Math in the Physical Sciences

Astronomy and Math

What are Kepler’s Laws of Planetary Motion?

A great deal of mathematics went into the formulation of Kepler’s Laws of Planetary Motion. These laws were devised by German astronomer and mathematician (and Danish astronomer Tycho Brahe’s [1546-1601] assistant) Johannes Kepler (1571–1630). He presented the first and second laws in his work Astronomia nova (New Astronomy) in 1609; the third law was published in 1619 in Harmonice mundi. The three laws are as follows:

Kepler’s first law (or law of elliptic orbits)—Each planet moves about the Sun in an orbit that is an ellipse, with the Sun at one of the two foci of the ellipse.

Kepler’s second law (or the law of areas)—An imaginary straight line joining a planet to the Sun will sweep out equal areas of the ellipse in equal periods of time.

Kepler’s third law (or the harmonic law)—The square of the period of a planet’s revolution is directly proportionate to the cube of the semi-major axis of its orbit.


Halley’s Comet, named after Edmond Halley, last appeared near Earth in 1986 and will be seen again in the night sky in 2062.


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