Newton's form of Kepler's law of periods (10-16)
Question 1 of 4
Question
Semimajor axis of the object’s orbit
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Review
The first two of Kepler’s laws describe how a given planet moves in its orbit. His third law, the law of periods, compares the orbital periods of orbits of different sizes:
The square of the period of a planet’s orbit is proportional to the cube of the semimajor axis of the orbit.
This is precisely the relationship that we found for circular orbits in Equation 10-12. Newton was able to show that the law of periods follows from the law of universal gravitation even for elliptical orbits, if we replace the orbital radius r in Equation 10-12 with the semimajor axis a. For objects orbiting the Sun, we must also replace Earth’s mass mEarth with the mass of the Sun:
