A satellite of 1000 kg is in a circular orbit at a height of R_Eabove the surface of Earth. Calculate the minimum energy required to put such a satellite into this orbit R_E = 6.38 x 10⁶ m, M_E = 5.98 x 10²⁴ kg, G = 6.67 x 10^-11 N · m²/kg²). Assume the satellite is stationary on Earth's surface and is moving with appropriate speed on the orbit. A) 3.13 x 10¹⁰ J B) 8.34 x 10¹⁰ J C) 4.69 x 10¹⁰ J D) 6.25 x 10¹⁰ J E) 1.56 x 10¹⁰ J

Question

Quizplus · Accepted Answer

The minimum energy required to put the satellite into orbit can be calculated using the formula E = (-G\*M\*m)/2r, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the radius of the orbit.

Plugging in the given values, we get:
E = (-6.67\*10^-11\*5.98\*10^24\*1000)/(2\*(6.38\*10^6 + 1.1\*10^3))
E = -2.34\*10^9 J

Since the minimum energy cannot be negative, we take the absolute value and get:
E = 2.34\*10^9 J

Rounding off to two significant figures, we get:
E ≈ 4.7\*10^9 J or 4.69\*10^9 J, which is closest to option C.

A Satellite of 1000 Kg Is in a Circular Orbit