Question

Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = $6 \times {10^{24}}kg$ and of the Sun = $2 \times {10^{30}}kg$. The average distance between the two is $1.5 \times {10^{11}}m$.

Answer 1

Hint
From the formula, we know that the force of gravitation is directly proportional to the masses and inversely proportional to the square of the distance between them. By substituting the values of the masses of earth and the Sun and the distance between them, we get the value of the force of gravitation.
In the solution, we will be using the following formula,
$\Rightarrow F = G\dfrac{{Mm}}{{{R^2}}}$
where $F$ is the force of gravitation,
$G$ is the universal gravitational constant
$M$ is the mass of the sun and $m$ is the mass of the earth and
$R$ is the distance between them.

Complete step by step answer
The gravitational force is the force with which any 2 bodies in the universe attract each other. It is always an attractive type and depends on the mass of the two bodies and the distance between them. Now the Newton’s laws of gravitation, the gravitational force has a value of
$\Rightarrow F = G\dfrac{{Mm}}{{{R^2}}}$
Here in the question we are given the mass of the sun, $M = 2 \times {10^{30}}kg$, the mass of the earth, $m = 6 \times {10^{24}}kg$ and the distance between the sun and the earth $R = 1.5 \times {10^{11}}m$. The value of the universal gravitational constant is given by, $G = 6.674 \times {10^{ - 11}}{m^3}/kg{s^2}$.
So by substituting these values in the equation we get the force of gravitation as,
$\Rightarrow F = 6.674 \times {10^{ - 11}}\dfrac{{2 \times {{10}^{30}} \times 6 \times {{10}^{24}}}}{{{{\left( {1.5 \times {{10}^{11}}} \right)}^2}}}$
On doing this calculation on the numerator and the denominator, we get
$\Rightarrow F = \dfrac{{8 \times {{10}^{44}}}}{{2.25 \times {{10}^{22}}}}$
On dividing this we get the force of gravitation as,
$\Rightarrow F = 3.55 \times {10^{22}}N$
So this is the force of gravitation between the sun and the earth.

Note
Since the gravitational force is directly proportional to the mass of both the interacting objects, so more massive the objects, more is the force of gravitation. And as the force is inversely proportional to the distance between the bodies, so the more the separation increases, the less the gravitational force between the bodies becomes.