91Ó°ÊÓ

Mass of Sun,$m_s=1.99×{10}^{30}kg$

Mass of Earth,$m_s=5.98×{10}^{24}kg$

Distance between Earth and Moon,$r_{ms}=3.82×{10}^{10}m$

Distance between Sun and Moon,$r_{em}=1.5×{10}^{11}$

According to Newton’s law of gravitation, the force between two objects is directly proportional to their masses and inversely proportional to the square of distance between them.

Formula:

Gravitational force between two particles, ${}^{F=\frac{G{m}_1{m}_2}{r^2}}$ (i)

Using equation (i), Force between Sun & Moon can be given as:

$F_{sm}=\frac{G×m_s×m_m}{r_{ms}^2}$

Using equation (i), Force between Earth & Moon can be given as:

$F_{em}=\frac{G×m_m×m_e}{r_{em}^2}$

Ratio of two forces becomes:

$$\begin{gathered} \frac{F_{sm}}{F_{em}}=\frac{G×m_s×m_m}{r_{ms}^2}×\frac{r_{em}^2}{G×m_m×m_e} \\ =\frac{m_s}{m_e}×\frac{r_{em}^2}{r_{sm}^2} \\ =\frac{1.99×{10}^{30}}{5.98×{10}^{24}}×\frac{\left(3.82×{10}^{10}\right)}{\left(1.5×{10}^{11}\right)} \\ =2.16×{10}^4 \end{gathered}$$

The value of the ratio is$2.16×{10}^4$