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A satellite of the Earth has a mass of 101 kg and is at an altitude of 1.98×10^6 m. (Assume that U=0 as r→[infinity].) (a) What is the potential energy of the satellite-Earth system?____ J (b) What is the magnitude of the gravitational force exerted by the Earth on the satellite?___- N (c) What force does the satellite exert on the Earth? ____N

User Saeb Amini
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Final answer:

The potential energy of the satellite-Earth system is -9.1×10^9 J, the gravitational force exerted by the Earth on the satellite is 815 N, and the force that the satellite exerts on the Earth is also 815 N.

Step-by-step explanation:

The subject of this question is the gravitational interaction between the Earth and a satellite, specifically examining potential energy, gravitational force, and the principle of action and reaction.

(a) The potential energy of the satellite-Earth system can be calculated using the formula -GMm/r, where G is the gravitational constant (6.673×10^-11 N(m/kg)^2), M is the mass of the Earth (5.972×10^24 kg), m is the mass of the satellite (101 kg), and r is the distance from the center of the Earth to the satellite, which is the radius of the Earth (6.371×10^6 m) plus the altitude of the satellite (1.98×10^6 m). After calculating, we get the potential energy as -9.1×10^9 J.

(b) The magnitude of the gravitational force exerted by the Earth on the satellite can be calculated using the formula GMm/r^2. After calculating, we get the gravitational force as 815 N.

(c) According to Newton's third law of motion, the force that the satellite exerts on the Earth is equal in magnitude and opposite in direction to the force that the Earth exerts on the satellite. So, the satellite also exerts a force of 815 N on the Earth.

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User Bordz
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