Question

A planet is in a circular orbit around the sun. Use Newton's law of gravity and his second law of motion to calculate the period of the planet (in day). Data: Mass of sun = 1.989 e+30 kg; Mass of planet = 6.0 e+24 kg; Orbit radius = 1.496 e+11 m.

Answer 1

Given Mass os sun,M = 1.989*10³⁰ kg

mass of planet ,m =6.0*10²⁴ kg

Radius ,r = 1.496*10¹¹ m

From Newton's law of Gravity

F = GMm/r² ---------------(1)

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From Newton's 2nd Law ,F =ma

but in a circular motion ,acceleration in centripetal accleration a_c =v²/r

so Force is centripetal Force

F=mv²/r ---------------(2)

Now to stay in a circular orbit Gravitational Force should be equal to centripetal force

From(1) and (2)

mv²/r = GMm/r²

v² = GM/r

Velocity =distance/Time

in circular motion distance traveled is circumference =2r an dtime is Time period

Convert sec to days ,divide by (60*60*24)

ANSWER:

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