The Universal Law of Gravitation

# The Universal Law of Gravitation

## Introduction

For a long time, the motion of celestial entities such as the moon, the earth, the planets, and so on has piqued people’s interest. Aryabhat, a famous Indian astronomer and mathematician, researched these motions in great detail in the 5th century A.D. and published his findings in the book Aryabhatiya. He demonstrated that the world rotates on its own axis. In addition, he described the movements of other heavenly bodies as seen from Earth, which we will later discuss.

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Satellite revolving around the earth

On the other hand, several centuries later, Isaac Newton, at the age of 23, had a very productive year in 1665. After his college at Cambridge was closed for an indefinite period owing to plague, he was compelled to rest at his home in Lincolnshire. He excelled in this year’s theoretical and experimental work, primarily in the fields of mechanics and optics.

He focused his attention on the motion of the moon around the earth in the same year. As the moon revolves around the earth. Before Newton, the first question was: what is the force that causes this acceleration? The acceleration is directed toward the orbit’s center, which is the earth’s center. As a result, the force must act in the direction of the earth’s center.

The moon is attracted to the earth, therefore that was a natural assumption. According to legend, Newton was seated under an apple tree when an apple dropped from the tree and landed on the ground. The belief that the earth draws all bodies to its center arose from this. What is the law that governs this force, was the following query? Newton had to make a number of risky assumptions that turned out to be pivotal in science and philosophy.

The rules of nature are the same for earthly and celestial bodies, he claimed. The force acting between the earth and an apple must obey the same principles as the force acting between the earth and the moon. This remark may seem self-evident today, but prior to Newton, there was a widespread assumption in western countries that earthly bodies are regulated by certain rules and celestial bodies by different rules.

In this article, we will be discussing some of the rules that regulate celestial body revolution around the sun and we’ll discuss The Universal Law of Gravitation and other related topics.

### The Universal Gravitational Constant

During his research, Newton hypothesized that the acceleration of a body moving towards the earth is inversely related to the square of the body’s distance from the earth’s center.

Thus,

a∝1 / r2

The force is also proportional to the body’s mass because it is mass times acceleration.

Hence,

F∝m/ r 2

The force on a body due to the earth must equal the force on the earth due to the body, according to the third rule of motion. As a result, this force should be proportionate to the earth’s mass. As a result, the force that exists between the earth and a body is ,

F∝Mm / r2

F=GMm / r2

And further, Newton went on to argue that not only the earth, but all material bodies in the universe are attracted to each other by equation F=GMm / r2 with the same value of G. The constant G is known as the universal constant of gravitation, and its value is 6.67 x 10 N-m/kg.

### Gravitational Constant G

The universal gravitational constant (G) is a formula that links the magnitude of gravitational attraction between two bodies to their masses and separation. It is quite difficult to measure its utility in an experimental setting. G has been suggested to have changed over time throughout history.

The gravitational force in Newton’s equation may not be constant. Studies of Moon accelerations and radar signal reflections from Mercury, Venus, and Mars have been used to look for a secular change in G.

### Weight and the Gravitational Force

The gravitational pull of planets and other bodies in the Universe, as well as the effect it has on objects, is referred to as weight. It’s vital to understand that weight is not the same as mass; the weight and mass of an object are proportionate. This means that the bigger the object’s mass, the greater its weight for a given gravitational field intensity.

Gravity exerts its force through a field, hence weight is a non-contact force. It is not necessary for an object to be in contact with the Earth in order for it to have weight. A calibrated spring balance, also known as a Newton meter, can be used to determine the weight of an object. Gravity force is another term for weight.

Gravitational force = mass x gravitational field strength

Example: Calculate the gravitational force (weight) of an 80 kg skydiver descending towards the Earth.

Solution:

weight = mass × gravitational field strength

weight = 80 × 10 ⇒800 N

### The universality of Gravity:

Gravity is extended beyond the earth via Newton’s universal gravitational law. The universality of gravity is the subject of Newton’s law of universal gravitation. It is Newton’s finding that gravitation is universal rather than his discovery of gravity that made him eligible to be inducted into the Gravity Hall of Fame.

Gravitational attraction is a force that attracts all objects. Gravity is a ubiquitous phenomenon. This gravitational attraction is proportional to the square of the distance between their centers and is directly proportional to the masses of both objects. The magnitude of gravitational forces is symbolically expressed by Newton’s conclusion:

F=GMm / r2

### What is the difference between G and g?

There is a primary difference between g and G in that g refers to gravitational acceleration, whereas G refers to gravitational constant. G's value varies with altitude, whereas G's value remains constant. Gravitational acceleration is a vector quantity, while the gravitational constant is a scalar number.

### What is gravitational potential energy?

The energy held in an object as a result of its vertical position or height is known as gravitational potential energy. A gravitational pull from the Earth stores the energy in an object.

### What is the difference between gravitational potential energy and potential energy?

The energy of an object due to its placement is known as its potential energy. The potential energy that an item with a mass gets as a result of its placement is known as gravitational potential energy.

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