Newton’s law of gravitation

Newton’s Law of Gravitation - Basics

The Law of Universal Gravitation asserts that every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the distance squared between their centres.
It’s this force that gives weight to physical objects and causes the earth and the other planets to orbit the sun.
The law is usually stated mathematically as F = G(m1m2)/r², where F is the force of attraction between the two bodies, m1 and m2 are the masses of the two bodies, r is the distance between the centres of the two bodies, and G is the gravitational constant.

The Gravitational Constant (G)

The Gravitational Constant (G) is a proportionality constant involved in the calculation of gravitational effects in Newton’s Law of Universal Gravitation.
It is traditionally measured in Newton’s square meters per kilogram squared (N(m²/kg²)).
In the equations of physics where G appears, it is often necessary to convert G to the appropriate unit based on the problem.

Gravity and Distance

Gravity diminishes as you get farther away from an object. This is due to the inverse-square law, which states that the intensity of an effect such as illumination or gravitational force changes in inverse proportion to the square of the distance from the source.
According to this law, the gravitational force exerted on one object by another is proportional to the square of the distance separating them.

Difference between Mass and Weight

Mass is the amount of matter in an object and does not change in different gravitational fields.
Weight, however, is the force of gravity pulling down on an object and can vary based on an object’s location. Weight = Mass x Gravity.

Newton’s Law of Universal Gravitation in Everyday Life

Understanding Newton’s Law of Universal Gravitation is crucial to understanding many common phenomena we observe.
For example, when you throw a ball into the air it falls back down because it is attracted to the large mass of the earth. At the same time, the earth gets pulled towards the ball a tiny bit but since it’s so massive this motion isn’t noticeable.
Newton’s Law of Gravitation also explains why the planets revolve around the sun and why the moon revolves around the Earth.

Practice Problems

Familiarise yourself with the equation of Newton’s law of gravitation. Practice by trying various problems, applying the formula: Force of gravity = G(m1m2)/r².
When solving problems, remember to be mindful of units and converting them appropriately before any calculations.
Try real-world scenarios like calculating your weight if you were on the moon or another planet.