Home Famous Equations #7 Newtons’ Law of Gravitation – An eye opener

#7 Newtons’ Law of Gravitation – An eye opener

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#7 Newtons’ Law of Gravitation – An eye opener
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It was in 1666, and “Eureka” something great was found.

Welcome back, guys! So most of you may wonder what’s such an exciting thing to be found in the late 1660s. Well, let’s know.

It is one of the foremost famous anecdotes within the history of science. Trying to recollect it. It’s okay if you can’t.

A Young physicist was sitting in his garden when an apple fell on his head and, in a very stroke of brilliant insight, he suddenly came up with his theory of gravity. So that’s today’s topic. It’s about the famous Newton’s Universal Law of Gravitation.

HISTORY

It was in 1666 that the plague had closed many public buildings and meetings. Newton had to abandon Cambridge. So he returned to Woolsthorpe Manor, near Grantham in Lincolnshire, where he was born, to consider the astronomical problems he had been pursuing at the University.

Well, as the myth suggests, an apple may not have struck Sir Isaac Newton’s head, but the falling of apple motivated Newton to ponder why the apple never drops sideways or upwards or any other direction except perpendicular to the ground—thus making him realize that Earth itself must be responsible for the apple’s downward motion.

THEORY

It encapsulates the thought that each particle of matter in the universe attracts one another through the force of gravity–Newton’s Law tells us how strong that attraction is. Newton thus theorizes this. He formulates a law by induction that this force must be proportional to the masses of the two objects involved and using previous intuition about the inverse-square relationship of the force between the Earth and also the moon.

Newton’s equation first appeared in the Philosophiæ Naturalis Principia Mathematica, July 1687.

THE LAW:

The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to the square of their separation. This force always points inward, from one point to the other.

The Law applies to all objects with masses, big or small.we can consider two big objects as point-like masses, if the distance between them is considerable compared to their sizes or if they’re spherically symmetric. For these cases, we can represent the mass of every object to some extent, mass at its center-of-mass.

 

THE EQUATION:

Newton was able to articulate his Law of Universal Gravitation and verify it experimentally. But it was Henry Cavendish’s verification of the universal gravitational constant that the Law received its final algebraic form.

Newton Law of Gravitation

This is the equation of the Law of Universal Gravitation.

where

F represents the force in Newtons

M and m represent the 2 masses in kilograms

r represents the separation in meters.

G represents the universal gravitational constant which contains a value of 6.674*10-11N (m/kg) 2.

The magnitude of G, gravitational attraction is minimal unless large masses are involved.

The equation as it seems is such an easy equation. But it’s overwhelmingly compelling. By fitting the numbers within the equation, we can predict the positions of all the planets anywhere in the solar system and beyond.

Newton’s formula helped engineers figure out what quantity of energy we wanted to interrupt the gravitational bonds of Earth. The path of each astronaut and also the orbit of each satellite from which we benefit–whether for communications, Earth observation, research around Earth or other planets, global positioning information–was calculated using this simple yet useful formula.

So, those were a few things about the simple yet compelling equation