Can Kepler's laws apply for circular motions? (First law states planets take an elliptical orbit)

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    $\begingroup$ a circle is an ellipse. $\endgroup$ – Trebor Aug 21 '18 at 4:28

Yes, they apply. Kepler's first law states planets take an elliptical orbit, and circles are special cases of ellipses. In principle, one can also call a circle an ellipse with eccentricity zero.


The circle (eccentricity $\epsilon = 0$) and the ellipse ($0<\epsilon <1$) are two of the four conic sections; the others being the parabola ($\epsilon = 1$) and the hyperbola ($\epsilon >1$).

All four conic sections are possible trajectories for orbits with the Sun at one focus.
You can think of a circle as a degenerate ellipse with the two foci that an ellipse has being at the same position for a circle.

The equal areas in equal times law is also followed for all of the conic section orbits as angular momentum is conserved for each of them.

The period -distance law is only obeyed for the bound obits - circular and elliptical.


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