An 825-kg space vehicle is circling Earth in a circular orbit with a radius of 10,300 km. Its orbit is to be changed to a larger circle with a radius of 17,400 km. How much energy is required to accomplish this? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 x 10^-11 N·m²/kg². A) 1.00 × 10⁹ J B) 1.30 × 10¹⁰ J C) 6.51 × 10⁹ J D) 4.45 × 10⁹ J E) 4.50 × 10¹⁰ J

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Quizplus · Accepted Answer

The change in potential energy is:$$\Delta U = -\frac{GMm}{r_f} + \frac{GMm}{r_i}$$$$= -\frac{(6.67 	imes 10^{-11} 	ext{ N$\cdot$m}^2/	ext{kg}^2)(5.97 	imes 10^{24} 	ext{ kg})(825 	ext{ kg})}{17,400 	imes 10^3 	ext{ m}} + \frac{(6.67 	imes 10^{-11} 	ext{ N$\cdot$m}^2/	ext{kg}^2)(5.97 	imes 10^{24} 	ext{ kg})(825 	ext{ kg})}{10,300 	imes 10^3 	ext{ m}}$$$$= 1.30 	imes 10^{10} 	ext{ J}$$

An 825-Kg Space Vehicle Is Circling Earth in a Circular