Question.
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6 \times 10^{24} \mathrm{~kg}$ and of the Sun $=2 \times 10^{30} \mathrm{~kg}$. The average distance between the two is $1.5 \times 10^{11} \mathrm{~m}$.
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6 \times 10^{24} \mathrm{~kg}$ and of the Sun $=2 \times 10^{30} \mathrm{~kg}$. The average distance between the two is $1.5 \times 10^{11} \mathrm{~m}$.
Solution:
Given mass of earth, $\mathrm{M}_{\mathrm{e}}=6 \times 10^{24} \mathrm{~kg} ;$ mass of Sun, $\mathrm{M}_{\mathrm{s}}=2 \times 10^{30} \mathrm{~kg} ;$ distance between them,
$\mathrm{r}=1.5 \times 10^{\mathrm{M}} \mathrm{m}$
Now, force of gravitation between them,
$\mathrm{F}_{\mathrm{g}}=\frac{\mathrm{GM}_{\mathrm{e}} \mathrm{M}_{\mathrm{s}}}{\mathrm{r}^{2}}$
$=\frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 2 \times 10^{30}}{1.5 \times 10^{11} \times 1.5 \times 10^{11}}$
$=35.57 \times 10^{21} \mathrm{~N}$
Given mass of earth, $\mathrm{M}_{\mathrm{e}}=6 \times 10^{24} \mathrm{~kg} ;$ mass of Sun, $\mathrm{M}_{\mathrm{s}}=2 \times 10^{30} \mathrm{~kg} ;$ distance between them,
$\mathrm{r}=1.5 \times 10^{\mathrm{M}} \mathrm{m}$
Now, force of gravitation between them,
$\mathrm{F}_{\mathrm{g}}=\frac{\mathrm{GM}_{\mathrm{e}} \mathrm{M}_{\mathrm{s}}}{\mathrm{r}^{2}}$
$=\frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 2 \times 10^{30}}{1.5 \times 10^{11} \times 1.5 \times 10^{11}}$
$=35.57 \times 10^{21} \mathrm{~N}$