Question

Calculate the mass of the sun given that the distance between sun and the earth is 1.49 x 10¹¹ m and G = 6.66 x 10-¹¹ M.K.S. units. Take the year to consist of
365 days.
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Answer 1

Answer:

We can compute the mass of the sun given the mass of earth, distance between the sun and earth and the gravitational force between sun and earth. The force of gravity between sun and earth is given by the following equation.

F = (G*M*m)/R*R

G is gravitational constant, and its value is 6.67 * 10^(-11) Nm^2/kg^2.

M is the mass of Sun (which we need to find out)

m is the mass of Earth (6 * 10^24 kg approx)

R is the average distance of earth from sun (14.96 * 10^10 meters)

F is the force of gravity between sun and earth (3.6 * 10^22 N)

All the quantities are in MKS system. Try to put all these values in above equation and solve for M. You will get that M is 2.013207 * 10^30 kg.

Explanation:

Answer 2

Answer:

The mass of the sun is 1.972×10²²kg.

Explanation:

The orbital velocity of the earth around the sun is given as,

$v=\sqrt{\frac{GM}{r} }$          (1)

Where,

v=orbital velocity of the earth around the sun

G=universal gravitational constant=6.6×10⁻¹¹Nm²/kg²

M=mass of the sun

r=radius of the earth

Also, the time period(T) is given as,

$T=\frac{2\pi r}{v}$      (2)

Using equation (1) in equation (2) we get;

$T=\frac{2\pi r}{\sqrt{\frac{GM}{r} }}$

$M=\frac{4\pi^2 r^3}{GT^2}$       (3)

From the question we have,

r=1.49×10¹¹ m

T=365 days

By substituting the required values in equation (3) we get;

$M=\frac{4\pi^2\times (1.49\times 10^1^1)^3}{6.6\times 10^-^1^1\times (365\times 24\times 3600)^2}$

$M=1.972\times 10^2^2kg$

Hence, the mass of the sun is 1.972×10²²kg.