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.

We know that earth revolves around sun in elliptical orbit due to gravitational force applied by sun, we also know that in one complete revolution earth takes 365.25 days and we are given mean orbital radius of earth around sun, now we know that If a body orbits around other heavier body due to gravitational force of attraction then we have a relation between mass of heavier body, time period of revolution and, radius of the orbit as

Where M is the mass of the heavier body, R is the radius of the orbit, G is universal gravitational Constant and T is time period of revolution

Now here unknown mass is mass of the sun, M =?

Orbital radius of earth around sun, R = 1.5 × 10⁸ km

Time period of one revolution, T = 365.25 days

Converting into seconds

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

So we get time of 1 year as

T = 365.25 × 24 × 60 × 60 s = 3.15 × 10⁷ s

Value of universal gravitational Constant

G = 6.67 × 10^-11 Nm²Kg^-2

Putting these values in above relation

Solving we get the mass of sun as 2.0 × 10³⁰ Kg