###### By Robert M. Hazen, Ph.D., George Mason University

## Isaac Newton made a conceptual breakthrough by recognizing two different kinds of motion—uniform and accelerating. He defined force as any phenomenon that causes an object to accelerate and applied this definition to his own studies of gravity, describing it as an attractive force that exists between any two masses anywhere in the universe.

### Newton’s Three Laws of Motion

Isaac Newton’s analysis of the force of gravity was rooted in his understanding of the relationship between motion and force. According to that understanding, Newton proposed three laws of motion:

Uniform motion, which is an object moving at a constant velocity in a constant direction, or an object at rest sitting on a table, for example. This law states that nothing happens without force, and an object remains in uniform motion unless it is acted upon by a force.

Acceleration motion, which is any change in either the speed of an object or in the direction of its movement. As an example, circular motion (not uniform motion) at a constant speed is acceleration. This law puts the whole idea in quantitative terms, it says force equals mass times acceleration, and numbers can be plugged into that equation.

The third law presents the idea that forces act in pairs. Equal and opposite forces occur simultaneously. When you push on an object, it pushes back on you with the same force at the same time.

This is a transcript from the video seriesThe Joy of Science. Watch it now, on The Great Courses Plus.

### Newton’s Remarkable Discovery

During 1665–1666, the bubonic plague struck England, and that’s the period when Newton retreated to his family farm as a consequence of Cambridge University being shut down.

On the farm, he had a year and a half to think and reflect, to ponder the things he’d learned about Kepler’s laws, Galileo’s ideas, and other concepts he had studied as an undergraduate at Cambridge. During those years he burst a remarkable discovery which was deducing a mathematical description of the universal force of gravity.

To Newton’s contemporaries, gravity was a terrestrial force; it was restricted to objects near the Earth’s surface. What Newton discovered in the family apple orchard was that gravity is a universal force. It extends all the way out to the planets, to the Moon, to the stars, and farther. The young scholar looked up to see an apple ripening on the tree, and above it, he saw the Moon in its orbit. Newton’s great advance was realizing that it’s a singular force that is acting on both of these objects.

Learn more about the nature of energy.

### Why Doesn’t the Moon Fall!?

The whole discovery was “occasioned by the fall of an apple”. The young Isaac was sitting in the garden thinking about the universe and how it worked and pondering about the difference between the apple and the Moon. The apple falls but the Moon does not. He tried to discover the mystery behind this issue, and finally, he found the answer.

Here’s the gist of Newton’s idea. When the apple breaks loose, it falls to Earth, straight down. But if someone picks up that apple, and throws it sideways with a certain amount of horizontal velocity, as Galileo says, the apple adopts a parabolic path. The harder the apple is thrown, the more horizontal distance it adopts and the farther it goes.

What Newton realized is that if the apple is thrown hard enough, it would go into orbit. It would continuously fall, but as it fell it would move horizontally, and it would keep going around the Earth. That’s what the Moon is doing, it’s going around the Earth, constantly falling, but it has sufficient horizontal velocity to keep it in orbit. The same thing happens with any planet, with any moon, anything that’s orbiting the Sun, anything that’s orbiting the Earth.

Learn more about universal gravitation.

### The Mathematical Equation of Gravity

Newton’s concept of qualitative and quantitative gravity is simple. He derived a mathematical equation to explain this force. He described a force in terms of four measurable quantities. The first one is the mass of an object. The second variable is the mass of a second object. The third variable is the distance between these two objects.

And finally, there is the force—the gravitational force that ensues. And this is the equation that Newton came up with. He said: force equals a constant—a capital G for the gravitational constant—times the first mass, times the second mass, divided by the distance squared.

(F = G x [m1 x m ]/d )

Consequently, there exists an attractive force of gravity between any two objects that is proportional to the product of their masses, divided by the distance between them squared.

Learn more about celestial and terrestrial mechanics.

### So, How Does Newton’s Equation Work?

Newton used rather complicated mathematical reasoning and he demonstrated that stable orbits are possible only if there is a 1 over d2 kind of relationship.

If there is an exponent less than 2, it leads to a steadily decaying orbit because the force doesn’t drop off sufficiently with increasing distance. And if there is an exponent greater than 2, 2.1, or 2.2, for example, it allows the orbiting body to escape because the force drops off too quickly and the body just keeps moving outward. Only with 1 over d2 is the exact relationship obtained.

Newton’s powerful equation reveals that an equal gravitational force is experienced by any two objects, for example, the Earth and the Moon. In fact, when an apple falls to the Earth, the Earth also falls a minuscule distance toward the apple, and there’s a kind of lever law here.

To explain more about this, imagine a seesaw between two children that don’t weigh the same, the heavier one has to sit closer to that fulcrum point, and the one who’s farther away experiences a much larger motion on the seesaw.

### Common Questions about the Discovery of Gravity by Isaac Newton

**Q: What is the definition of force according to Newton’s laws of motion?**According to Newton’s laws of motion, force is a phenomenon that induces objects to move either by constant or accelerated speed.

**Q: What is Newton’s first law of motion, and what does it state?**The first law of motion is called uniform motion, and it states that objects move at a constant speed unless they are acted upon by another force.

**Q: What was Newton’s most remarkable discovery?**Newton‘s most remarkable discovery was interpreting a mathematical explanation of gravity.