a planet moves around the sun in nearly circular orbit its speed of revolution depends upon radius of orbit 2.mass(m)of the sun 3.gravitational constant(g) show that T2 is directly propotional to R3

CBSE Class 11-science Answered

Asked by krishnamurthyganapathy1968 | 13 Jun, 2019, 06:17: PM

Expert Answer

when a planet moves in a circular orbit aroun the sun, centripetal force equals the gravitational attraction force

between planet and sun.

Hence we have,

begin mathsize 14px style m v squared over R space equals space G fraction numerator m M over denominator R squared end fraction space.................... left parenthesis 1 right parenthesis end style

where m is mass of planet, M is mass of sun, v is orbital velocity, R is orbital radius and

G is universal gravitational constant.

If T is period of revolution, then we have, v = (2πR) / T ......................(2)

By substituting v from eqn.(2) in eqn.(1) and after simplification, we get,

begin mathsize 14px style T squared equals space fraction numerator 4 straight pi over denominator G space M end fraction space R cubed end style

Answered by Thiyagarajan K | 13 Jun, 2019, 07:09: PM

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