Question

A satellite of mass 120 kg is in circular orbit at a height h = r above the surface of earth, where r is the radius of earth. The radius and mass of earth are 6.4 x 10⁶ m and 6.0 x 10²⁴ kg, respectively. The gravitational potential energy of the satellite-earth system is most nearly?

1) -1.51 x 10¹⁰ J
2) -3.75 x 10⁹ J
3) 3.75 x 10⁹ J
4) 7.50 x 10⁹ J
5) 1.51 x 10¹⁰ J

Answer 1

The gravitational potential energy of a 120 kg satellite in circular orbit at a height equal to the radius of Earth is calculated using the formula U = -G * (m1 * m2) / r, resulting in approximately -1.51 x 10^10 J.

Step-by-step explanation:

The question is about calculating the gravitational potential energy of a satellite of mass 120 kg in circular orbit at a height equal to the radius of Earth. The formula for gravitational potential energy (U) is U = -G * (m1 * m2)/ r, where G is the gravitational constant (6.674 x 10-11 Nm2/kg2), m1 and m2 are the masses of the satellite and Earth, and r is the distance between the centers of the masses, which in this case is 2r (twice the radius of Earth).

Using the given values, we have U = -6.674 x 10-11 * (120 kg * 6.0 x 1024 kg) / (2 * 6.4 x 106 m). Calculating this gives a value of U ≈ -1.51 x 1010 J, which means that the correct answer is option 1).