# SUMMARY

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Newton’s law of gravitation: Any two particles with masses m1 and m2, a distance r apart, attract each other with forces inversely proportional to r2 . These forces form an action–reaction pair and obey Newton’s third law. When two or more bodies exert gravitational forces on a particular body, the total gravitational force on that individual body is the vector sum of the forces exerted by the other bodies. The gravitational interaction between spherical mass distributions, such as planets or stars, is the same as if all the mass of each distribution were concentrated at the center.

Gravitational force, weight, and gravitational potential energy: The weight w of a body is the total gravitational force exerted on it by all other bodies in the universe. Near the surface of the earth (mass mE and radius RE), the weight is essentially equal to the gravitational force of the earth alone. The gravitational potential energy U of two masses m and mE separated by a distance r is inversely proportional to r. The potential energy is never positive; it is zero only when the two bodies are infinitely far apart.

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Orbits: When a satellite moves in a circular orbit, the centripetal acceleration is provided by the gravitational attraction of the earth. Kepler’s three laws describe the more general case: an elliptical orbit of a planet around the sun or a satellite around a planet.

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Black holes: If a nonrotating spherical mass distribution with total mass M has a radius less than its Schwarzschild radius RS, it is called a black hole. The gravitational interaction prevents anything, including light, from escaping from within a sphere with radius RS.

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