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

and: http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Newton and Kepler: http://csep10.phys.utk.edu/astr161/lect/history/Newtonkepler.html

And here is a derivation of Kepler from Newton:
https://www.uu.edu/dept/math/SeniorPapers/09-10/DavisEmily.pdf

 

[d-richard]

thanks for the links, and yeah I forgot that circles are ellipses. Thanks for reminding me