Applying Gauss's Law for Gravitation. Using Gauss's law for gravitation ∮g⃗ ⋅dA⃗ =−4(pi)GMenclosed where Menclosed is the total mass enclosed within the closed surface, show that the following statements are true: (a) For any spherically symmetric mass distribution with total mass M, the acceleration due to gravity outside the distribution is the same as though all the mass were concentrated at the center. (b) At any point inside a spherically symmetric shell of mass, the acceleration due to gravity is zero. (c) If we drill a hole through a spherically symmetric planet to its center, and if the density were uniform, we would find that the magnitude of g⃗ is directly proportional to the distance r from the center.
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Applying Gauss's Law for Gravitation. Using Gauss's law for gravitation ∮g⃗ ⋅dA⃗ =−4(pi)GMenclosed where Menclosed is the total mass enclosed within the closed surface, show that the following statements are true: (a) For any spherically symmetric mass distribution with total mass M, the acceleration due to gravity outside the distribution is the same as though all the mass were concentrated at the center. (b) At any point inside a spherically symmetric shell of mass, the acceleration due to gravity is zero. (c) If we drill a hole through a spherically symmetric planet to its center, and if the density were uniform, we would find that the magnitude of g⃗ is directly proportional to the distance r from the center.
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