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8.13 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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Vishal Baghel | Contributor-Level 10

4 months ago

Orbital radius of the Earth around the Sun, r = 1.5 × 10⁸ km = 1.5 × 10¹¹m

Time taken by the Earth to complete 1 revolution around the Sun, T = 1 year = 365.25 days = 365.25 $\times$ 24 $\times 24 \times 60 \times 60 s$

Universal gravitational constant, G = 6.67 $\times 10^{- 11}$ N $m^{2} / {k g}^{2}$

Thus, mass of the Sun can be calculated as,

M = $\frac{4 π^{2} r^{3}}{G T^{2}}$ = $\frac{4 {\times {(3.1416)}^{2}}^{} {\times (1.5 \times 10^{11})}^{3}}{6.67 \times 10^{- 11} {\times (365.25 \times 24 \times 60 \times 60)}^{2}}$ = 2.0 $\times 10^{30}$ kg

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8.13 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.