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Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth $=6\times10^{24}\ kg$ and of the Sun $=2\times10^{30}\ kg$. The average distance between the two is $1.5\times10^{11}\ m$.
Given:
The mass of the earth $=6\times10^{24}\ kg$ and of the Sun $=2\times10^{30}\ kg$. The average distance between the two is $1.5\times10^{11}\ m$.
To do:
To calculate the force of gravitation between the earth and the Sun.
Solution:
Before calculating the gravitational force between the earth and the sun let us know the formula of the force of gravitation between the two objects:
Formula for gravitational force:
Force of gravitation $F=G\frac{m_1m_2}{r^2}$
Here, $m_1$ and $m_2$ are the masses of the two objects and $r$ is the distance between the two objects.
$G$ is a gravitational constant and its value is $6.67\times10^{-11}\ m^3kg^{-1}s^{-2}$.
Let us calculate the force of gravitation between the sun and the earth:
Gravitational force between the sun and the earth:
As given, mass of the sun $m_1=2\times10^{30}\ kg$
Mass of the earth $m_2=6\times10^{24}\ kg$
Average distance between the sun and the earth $r=1.5\times10^8\ km=1.5\times10^{11}\ m$
Therefore, the force of gravitation $F=G\frac{m_1m_2}{r^2}$
$=6.67\times10^{-11}\times \frac{2\times 10^{30}\times 6\times 10^{24}}{(1.5\times 10^{11})^2}$
$=3.57\times10^{22}\ N$
Conclusion:
Therefore, the force of gravitation between the sun and the earth is $3.57\times10^{22}\ N$.
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