Satellites: Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10^-11 N ∙ m²/kg²) The mass of Ekapluto is closest to A) 1.0 × 10²² kg. B) 3.0 × 10²² kg. C) 1.0 × 10²³ kg. D) 3.0 × 10²³ kg. E) 1.0 × 10²⁴ kg.

Question

Quizplus · Accepted Answer

According to Newton's law of gravitation, F = G(m1m2)/(r^2). We know the radius and period of orbit of both moons. Using the equation v = 2πr/T, we can find their velocities, and from there we can find the centripetal force needed for them to stay in orbit, which is also equal to the gravitational force between the moon and Ekapluto. Solving for the mass of Ekapluto using the gravitational constant G, we get a value of approximately 3.0 × 10^23 kg, which is closest to choice D.

Satellites: Ekapluto Is an Unknown Planet That Has Two Moons