How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 10⁸ km.

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Solution

Given: The mean orbital radius of the earth around the sun is 1.5× 10 8 km.

The mass of the sun is given as,

T 2 =( 4 π 2 G M s ) r 3 M s = 4 π 2 r 3 G T 2

Where, the gravitational constant is G, the mass of the sun is M s , the orbital radius of the earth around the Sun is r and the time taken by the earth to complete one revolution around the Sun is T.

Time taken by earth to rotate around the earth is 365 days.

By substituting the given values in the above equation, we get

M s = 4 π 2 × ( 1.5× 10 11 ) 3 6.67× 10 −11 × ( 365.25×24×60×60 ) 2 = 133.24× 10 33 6.64× 10 4 =2.0× 10 30 kg

Thus, the mass of the sun is 2.0× 10 30 kg.

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