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How to Calculate the Orbital Period of a Comet Given its Closest and Furthest Orbital Distance

-- David | April 20, 2020

Question:

If you observe a comet going around the sun and you know the exact mathematical units in which it is closest to the sun and when it is farthest from the sun, then how do you calculate its sidereal orbit time?

-- David

Answer:

Given the minimum and maximum distance of the orbit of a comet in an elliptical orbit, you can use Kepler’s Third Law and the definition of the semi-major axis of an ellipse to calculate its orbital period. The semi-major axis of an ellipse is related to the minimum and maximum distance of a comet from the Sun as follows:

Finally, Kepler’s Third Law of orbital motion states that the square of the orbital period of a comet is proportional to the cube of its semi-major axis. The full equation looks like the following:

where P is the orbital period of the comet, is the mathematical constant pi, a is the semi-major axis of the comet’s orbit, G is the gravitational constant, M is the mass of the Sun, and m is the mass of the comet. Since M is much greater than m, you can safely ignore the mass of the comet in this equation. Solve for P in the above equation and you have solved for the orbital period of a comet.

-- Jeff Mangum

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