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Motion In Straight Line

Question
CBSEENPH11017780

Estimate the mass of the sun from the data given below:

(i) Time period of revolution of the earth is 365 days

(ii) Radius of the orbit of the earth is 1 A.U.

Solution
Earth revolves around the sun.
The necessary centripetal force required for the orbital motion of Earth around the Sun is provided by gravitational pull of the sun,
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rightwards double arrow              straight M space equals space fraction numerator straight omega squared straight r cubed over denominator straight G end fraction equals fraction numerator 4 straight pi squared straight r cubed over denominator GT squared end fraction 
                    straight M equals fraction numerator 4 straight pi squared left parenthesis 1.5 cross times 10 to the power of 11 right parenthesis squared over denominator left parenthesis 6.67 cross times 10 to the power of negative 11 end exponent right parenthesis space left parenthesis 365 space cross times space 86400 right parenthesis squared end fraction 
                     space space equals 2 cross times 10 to the power of 30 kg
This is the required mass of the sun.