1.

A planetof massm movesin a ellipticalorbitaroundan unknownstarof massM suchthatitsmaximuman minimumdistances fromthe starare equaltor_1 and R_2respectively. Theangularmomentumof theplanetrelativetothe centreof thestar is

Answer»

`m sqrt((2GM r_1 r_2)/(r_1 +r_(2)))`
`0`
`m sqrt((2GM(r_1+r_(2)))/(r_1r_2)`
`sqrt((2GM mr_1)/((r_1+r_2)r_(2))`

Solution :` (##ARH_5Y_SP_17_E01_033_S01.png" width="80%">
ACCORDING to theof conservationof ANGULARMOMENTUM
` mv _1r_1 = mv _2 r_2 `
` impliesv_2 = (v_1r_1)/(r_2)`
FROMTHE lawof conservationof totalmechanicalenergy .
`(-GMM)/(r_1)+(1)/(2)mv _1^(2) =-(GMm)/(r_2)+(1)/(2) mv_(2)^(2)` .... (ii )
FromEqs.(i )and (ii )we get
`V_1 =sqrt((2Gmr_2)/((r_1 +r_2)r_1)`
Angularmomentum,
` L = mv _1 r_1 = m (sqrt((2GMr_2)/((r_1+r_2)r_1)))xxr_1`
` L= m sqrt((2GMr_1 r_2)/(r_1 +r_2))`


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