An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial kinetic energy is needed by the satellite in order to reach a great (i.e., infinite) distance from the Earth, neglecting the effects of air resistance in the atmosphere? (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 10⁶ m.)

Question

Quizplus · Accepted Answer

The correct answer is A because the initial kinetic energy needed by the satellite is equal to the negative of its gravitational potential energy at infinity, which is given by:$$K = -\frac{GM_Em}{r}$$where:* G is the gravitational constant* M_E is the mass of the Earth* m is the mass of the satellite* r is the distance between the satellite and the center of the EarthAt infinity, r approaches infinity, so the potential energy approaches zero and the kinetic energy becomes:$$K = \frac{GM_Em}{\infty} = 0$$Therefore, the initial kinetic energy needed by the satellite is zero.

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