An 8000 kg satellite is launched from the surface of the earth,and injected into outer space a long distance from the earth.The kinetic energy needed to launch the satellite into outer space is (G = 6.67 $\times$ 10^-11 Nm²/kg², Me = 5.98 $\times$ 10²⁴ kg, Re = 6.38 $\times$ 10⁶ m) A) 5.00 $\times$ 10¹¹ J. B) 4.03 $\times$ 10¹¹ J. C) 3.57 $\times$ 10¹¹ J. D) 3.00 $\times$ 10¹¹ J. E) 2.35 $\times$ 10¹¹ J.

Question

Quizplus · Accepted Answer

The kinetic energy needed to launch the satellite into outer space is equal to the gravitational potential energy of the satellite at the surface of the earth. The gravitational potential energy of a satellite of mass m at a distance r from the center of the earth is given by:$$U = -G * \frac{Mm}{r}$$where G is the gravitational constant, M is the mass of the earth, and r is the distance from the center of the earth to the satellite.At the surface of the earth, r = Re, so the gravitational potential energy of the satellite is:$$U = -G * \frac{Mm}{Re}$$The kinetic energy needed to launch the satellite into outer space is equal to the negative of the gravitational potential energy, so:$$K = -U = G * \frac{Mm}{Re}$$Substituting the given values, we get:$$K = (6.67 * 10^{-11} Nm^2/kg^2) * \frac{(5.98 * 10^{24} kg)(8000 kg)}{6.38 * 10^6 m}$$$$K = 5.00 * 10^{11} J$$Therefore, the correct answer is A.

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