write the law T2 a r3
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period (T) of a planet is proportional to the. cube of the average orbital radius (R), or. ● T2 α R3, or. ● T2/R3 = constant = 4π2/GM
Explanation:
Kepler's Third Law. Kepler's Third Law relates the period of an orbit to the radius of an orbit, if the orbit is circular, and to the semimajor axis if the orbit is elliptical. Let's derive it for a circular orbit, assuming a mass m is orbiting a mass M, with r being the radius of the orbit.
Kepler's 3rd law is a mathematical formula. It means that if you know the period of a planet's orbit (P = how long it takes the planet to go around the Sun), then you can determine that planet's distance from the Sun (a = the semimajor axis of the planet's orbit).
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