- Kepler's 1st law:
A planet orbits the
Sun in
an ellipse with the
Sun at one
ellipse
focus.
- Kepler's 2nd law:
The planet orbital radius sweeps out
equal areas in equal times.
This means the planets move faster the nearer they are to the Sun, fastest at perihelion, and slowest at perihelion.

- Kepler's 3rd law:
The square of the
orbital period is proportional to the
cube of the
semi-major axis
of the elliptical orbit.
The semi-major axis is mean
mean orbital radius
a conventional definition.

The formula version for the limit that Kepler's 3rd law is exact (see discussion below) isP_y = [1/sqrt(M/M_☉)]*r_AU**(3/2) ,

where P_y is orbital period in Julian years to 6-digit accuracy/precision, M_☉ is solar mass unit = 1.98855*10**30 kg, and r_AU is mean orbital radius in astronomical units. Note Julian year = 3652.25 exactly by definition.

Caption: Kepler's 3 laws of planetary motion are given below. The first 2 of Kepler's 3 laws of planetary motion illustrated compactly in the adjacent diagram.

Kepler's 3 laws of planetary motion:

The 3 laws also are exact for ideal gravitationally-bound gavitational two-body system in the limit of one body being infinitely massive. The infinitely massive body remains at one ellipse focus while the other body orbits it obeying the 3 laws.

Credit/Permission: ©
Han-Kwang Nienhuys (AKA User:Hankwang),
2007 /
Creative Commons
CC BY-SA 3.0.

Image link: Wikimedia Commons.

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