Question

The mass of the earth is $6\times {10}^{24}kg$. The distance between the earth and the Sun is $1.5\times {10}^{11}m$. If the gravitational force between the two is $3.5\times {10}^{22}N$, what is the mass of the Sun?
Use $G=6.7\times {10}^{-11}N{m}^2{kg}^{-2}$

Answer 1

Step 1, Given data

Mass of the earth = $6\times {10}^{24}kg$

Distance between the earth and sun = $1.5\times {10}^{11}m$

Gravitational force = $3.5\times {10}^{22}N$

Step 2, Finding the mass of sun

The gravitational force between the Sun and the Earth can be found using the formula,
$F=G\frac{M_e{M}_s}{R^2}$
where $M_e$ and $M_s$ are the masses of the Earth and the Sun, respectively.

Now,

Putting all the values in the formula

We get,
$3.5\times {10}^{22}=(6.7\times {10}^{-11})\frac{(6\times {10}^{24})\times M_s}{(1.5\times {10}^{11}{)}^2}$

Or, it can be written as

$⟹M_s=\frac{(3.5\times {10}^{22})\times (1.5\times {10}^{11}{)}^2}{(6.7\times {10}^{-11})\times (6\times {10}^{24})}=1.96\times {10}^{30}kg$

Hence the mass of the sun is $1.96\times {10}^{30}kg$