Final answer:
Kepler's third law of planetary motion, which describes the proportional relationship between a planet's orbital period and the semi-major axis of its orbit, was supported by Newton's explanation of gravitational force as the cause behind this relationship.
Step-by-step explanation:
The law announced by Kepler that was supported by Newton's laws is C) the law of orbits, specifically Kepler's third law of planetary motion. This law states that there is a proportional relationship between the square of a planet's orbital period (P) and the cube of the semi-major axis (a) of its orbit, represented by the equation P2 = a3. Newton's law of universal gravitation further explained this by determining that gravitational force was the cause behind the relationship that Kepler had observed. Newton's formula incorporates the masses of the objects, showing the connection between the motion described in Kepler's laws and the force of gravity.