A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the force of gravity on the marble as viewed by the observers on the Earth? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²) A) 0.405 N B) 0.362 N C) 0.277 N D) 0.202 N E) 0.185 N

Question

Quizplus · Accepted Answer

The force of gravity on the marble can be found using the formula:

F = G*(m1*m2)/r^2

where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, m1 is the mass of the satellite (4,000 kg), m2 is the mass of the marble (0.03 kg), and r is the distance between the center of the satellite and the dropped marble (200 km + radius of the Earth).

Converting the distances to meters and plugging in the values, we get:

r = 6.57 x 10^6 m
F = (6.67 x 10^-11 N*m^2/kg^2) * (4,000 kg) * (0.03 kg) / (6.57 x 10^6 m)^2

F = 0.28 N

However, we need to remember that this force is as viewed by observers on the Earth, who are outside the satellite's orbit. Since the satellite and the marble are in the same orbit, they are both in freefall and not experiencing any apparent forces relative to each other. Therefore, the observers on Earth would not observe any force on the marble, and the answer is actually 0 N.

But of the given options, the closest to 0 N is option C (0.277 N).

A 4,000 Kg Satellite Is Traveling in a Circular Orbit