Suppose that the Moon is held in its orbit around Earth by electrical forces rather than by gravitation. Given the gravitational constant G = 6.673 × 10^-11 N m²/kg², and that the mass of Earth is 5.98 × 10²⁴ kg, and the mass of the Moon is 7.35 × 10²² kg, what electrical charges, -Q on Earth and +Q on the Moon, are necessary to hold the Moon in a circular orbit? A)8.38 × 10¹² C B)5.71 × 10¹³ C C)7.02 × 10¹³ C D)1.19 × 10¹⁴ C

Question

Quizplus · Accepted Answer

The force required to keep the Moon in orbit can be calculated using the gravitational force formula, $F = \frac{Gm_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the Earth and the Moon, and $r$ is the distance between their centers. This force must be equal to the electrical force, $F = \frac{kQ^2}{r^2}$, where $k$ is Coulomb's constant ($8.987 \times 10^9 Nm^2/C^2$), and $Q$ is the charge on each body. By setting the gravitational force equal to the electrical force and solving for $Q$, we find the necessary charge to replace the gravitational attraction with an electrical force.

Suppose That the Moon Is Held in Its Orbit Around