Question
Tue March 10, 2015 By: Yashrananaware

Assuming that earths orbit is a circle of radius 1.5 * 10^8 km calculate the mass of sun?

Expert Reply
Priyanka Kumbhar
Wed March 11, 2015
begin mathsize 14px style The space distance space between space sun space and space earth comma space straight r space equals space 1.5 space cross times 10 to the power of 8 space km space equals space 1.5 space cross times 10 to the power of 11 space straight m space straight G space equals space 6.67 space cross times space 10 to the power of negative 11 end exponent space Nm squared space kg to the power of negative 2 end exponent straight T space equals space 365 space cross times space 24 space cross times space 60 space cross times space 60 space equals space 31.536 space cross times space 10 to the power of 6 space straight s straight G fraction numerator straight M subscript straight s straight M subscript straight e over denominator straight r squared end fraction space equals straight M subscript straight e rω squared space equals space space straight M subscript straight e straight r open square brackets fraction numerator 2 straight pi over denominator straight T end fraction close square brackets squared straight M subscript straight s space equals space fraction numerator 4 straight pi squared straight r cubed over denominator GT squared end fraction straight M subscript straight s space equals space fraction numerator 4 space cross times space left parenthesis 3.14 right parenthesis squared space cross times space left parenthesis 1.5 space cross times 10 to the power of 11 right parenthesis cubed over denominator 6.67 space cross times space 10 to the power of negative 11 end exponent space cross times space open parentheses 31.536 space cross times space 10 to the power of 6 close parentheses squared end fraction straight M subscript straight s space equals 2.006 space cross times space 10 to the power of 33 space kg Hence comma the space mass space of space the space Sun space is space 2.006 space cross times space 10 to the power of 33 space kg space space space space space space space space space space space space space space space space 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