An 8000 kg satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of 100 km above the surface of the Earth. The gravitational potential energy of the satellite in the circular orbit is (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 10⁶ m) A) −5.01 × 10¹¹ J. B) −4.92 × 10¹¹ J. C) −4.75 × 10¹¹ J. D) −4.02 × 10¹¹ J. E) −3.85 × 10¹¹ J.

Question

Quizplus · Accepted Answer

The gravitational potential energy of an object in orbit can be found using the formula:

U = -G*M*m/r

where U is the gravitational potential energy, G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the centers of the two objects.

In this problem, we are given that the mass of the satellite is 8000 kg, the altitude of the orbit is 100 km (which gives us the distance between the centers of the Earth and the satellite), and the values of G, M, and R are also given.

Using the formula and plugging in the values, we get:

U = -6.67 × 10^-11 * 5.97 × 10^24 * 8000 / (6.37 × 10^6 + 100000)

U = -4.92 × 10^11 J

Therefore, the gravitational potential energy of the satellite in the circular orbit is -4.92 × 10^11 J. The best choice is B.

An 8000 Kg Satellite Is Launched from the Surface of the Earth