Solveeit Logo
Login

Question

Question: The mass of the sun is \(2 \times {10^{30}}kg\) and the mass of earth is \(6 \times {10^{24}}kg\). I...

The mass of the sun is 2×1030kg2 \times {10^{30}}kg and the mass of earth is 6×1024kg6 \times {10^{24}}kg. If the average distance between the sun and the earth is 1.5×108km1.5 \times {10^8}km, calculate the force of gravitation between them.

Explanation

Solution

In order to find the solution of the given question, we need to know the formula for Gravitational force between two bodies. This question is directly based on the formula for Gravitational force. After that we need to apply the formula of gravitational force between the sun and the earth. Then after solving the equation, we can conclude with the correct solution of the given question.

Complete step by step solution:
The mass of the sun is given in the question as, M1=2×1030kg{M_1} = 2 \times {10^{30}}kg
And the mass of the earth is given in the question as, M2=6×1024kg{M_2} = 6 \times {10^{24}}kg
Also the distance between the sun and earth is given in the question as, d=1.5×108kmd = 1.5 \times {10^8}km.
We know that the Force of Gravitation between two bodies is given by,
FG=GM1M2d2{F_G} = G\dfrac{{{M_1}{M_2}}}{{{d^2}}}…………………. (i)
Where, GG is the Universal Gravitational constant and whose value is 6.67×10−11Nm2kg−26.67 \times {10^{ - 11}}N{m^2}k{g^{ - 2}}.
Now, we need to put the values in equation (i).
Putting the values in the above equation, we get,
FG=6.67×10−112×1030×6×1024(1.5×108)2{F_G} = 6.67 \times {10^{ - 11}}\dfrac{{2 \times {{10}^{30}} \times 6 \times {{10}^{24}}}}{{{{(1.5 \times {{10}^8})}^2}}}
⇒FG=80.04×10432.25×1016\Rightarrow {F_G} = \dfrac{{80.04 \times {{10}^{43}}}}{{2.25 \times {{10}^{16}}}}
∴FG=35.573×1021N\therefore {F_G} = 35.573 \times {10^{21}}N
Therefore, the required value of Gravitational force between the sun and the earth is 35.573×1021N35.573 \times {10^{21}}N.

Note: According to Newton’s law of universal gravitation, each body with a nonzero mass attracts every other body in the universe. The force is attractive in nature and is known as the force of gravity. The gravitational force is directly proportional to the masses of two bodies and inversely proportional to the square of the distance between them. Mathematically, it can be represented as, FG=GM1M2d2{F_G} = G\dfrac{{{M_1}{M_2}}}{{{d^2}}} where GG is the constant of proportionality and is known as Universal Gravitational Constant.