Question

Two particles moving under the influence of their mutual gravitational force describe circular orbits about one another with period r. a. Use Newton's second law to find an expression for ro, the radius of the particles' orbit around each other in terms of r b. Write an expression for the total energy of the system. (You don't have to use your answer to part a; keep it as ro.) c. Both particles are pushed inward such that their separation is ro, while the system's energy remains the same. Find an expression for r d. Set up an equation that you would use to find r(t). DO NOTATTEMPT TO SOLVE IT.

Answer 1

8 m,am Let massm, and my are moving Under the mutual attraction from Centre of urdhero/2) . Let the speed of particle is v. 1. Статьи » Госдуха bu мам, фу a mivo? No To Time perio of revolution. Т. 2т Rolb) (*) - Сотт та утел

③ Total Energy of two body gruenby = - Grimer F ) when distonde between them d= rol force between them, fg: Gooying * : 4 , 4- р - насу ча In equilibrium . fg a fe mw2 - 44 m ) varam) But here particle are moving unward from robotol Since_mv² Gm² = ma acceleration is along radial direction using angular momentum conservation 1. Mvoro = mur ) Nr= voro AV en Vo le . - memvol² + Gm² = m du ha et r: 2012 Iva have to 3 er = am [$-$] lv Sar: amic t to] de T32 IV: 2 Vo a mržan tro v B = GMT-?cm- t )] li en del = 6m [²( 2 ) - ( 4 2 - 1)] date Gm [2love to the hos Da Ghosho so ?w= samen [ 26 ] at
In section C, by substituting the value
T = 70/2, V = GM/ro(3/ro - 1)
here view is radial velocity.