General Planetry Motion, Lecture Notes - Mechanics 1, Study notes of Mechanics

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Porevtial Energi of a. Spheve and Particle aq-l mt Consider wy particle of mass mM ay wie is bcated at a. nad ius ¥ ye) Brom 4e certey oR ao Romegeneou s solid > opheve_ of ' mass M and yadius R. ‘| (ns | Case T: < >R Figure The force on a par- ticle when it is outside a uniform . : : solid sphere is given by GMm/r? Solid spheve is mad ep of and is directed toward the center. Q \ Q 4, The force on the particle when it is . inside such a sphere is proportional may > el S Semmne MaKe NW to rand goes to zero at the center. Q ~o vadins R. ner - Since. force ond potential, ve tow Mell depend ov on mass of sRel( and distence +o pokicle mM Brom center ; F=-GmM ¢ (vzR) x3 Us -Gmm (wz R) Cv Case it: e§ R ~From cor vesolt on spherical ells , te force Mm aw pavticle is doe nly a\\ the mass hetucenw cr and CE. No Savce doe to Be mass between cerand BR. E= Gm wir) (esr) 4