# Sir Isaac Newton And Astronomy

## Sir Isaac Newton

You know you must be special if you have two birthdays! One such special individual was Sir **Isaac Newton**, an English mathematician and physicist. He was born on December 25, 1642. No, wait; it was January 4th, 1643. Actually, he was born on both dates. And it wasn't due to a spiritual re-awakening of some sort. It was because Protestant England used the Julian calendar, while the rest of Europe adopted the Gregorian calendar. Eh, whatever.

Newton was a bright child that attended college to study math and physics. But a plague swept through England and the colleges closed. So poor Newton had to meander back and study at home. Unfortunately, he didn't get much done as a result of this. He only managed to make discoveries in the field of optics, invent an entirely new mathematical field (that of calculus), and develop three laws of motion that changed the world - you know, normal college-student-on-a-break type stuff.

## Newton's First Law of Motion

**Newton's first law of motion**states that a body remains at rest or continues in uniform motion in a straight line unless acted upon by a force.

Thinking about this, Newton knew that something must pull our moon toward the Earth, meaning if no force altered the moon's motion, it would continue in a straight line and fly away into space. If we had no moon, that would really mess up the whole werewolf thing.

Anyways, Newton's thoughts point to the fact that the moon circles our Earth because the Earth attracts it through some force. Newton realized it was gravity that was this force.

## Newton's Second Law of Motion

**Newton's second law of motion**states that the net force, F, on a body is equal to its acceleration, a, multiplied by its mass, m. In other words, F = ma.

The **mass** in the second law of motion is not the same thing as weight. Mass is a measurement of the amount of matter that makes up an object. An object's weight is actually the force that our Earth's gravity exerts on that object. Floating in space far away from Earth, you would have no weight despite having the same amount of matter as you have now on Earth.

## Newton's Third Law of Motion

**Newton's third law of motion**says that when one body exerts a force on a second body, the second body exerts an equal and opposite force back on the first body.

But Newton also realized that the force between two bodies is dependent upon their masses and the distance between them.

As the square of the distance between two objects increases, the force of gravity decreases. Such a relationship is called an inverse square relation. For instance, if the distance from the Earth to the moon doubled, the gravitational force between the Earth and moon would decrease by 4, because 2 squared is equal to 4.

## Newton's Law of Gravity

Knowing what mass is and what an inverse square relation is, you can boil down Newton's law of gravity to the equation shown on the screen.

In this equation, F is the force of gravity between two objects, one of mass M and the other of mass m. Little r is the distance between the centers of these two objects, and big G is known as the gravitational constant. The gravitational constant is a number that depends on the units we use for mass, force, and distance. The reason there's a minus sign in the equation is because the force of gravity is attractive, which means little r tends to decrease.

In summary, **Newton's law of universal gravitation** states that the force of gravity attracting two objects to each other is directly proportional to the product of their masses and inversely proportional to the square of their distance away from each other. In very simple terms, as the distance between two objects increases, the force of gravity diminishes, and vice versa. As the mass of one or both objects increases, the force of gravity increases, and vice versa.

## Newton and Orbital Motion

So, now we know why the moon doesn't fly away into space. It's thanks to gravity! But why doesn't the moon fly into the Earth, then, because of this same gravity?

Think of our moon's orbital motion as a form of falling. As the moon orbits Earth, it's actually falling, or being accelerated, toward the Earth's center. But it's traveling so fast that it cannot actually hit the Earth.

The classical cannonball example will help explain what I mean. Think of a big cannon shooting a cannonball from atop a really high mountain on Earth. If you load the cannon with a small amount of gunpowder, the cannonball won't go very far before it falls back down to Earth. But if you load the cannon with a ton of gunpowder, the cannonball will go so fast that it won't hit the ground at all.

That's because while Earth's gravity will pull the cannonball toward the Earth's center, the Earth's surface will curve away from the cannonball at the same rate that it falls when it travels really fast. This means the cannonball 'misses' the Earth as it falls towards it because of its high rate of speed and the curvature of the Earth itself.

## Lesson Summary

Sir **Isaac Newton** was an English mathematician and physicist whose laws of motion are very famous!

**Newton's first law of motion**states that a body remains at rest or continues in uniform motion in a straight line unless acted upon by a force.**Newton's second law of motion**states that the net force, F, on a body is equal to its acceleration, a, multiplied by its mass, m. In other words, F = ma.

The **mass** in the second law of motion is not the same thing as weight. Mass is a measurement of the amount of matter that makes up an object.

**Newton's third law of motion**says that when one body exerts a force on a second body, the second body exerts an equal and opposite force back on the first body.

**Newton's law of universal gravitation** states that the force of gravity attracting two objects to each other is directly proportional to the product of their masses and inversely proportional to the square of their distance away from each other.

## Learning Outcomes

Once you have watched this lesson, you should be ready to:

- Describe Newton's three laws of motion and his law of universal gravitation
- Differentiate mass from weight
- Recall the equations for Newton's second law and law of universal gravitation

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