The gravitational force on the particle is due only to the mass of the earth that is inside the particle’s instantaneous displacement from the center of the earth, r. The net effect of the mass of the earth outside r is zero (See Problem 6.2). 3rπρ=43M4ˆˆ3rrFGmrekreπρ=−GThe force is a linear restoring force and induces simple harmonic motion. r FG23224mTkGππω===The period depends on the earth’s density but is independent of its size. At the surface of the earth, 343eeeGMmGmmgRRR⋅43eGgR=626.38 1011.9.83600eRmhrThgmss−××≈⋅4r6.4
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