Question

The mass of Jupiter is $1.9\times 10^{27}kg$ and the Sun is $1.99\times 10^{30}kg$. The mean distance of Jupiter from the sun is $7.8\times 10^{11}m$. Calculate the gravitational force which sun exerts on Jupiter.($G=6.67\times 10^{-11}Nm^{2}kg^{-2}$)

& A.5\times {{10}^{23}}N \\\ & B.4.15\times {{10}^{23}}N \\\ & C.15\times {{10}^{23}}N \\\ & D.1\times {{10}^{23}}N \\\ \end{aligned}$$

Answer 1

Newton’s law of universal gravitation gives the force acting between two bodies of mass $M_{1}$ and $M_{2}$ which is separated by a distance $r$ between them. Then, the force is inversely proportional to the square of the distances and directly proportional to the product of the masses of the bodies.

Formula used:
$F=\dfrac{GM_{1}M_{2}}{r^{2}}$

Complete answer:
Given that,
Mass of Jupiter $M_{1}=1.9\times 10^{27}kg$
Mass of Sun $M_{2}=1.99\times 10^{30}kg$
Mean distance $r=7.8\times 10^{11}m$
$G=6.67\times 10^{-11}Nm^{2}kg^{-2}$

Substituting, we get gravitational force $F=\dfrac{GM_{1}M_{2}}{r^{2}}$
$F=\dfrac{6.67\times 10^{-11}Nm^{2}kg^{-2}\times 1.9\times 10^{27}kg\times1.99\times 10^{30}kg}{(7.8\times 10^{11}m)^{2}}=4.15\times 10^{23}N$

So, the correct answer is “Option B”.

Additional Information:
Newton's law of gravitation is derived from Kepler's laws of gravity and also known as Newton-Kepler law of gravitation. This law is valid for force between planets and also for anybody on the earth surface. This force is generally known to be attractive and is thus the intuitive reason behind how the planets are stable on their orbits.
Also, it was assumed from Newton's third law that, if anybody exerts an attractive force on another, then, the second body also exerts the same amount of attractive force on the first body. Which is to say, that if a human and the earth are the two bodies, then we exert the same amount of attractive force on the earth, as the earth exerts on the human.
The discovery of this later led to the study of space and the current emerging study of gravitational waves.

Note:
The distance is taken from the centre of the mass of the bodies, as it is said that the mass of the body is concentrated in its centre. Here, the mass is assumed to be constant with time .i.e. the body doesn’t lose its mass during the interaction.