Use of the universal law of gravitation

The Universal Law of Gravitation

The Universal Law of Gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
Formally represented as F = G(m1m2/r^2), where F is the force of attraction between the two bodies, m1 and m2 are the masses of the bodies, r is the distance between the centres of the two bodies, and G is the universal gravitational constant.

Newton’s Law of Universal Gravitation introduced the concept of a gravitational field, a force field that exists in the space around every mass or group of masses.
A gravitational field is the region of space surrounding a body in which another body would experience a force of gravitational attraction.
The strength of the gravitational field is given by g = F/m, where g is the gravitational field strength, F is the force, and m is the mass.

The gravitational field strength (g) at a point in the field is defined as the force per unit mass experienced by a small test mass placed at that point.
Direction of the field is the direction of the force it exerts on a positive test mass.
The unit of gravitational field strength is N kg^-1 (newtons per kilogram), which can also be regarded as acceleration (m s^-2).

Gravitational potential energy is the work done against gravity to reach a certain point within a gravitational field.
The formula for finding the gravitational potential energy (E) is E = mgh, where m is the mass of the object, g is the gravitational field strength, and h is the height above the ground.

A circular orbit occurs when an object moves in a circular path under the influence of gravitational force.
Orbital motion involves a balance between the inertia of the object and the gravitational force exerted on it.
For something to maintain a steady circular orbit, it must have the correct velocity – too slow and it will spiral inwards, too fast and it will spiral outwards.
The formula for the velocity needed for circular orbit can be represented as v = √(GM/r), where v is the velocity, G is the universal gravitational constant, M is the mass of the central body, and r is radius of the orbit.

The gravity from the moon and sun pull on Earth’s water, causing predictable rises and falls in sea levels known as tides.
The gravitational attraction of the moon is one main cause for tides on the Earth, but the sun’s gravitational force also plays an important role.
The gravitational pull of the sun and moon on the earth causes the sea’s water to bulge out in the direction of these celestial bodies, leading to high tide, and fall in areas perpendicular to them, leading to low tide.
The gravitational pull of celestial bodies is also responsible for the formation of solar systems, grouping of galaxies and other phenomena.