Login/Sign Up
Home » How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is .
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}.
CBSE | Class 11 | Gravitation | NCERT | Physics
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}.

Earth’s orbit has a radius of r=1.5 \times 10^{11} \mathrm{~m}

Time taken by the Earth for one complete revolution can be

\mathrm{T}=1 year =365.25 days

i.e. T=(365.25 \times 24 \times 60 \times 60) seconds

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

As a result, mass of the Sun, M=\frac{4 \pi^{2} r^{3}}{G T^{2}}

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

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

\Rightarrow M=\frac{1.331 \times 10^{35}}{66.425 \times 10^{3}}=2.004 \times 10^{30} \mathrm{~kg}

As a result, 2.004 \times 10^{30} \mathrm{Kg} is the estimated mass of the Sun.

i

More Material