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Law of universal gravitation | POINT classical mechanics

Law of universal gravitation


 The universe is in constant motion. For example:


-The moon revolves around the earth
-The planets revolve around the sun
-The sun revolves around the center of the galaxy.

All these bodies move in a circular or semi-circular motion.


The scientist Newton arrived at some basic assumptions, including:
- The existence of a mutual physical force of attraction between the moon and the Earth causing the moon to revolve around the Earth.

- The physical force of attraction arises between any two physical bodies and depends on:


1- The mass of the two bodies
Where the force of physical attraction between two bodies is directly proportional to the product of the masses of the two bodies when the distance between the centers of the two bodies is constant
2- The distance between the centers of the two bodies.
The force of physical attraction between two bodies is inversely proportional to the square of the distance between the two bodies when the product of the masses of the two bodies is constant.

 

F = GMm/r²

Based on this, Newton formulated the law of universal gravitation.

Newton's Law of Universal Gravitation :
Every material body in the universe attracts every other body 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.

The universal gravitational constant (G)
1) A universal constant numerically equal to the mutual force of attraction between two bodies, each with a mass of 1kg and the square of the distance between their centers, 1m².
2) Unit of measure: N.m²/kg²  or  m³/kg.s²
3) Dimensional formula: L³/M.T²
4) Numerical value: 6.67408×(1/10¹¹) N.m²/kg²

(1) The law of attractive forces between material bodies is known as the law of universal gravitation.This is due to the generality of this law.The force of attraction between any two bodies is a mutual force, as each body attracts the other body towards it with the same force.

(2) The force of attraction appears clearly between celestial bodies, while it is not clear between small mass bodies on the surface of the Earth, such as two people standing next to each other or two adjacent cars.This is due to the small value of the universal gravitational constant. The force of attraction between bodies is only effective and large when the mass of one or both bodies is very large.


Scientists who benefited humanity
Arab scientists played a great role in developing astronomy and benefiting from it. Examples of astronomers include:

Soviet postage stamp depicting Al Biruni, 1973

- Abu Rayhan Muhammad al-Biruni: who succeeded in measuring the circumference of the Earth.

- Ali ibn Isa al-Asturlabi

- Ali al-Buhturi.