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

(N/A) The mass of the Sun can be estimated using Kepler's Third Law of planetary motion and the law of universal gravitation.
Given:
Orbital radius of the Earth,$r = 1.5 \times 10^{11} \text{ m}$.
Time period of Earth's revolution,$T = 1 \text{ year} = 365.25 \times 24 \times 60 \times 60 \text{ s} \approx 3.156 \times 10^{7} \text{ s}$.
Gravitational constant,$G = 6.67 \times 10^{-11} \text{ Nm}^2\text{kg}^{-2}$.
The centripetal force required for Earth's orbit is provided by the gravitational force between the Sun and the Earth:
$\frac{M_s m_e}{r^2} = m_e \omega^2 r = m_e \left(\frac{2\pi}{T}\right)^2 r$
Rearranging to solve for the mass of the Sun $(M_s)$:
$M_s = \frac{4 \pi^2 r^3}{G T^2}$
Substituting the values:
$M_s = \frac{4 \times (3.14)^2 \times (1.5 \times 10^{11})^3}{6.67 \times 10^{-11} \times (3.156 \times 10^7)^2}$
$M_s \approx \frac{39.48 \times 3.375 \times 10^{33}}{6.67 \times 10^{-11} \times 9.96 \times 10^{14}}$
$M_s \approx 2.0 \times 10^{30} \text{ kg}$.
Thus,the estimated mass of the Sun is $2.0 \times 10^{30} \text{ kg}$.