Question

B. Determine the mass of the sun

Answer 1

B. $1.99\cdot 10^{30} kg$

Explanation:

The gravitational force between the Earth and the Sun is given by:

$F=G\frac{Mm}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constamt

M is the mass of the Sun

$m=5.98\cdot 10^{24} kg$ is the mass of the Earth

$r=1.50\cdot 10^{11} m$ is the distance between Earth and Sun

Since we know the magnitude of the gravitational force between Earth and Sun, $3.53\cdot 10^{22} N$ (from the table given), we can re-arrange the formula and find the mass of the Sun, M:

$M=\frac{Fr^2}{Gm}=\frac{(3.53\cdot 10^{22}N)(1.50\cdot 10^{11} m)^2}{(6.67\cdot 10^{-11})(5.98\cdot 10^{24} kg)}=1.99\cdot 10^{30} kg$

C. Because the mass of the Sun is much much greater than the mass of the Moon

Explanation:

We already know the gravitational force between Earth and Sun ($3.53 \cdot 10^{22} N$. By applying the same formula as before, we can calculate the gravitational force between Earth and Moon:

$F=G\frac{Mm}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constamt

$M=5.98\cdot 10^{24} kg$ is the mass of the Earth

$m=7.35\cdot 10^{22} kg$ is the mass of the Moon

$r=3.84\cdot 10^{8} m$ is the distance between Earth and Moon

Substituting into the formula, we find

$F=\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24} kg)()7.35\cdot 10^{22} kg)}{(3.84\cdot 10^8 m)^2}=1.99\cdot 10^{20} N$

And we see that this is smaller than the force exerted by the Sun.