- Physics Planet
- Wednesday September 20, 2017

While probably most famous today for his Three Laws, which translate into the Universal Law of Gravitation, he was also the first to understand the relationship of white light and the spectrum and developed a significant body of mathematics, including integral and differential calculus and infinite series. He also studied theology extensively.

There is the very popular story that Newton was sitting under an apple tree one day, and an apple fell on his head, and he suddenly thought up the Universal Law of Gravitation. While not true, there are elements of truth in this story.

Earlier, Newton had developed his Three Laws of Motion. There was first, “Every object in a state of uniform motion tends to remain in the state of motion unless an external force is applied to it”. This is essentially a restatement of Galileo’s idea of inertia.

Simplistically, thus means that unless you move a stone (apply force), it will stay in the same place. As well, once something is put into motion by a force, it will stay in motion unless other forces act on it. In the stone example, some of these other forces include gravity and friction, such that eventually it stops moving.

Newton’s Second Law of Motion extends the First Law and allows for quantitative calculations. When an object is in a state of uniform motion, all of the forces acting on it are balanced. The change in balance created when you push or throw the stone causes acceleration of the object until the forces acting upon it regain balance and the object returns to a state of uniform motion.

The Second Law say that there is a relationship between an object’s mass (m), its acceleration (a) and the applied force (f), where acceleration and force are vectors and where the direction of the force vector is the same as the direction of the acceleration vector. In other words, the force applied to the stone accelerates the stone in the same direction as the force.

Using the stone example further, if one were to throw two stones with equal force, and one stone was twice as heavy as the first, that stone would not travel as far as the first. When the forces are equal, the acceleration is inversely proportional to the mass of the object. This greatly oversimplifies, but is illustrative.

Newton’s Third Law is related to the first two. It simply states that for every action, there is an equal and opposite reaction. Think of a rocket. The fuel ignites, driving gases down out of the rear at tremendous speed and the rocket moves up (accelerates) in direct relationship to the gases being expelled.

This is the equal and opposite reaction. If the force is great enough, the rocket will accelerate to the point where it reaches escape velocity, meaning that it will leave earth’s atmosphere. It will have overcome the forces of gravity and friction.

How does this relate to the infamous apple? Newton saw the apple fall from the tree. It had been at rest (or in a state of uniform motion) just hanging there by its stem from a branch. Suddenly, it fell. According to his Second Law, there must have been a force acting on it to accelerate the apple, since it went from rest to moving toward the ground (was there a tension force keeping it in place?)

The force was gravity, and it overcame the tensional force of the stem, as the stem thinned and became weaker. The weight of the apple, which we know is the force of gravity, caused it to fall. Newton also noticed that there were apples all up and down the tree, some higher by a factor of two than others, and all would eventually fall.

Newton’s brilliance came into play and he realized that gravity could reach at least all the way to the moon. Thus the orbit of the moon could be caused by gravitational pull from the earth as well as gravitational pull from other bodies or objects in the universe. When he thought more about the elliptical nature of the orbit, he began to formulate his Law of Universal Gravitation.

The Law states that every object in the universe attracts every other object with a force directed along the line of the centers for the two objects that is proportional to the product of their masses, and inversely proportional to the square of the separation between the two objects. The constant of proportionality (G) is known as the universal gravitational constant, and is thought to be the same at all times and all places.

In simple terms, Newton realized that, in our planet-Sun system, the Sun is not stationary but has an orbit of its own around the common center of mass for the whole system. Everything was related to everything else through gravity and its position was determined by the position of everything else, and has an effect on everything else.

Newton remains recognized as one of our most famous physicists and thinkers. From these realizations, and pretty heavy analytical thinking and math, we seem to have the precursor to Chaos Theory, which is for another day.

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