The Moon, whose mass is 7.35 ×10^22 kg, orbits the Earth, whose mass is 5.98 ×10^24 kg, at a m

step 1 Hello and welcome to this video solution of numerate. It is given that the moon is having a mass

The Moon, whose mass is 7.35 ×10^22 kg, orbits the Earth,...

The Moon, whose mass is $7.35 \times 10^{22} \mathrm{~kg}$, orbits the Earth, whose mass is $5.98 \times 10^{24} \mathrm{~kg}$, at a mean distance of $3.85 \times 10^{8} \mathrm{~m}$. It is held in a nearly circular orbit by the Earth-Moon gravitational interaction. Determine the force of gravity due to the planet acting on the Moon. From the universal law of gravitation $$ F_{G}=G \frac{m M}{R^{2}} $$ we get $$ F_{G}=6.673 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg} \frac{\left(7.35 \times 10^{22} \mathrm{~kg}\right)\left(5.98 \times 10^{24}\right)}{\left(3.85 \times 10^{8} \mathrm{~m}\right)^{2}} $$ which yields $$ F_{G}=1.98 \times 10^{20} \mathrm{~N} $$ This is also the force on the Earth due to the Moon, and the force on the Moon due to the Earth.

The Moon, whose mass is $7.35 \times 10^{22} \mathrm{~kg}$, orbits the Earth, whose mass is $5.98 \times 10^{24} \mathrm{~kg}$, at a mean distance of $3.85 \times 10^{8} \mathrm{~m}$. It is held in a nearly circular orbit by the Earth-Moon gravitational interaction. Determine the force of gravity due to the planet acting on the Moon.
From the universal law of gravitation
$$
F_{G}=G \frac{m M}{R^{2}}
$$
we get
$$
F_{G}=6.673 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg} \frac{\left(7.35 \times 10^{22} \mathrm{~kg}\right)\left(5.98 \times 10^{24}\right)}{\left(3.85 \times 10^{8} \mathrm{~m}\right)^{2}}
$$
which yields
$$
F_{G}=1.98 \times 10^{20} \mathrm{~N}
$$
This is also the force on the Earth due to the Moon, and the force on the Moon due to the Earth.

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Key Concepts

Universal Law of Gravitation

This law states that every pair of objects in the universe attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It forms the foundational basis for understanding gravitational interactions between any two bodies, from apples falling from trees to the orbits of planets and moons.

Gravitational Constant

The gravitational constant (denoted as G) is a fundamental constant of nature that quantifies the strength of the gravitational force in Newton’s law of universal gravitation. Its value is essential in calculating gravitational forces and is used universally in astrophysics and mechanics to relate the masses of objects to the force between them.

Inverse Square Law

The inverse square law in gravity indicates that the gravitational force between two masses decreases as the square of the distance between their centers increases. This principle explains why objects further apart experience significantly weaker gravitational attractions, and it is central to understanding orbital dynamics and the behavior of gravitational fields in space.

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