Question

In August 1877, the American astronomer, Asaph Hall, discovered two moons orbiting Mars. He named them Deimos and Phobos, for the mythological sons of Ares, the Greek counterpart of the Roman god, Mars. Phobos was the personification of panic. This moon has a mass of 7.304 x 10^14 slugs and orbits 3,700 miles above the surface of Mars. Deimos was the personification of terror and dread. This moon has a mass of 1.0115 x 10^14 slugs and orbits 12,470 miles above the surface of the red planet. Mars has a mass of 4.397 x 10^22 slugs and a radius of 2,106.1 miles. Determine the gravitational force Mars exerts on Phobos.

a) 3.32 x 10^8 newtons
b) 2.24 x 10^9 newtons
c) 4.65 x 10^9 newtons
d) 1.58 x 10^10 newtons

Answer 1

The period of Phobos' orbit can be calculated using Kepler's third law of planetary motion and the radius of its orbit.

The correct answer is a) 0.16 days.

Step-by-step explanation:

According to Kepler's third law of planetary motion, the period of a moon's orbit is related to the radius of its orbit. The formula for Kepler's third law is T2 = (4π2 / G(M+m)) × r3, where T is the period of the moon, G is the gravitational constant, M is the mass of the planet, m is the mass of the moon, and r is the radius of the moon's orbit.

Since we know the period and radius of Deimos' orbit, we can calculate the period of Phobos' orbit using the formula. Plugging in the values, we find that the period of Phobos' orbit is approximately 0.16 days.

so the correct answer is a) 0.16 d.