Chapter 7, Problem 77A

To determine

To Explain: The mass of dwarf planet Pluto was not known until its satellite was discovered.

Explanation of Solution

Introduction:

From Kepler’s third law of planetary motion:

  $T^2=\frac{4{\pi }^2}{Gm}{r}^3$

Where, $G$ is the gravitational constant, $r$ is the orbital radius of the satellite, and m is the mass of the planet and T is the orbital period of the satellite.

From Kepler’s law, one can conclude that the mass of the planet can only be calculated when the orbital period and the orbital radius of its satellite is known.

Conclusion:

Thus, the mass of dwarf planet Pluto was not known until its satellite was discovered.