How will you ‘weigh the sun’, that is estimate its mass?


How will you 'weigh the sun', that is estimate its mass? The mean orbital radius of the earth around the sun is $1.5 \times 10^{8} \mathrm{~km}$.


Orbital radius of the Earth around the Sun, $r=1.5 \times 10^{11} \mathrm{~m}$

Time taken by the Earth to complete one revolution around the Sun,

$T=1$ year $=365.25$ days

$=365.25 \times 24 \times 60 \times 60 \mathrm{~s}$

Universal gravitational constant, $\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$

Thus, mass of the Sun can be calculated using the relation,

$M=\frac{4 \pi^{2} r^{3}}{G T^{2}}$

$=\frac{4 \times(3.14)^{2} \times\left(1.5 \times 10^{11}\right)^{3}}{6.67 \times 10^{-11} \times(365.25 \times 24 \times 60 \times 60)^{2}}$

$=\frac{133.24 \times 10}{6.64 \times 10^{4}}=2.0 \times 10^{30} \mathrm{~kg}$

$6.64 \times 10$

Hence, the mass of the Sun is $2 \times 10^{30} \mathrm{~kg}$.


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