Let the orbital radius of a planet be R and let the orbital period of the planet be T. What quantity is constant for all planets orbiting the sun, assuming circular orbits?
A) $T ^ { 2 } / R 3$
B) $T ^ { 2 } / R$
C) $T / R 2$
D) $T ^ { 3 } / R ^ { 2 }$
E) T/R

Question

Let the orbital radius of a planet be R and let the orbital period of the planet be T. What quantity is constant for all planets orbiting the sun, assuming circular orbits? 
A) $T ^ { 2 } / R 3$
B) $T ^ { 2 } / R$
C) $T / R 2$
D) $T ^ { 3 } / R ^ { 2 }$
E)  T/R

Quizplus · Accepted Answer

According to Kepler's third law of planetary motion, the square of the orbital period (T^2) of a planet is directly proportional to the cube of the semi-major axis of its orbit (R^3), which simplifies to the constant ratio $T^2/R^3$ for planets orbiting the same star in circular orbits.

Let the Orbital Radius of a Planet Be R and Let