courtesy http://microgravity.msfc.nasa.gov/education/WhatisMicrogravity/WhatMicro.htm
"If I have seen further, it is by standing on the shoulders of giants."
courtesy
http://microgravity.msfc.nasa.gov/education/WhatisMicrogravity/WhatMicro.htm
Sir Isaac Newton 1642 - 1727
The very fact that Isaac Newton was the first scientist ever to be knighted by royalty should indicate the degree of influence he had in the field. Newton made major contributions in the fields of optics, physics and astronomy in a relatively short period of time. During the plague years of 1665 and 1666, Newton left the city and spent his time in relative isolation and in deep thought. Here Newton laid down the foundations of modern physics which needs to be understood before we look at his astronomical contributions.
Galileo's concepts of "natural motion" were conceptually correct and a step in the right direction. Newton, however, took a more rigorous and mathematical approach to the subject ... which took science to a quantitative (rather than qualitative) level. He understood that if you wanted to understand the motion of an object, you first had to analyze the forces exerted on that object. From that approach, he developed three fundamental laws which became the foundation of modern physics.
Newton's First Law of Motion: An object at rest tends to remain at rest ... an object in motion will tend to remain in motion (in a straight line and constant speed) ... until some unbalanced force is exerted on that object. This is essentially what Galileo said many years earlier and is often called the Law of Inertia. You can experience this "law" every time you drive in your car. If you accelerate too quickly from a stoplight, you feel your head "snap back" ... as if it wanted to remain at the intersection. If you slam on your brakes, your body lunges forward (which is exactly why you should always wear your seatbelt). If your car turns quickly, you slide across the car seat.
Newton's Second Law of Motion:
This law covers "natural motion" when some net force does act on an object. Let's see if we can use a more "user friendly" approach to help understand this law. Imagine you are at the supermarket picking up some groceries with a cart. If your cart is at rest and you want to move down the aisle, you have to push it. That is, you have to exert some force on the handle of the cart. Actually what your cart is doing is speeding up ... or accelerating. Once you get your cart up to proper speed, you no longer have to push it so hard. In fact, if your cart had frictionless wheels ... you wouldn't have to push it at all because of Newton's First Law. But I have yet to see a frictionless shopping cart (I always seem to get the one that squeaks). So when you let go of your cart, it will slowly come to a state of rest ... because there is a force of friction which acts in the opposite direction as the cart is moving. This force makes the cart slow down ... or decelerate. A physicist would simply call this a negative acceleration. Finally, imagine your cart is moving down the aisle and another cart hits it from the side. Your cart would veer off its straight line path ... or change direction. A physicist would see this a special form of acceleration ... called centripetal acceleration. So what are some possible effects of a force? Speed up (accelerate), slow down (decelerate), or change direction (centripetal acceleration) ... and the bigger the magnitude of the force, the more dramatic the acceleration! I know all this and yet I still manage to forget to bring home bread and milk!
Stated another way ... magnitude of acceleration is proportional to size of force.
Now the motion you observe also depends on what is in your cart at the time. If your cart is filled with toilet paper, it becomes quite easy to alter the motion of the cart. The same cart filled with bags of rock salt and dog food goes through a much different change. This "loaded" cart shows a greater resistance to changes in motion. That is, you have to push it harder to get it moving ... it takes a bigger force get it to stop ... and if hit from the side, it veers only slightly. This is a concept Newton introduced called mass. This basically relates to "quantity of stuff" or how much matter it contains ... or could be understood as an object's resistance to changes in motion.
Now try this: Take a can of soup from your cupboard and shake it as in this animation.
You naturally feel some resistance as you constantly try to change the soup cans state of motion. Now repeat the same experiment with a gallon of milk (trying to match the same rpm). This is much harder to do!!! ... why? ... because the gallon of milk has more mass! Now try the same experiment with a bag of rock salt ... forget it, you will never be able to match the same motion because the rock salt has too much mass. In other words, as the mass increases, the acceleration decreases.
Newton summarized both of these ideas in the form of an equation which says:
where a is acceleration, F is magnitude of force and m is the mass of the object being accelerated. In plain English, it says: When a net force acts on an object, it will speed up, slow down or change direction (all forms of acceleration). The magnitude of the acceleration is proportional to the magnitude of the force (bigger force ... bigger acceleration) and inversely proportional to the mass of the object being accelerated (bigger mass ... lower acceleration).
A final note about circular motion ...
Tie a rope around the handle of a bucket of rocks and spin the bucket around your head (Ok, don't really try this). You have to pull pretty hard on the rope to accomplish this. The force you exert on the rope is always directed toward the center of the circle and is known as centripetal force (see blue arrow below). If this force were not present (i.e., the rope breaks) ... the bucket of rocks flies off tangent to the circle (green arrow). Newton realized that circular motion is actually a form of acceleration ... known as centripetal acceleration ... not because the speed changes but rather, the direction changes constantly. With this basic understanding of motion, Newton was able to apply the same principles to the orbit of the moon. Stay tuned ...
Centripetal force keeps objects moving in circles
Newton's Third Law of Motion: For every action, there is an equal and opposite reaction. That is, forces always act in pairs so that when "A" pushes on "B" , "B" pushes back on "A" with the same magnitude of force. This is often called the "law of reaction".
Newton eventually published these fundamental ideas in his famous book, The Principia in 1687. This book was written in two volumes, the Motion of Bodies (a physics book) and Systems of the World (physics of the sky). We can now take these basic foundations of physics and apply them to the motion of the planets and moon.
