Question

How will you weight the sun that estimates its mass? The mean orbital radius of the earth around the sun is

Answer 1

Mean orbital radius of earth around the sun $=1.5\times {10}^{11}m$

$Timeperiod\left(T\right)=1Yr$

$=365\times 24\times 3600s$

Let mass of the sun = Ms

Mass of the planet = m

We know,

Centripetal force = Gravitational force

$\frac{m{v}^2}{r}=\frac{GMsm}{r^2}$

$v²=\frac{GMs}{r}$

$(\frac{2\pi r}{T}{)}^2=\frac{GMs}{r}$

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

Put the values of r , G , and T

$Ms=4\times \left(3.14\right)²\times \frac{(1.5\times {10}^{11}{)}^3}{6.67}\times {10}^{-}11\times (365\times 24\times 3600)$

$\approx 2\times {10}^{30}Kg$