Question

The mass of Jupiter is $ 1.9 \times {10^{27}}kg $ and that of 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 the Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also calculate the speed of Jupiter. $ G = 6.67 \times {10^{11}}N{m^2}K{g^{ - 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 $

Answer 1

Hint: We are looking for the force exerted by the Sun on Jupiter. This could be calculated with the Gravitational formula. To calculate the amount of force, we use the equation:
 $ F = \dfrac{{G{M_1}{M_2}}}{{{r^2}}} $
Here, $ F $ is the Gravitational force,
 $ {M_1},{M_2} $ are the masses of the planets.
 $ r $ is the distance between them,

Complete step by step answer
It is already known that:
Mass of Jupiter = $ 1.9 \times {10^{27}}kg $
And mass of Sun = $ 1.99 \times {10^{30}}kg $
Mean distance between Jupiter and Sun = $ 7.8 \times {10^{11}}m $
And, $ F = \dfrac{{G{M_1}{M_2}}}{{{r^2}}} $
On putting the values,
 $ F = \dfrac{{6.67 \times {{10}^{ - 11}} \times 1.9 \times {{10}^{27}} \times 1.99 \times {{10}^{30}}}}{{{{\left( {7.8 \times {{10}^{11}}} \right)}^2}}} = 4.16 \times {10^{23}}N $
So, we need to see from the above options, and select the correct value.
Thus, the correct answer is option B.

Additional Information
The gravitational constant is the proportionality constant that is used in Newton's Law of Gravitation. The force of attraction between any two-unit masses separated by a unit distance is called universal gravitational constant. It is because of the set value of the gravitational constant that we're able to accurately determine the mass of two orbiting objects. We can calculate the amount of force imparted on us by the Earth to keep us on the Earth

Note
Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects. The examples are the force that holds the gases in the sun or the force that causes a car to coast downhill even when you aren't stepping on the gas.