The story of Newton and the apple really happened. The apple never hit him on the head, but the idea sure did when he witnessed an apple falling in an orchard. Having formalized all the basic laws of motion, Newton applies these laws to the falling apple. So what do you observe when an apple falls from a tree? It accelerates (speeds up) as it falls. This told Newton that there must be a force acting on it ... a force he called gravity. This force obviously exerts itself through the fabric of space but Newton is quite vague as to what causes it, saying ...
"To all objects there is a power of gravity, proportional to the several quantities of matter which it contains."
Meaning that gravity originates from all objects and the more mass it has, the stronger the gravity.
Newton realized that gravity of Earth was pulling the apple to the ground and this force comes from each and every particle that makes up Earth. In an effort to simplify this, he wondered if he could replace all the "pieces of Earth" with one "point mass" which acted from the center of Earth. This would certainly simplify his calculations. In his effort to show this, Newton invented calculus! Wow ... he develops his own branch of mathematics to help solve his problems ... that's genius!
The apple and Earth may be treated as "point masses"
The weight of any object is simply the gravitational force between the object (apple) and Earth (or any other world it rests on). Your weight comes from every piece of "you" being pulled by every piece of "Earth". If you move to the moon, or mars, or any other planet, you will experience a different weight. However, your mass remains the same no matter where you are in this universe. Click here to calculate your weight on other planets.
Next, Newton wonders just how far this "force" emanating from Earth extends into space. It certainly has to stretch all the way to the moon. Why? Because if it did not, the moon would fly off at a tangent (green arrow).
Gravity keeps the moon in orbit around Earth.
He also realized that it is the gravity from the sun that keeps the planets in orbit around the sun ... and suspects that it extends into space indefinitely. But does its strength change as you move further away?
Newton showed that Kepler's Third Law of planetary motion (P2 = a3) will only work if gravity gets weaker with distance according to an inverse square relationship. What does this mean? It means that as an object (the apple) moves further from Earth, it will weigh less in a very predictable way. To help illustrate this law, consider any two masses at a given distance. For simplicity, let us say these masses are 1 unit apart and at that distance, there is a gravitational attraction between them of 1 unit of force. How does this force change when the masses are moved 2 units apart?
At a distance of 2 units, the force drops to 1/4 the original value. An understanding comes from the very name of the law - inverse square. When we move the masses further away, we are doubling the separation (center-to-center). The inverse of double is half. The square of half is one quarter.
If the masses are now moved to a separation of 5 units, the force drops to 1/5 * 1/5 = 1/25 th the original force.
Suppose a person weighs 160 pounds at the surface of Earth. We can now predict how much less that person would weigh if they moved off the surface. Suppose you construct a ladder which is 4000 miles high and a bathroom scale is placed at the top of this ladder. What would the scale read if this person stood on it? First understand that all distances are measured from the center of all objects ... meaning that anyone standing on the earth's surface is actually 4000 miles away from the center of Earth. When this person moves to the top of the ladder, they will be 8000 miles from earth's center. This means they will be doubling their separation. The demonstration above shows that the force of gravity drops to 1/4 the original value ... so this person's weight would become 1/4 * 160 = 40 pounds!
| Person at the surface | Person at the top of the ladder | |
| distance from center of Earth | 4000 mi | 8000 mi |
| weight of person | 160 pounds | 1/4 * 160 = 40 pounds |
Can you see why the same person would weigh only 10 pounds on a ladder 12,000 miles high? In theory, the person's weight will never really drop to zero but for all practical purposes, it becomes rather insignificant at large distances.
This is an interesting idea .. but is it true? Newton was able to show it was by examining the orbit of the moon. He realized it was impractical to weigh objects as we have proposed above ... so he showed there was another way of determining the strength of gravity at any location ... simply measure how far it "falls" in one second. At the earth's surface, all objects fall 16 feet the first second they are dropped (in a vacuum). If the force of gravity were stronger, objects would fall further than 16 feet in the first second ... and less if gravity were weaker. The trick was to see how far the moon "falls" toward Earth each second and compare it to 16 feet.
We start with the moon in position "A" and consider two different scenarios, its position one second later if there were no gravity (position "B"), and one second later with gravity (position "C"). Newton considered the distance the moon "falls" toward Earth each second as the length of segment BC and he measured it. When he found it was only 1/20th of an inch, he knew that earth's gravity was much weaker at the moon's distance ... exactly what was predicted if it followed the inverse square law.
Isaac Newton summarized the law of gravity in one simple equation:
F is the force of gravity between any two masses M1 and M2 where d is the distance between their centers and G is a constant known as the "gravitational constant". It is interesting to note that your weight is dependent on 3 variables - your mass (eat a lot and you gain weight), the mass of Earth (if the mass of Earth were less, so too would be your weight), and how far you are from the center (remember the ladder). Want to lose weight? Go to the moon! The force of gravity there is only 1/6 the value on Earth because the moon has a different mass and radius.
Once Newton understood the behavior of gravity, it became possible for him to show why all of Kepler's laws work. That is, given this law of gravity, Newton showed that planets must travel in elliptical orbits, and change their speed according to Kepler's law of areas. It is interesting to wonder ... if Kepler never discovered these laws from observation, would Newton have discovered them from theory?
Newton resisted publications of his findings because he wished to avoid his critics. Many years after Newton had done this work, he was approached by another well known scientist, Sir Edmond Halley (of comet fame) with a problem. At this meeting, Newton showed Halley his ideas about gravity. Halley was so impressed that he begged Newton to publish his ideas ... offering to pay all costs. The result was Newton's masterpiece - The Principia.
ŠJim Mihal 2004, 2014- all rights reserved