Mouse Over to View AnimationTyco Brahe was born soon after Copernicus died. He spent his life making measurements of the planet's orbits. His assistant was Johannes Kepler. After Brahe's death, Kepler worked with Brahe's measurements to discover the paths the planets follow. his discovery shattered common conceptions: He found that the path of the planets are ellipses. Kepler's first law states that the orbit of all planets are ellipses with the sun at one foci. Kepler also discovered that the planets do not move at the same speed at every point in their orbits. They move faster closer to the sun and slower further from the sun. They do this in such a way that if an imaginary line is drawn from the planet to the sun, the area swept out by the line in a time interval while the planet is far from the sun is the same as the area swept out in the same time interval while the planet is close to the sun. This is Kepler's second law.
Mouse Over to View Animation10 years later, Kepler discovered a third law relating the size of a planet's orbit to the time it takes a planet to make one full orbit around the sun. The third law states that the square of the orbital period of a planet is directly proportional to the cube of the planet's average distance from the sun, or T2~r3.
Newton was among the first people to think that there was a force holding the planets in motion. Most people believed that the planet's motions were natural, and that they were not governed by the same laws that govern things on the earth. Newton believed that the force holding the planets in orbit was the same as the force that makes an apple fall: gravity. Newton reasoned that a body in orbit, like the moon, falls like an apple. He reasoned that the moon falls beneath the straight line path it would follow if there was no forces acting on it.
Mouse Over to View AnimationFrom his observations, and from Kepler's laws, Newton deduced the Universal Law of Gravitation: Every two objects pull on each other with a gravitational force that is proportional to the product of their masses and inversely proportional to the distance between them squared, or F~mM/d2. This proportionality can be written as an exact equation when the universal gravitation constant, G, is introduced. Then F=GmM/d2. G was first measured by Henry Cavendish, an English physicist, who measured the gravitational force between two lead masses. G was found to be 6.67*10-11 N*m2/Kg2.(6.67 times ten to the negative eleventh Newton meters squared/kilograms squared.)
Gravity decreases with the square of the distance between two objects. This is the inverse square law. Understand that d means the distance between the centers of mass of the two objects. The graph of the inverse square law is a hyperbola, meaning that the gravitational force from an object never reaches zero. Every object pulls on every other object.
When you step on a scale, a spring inside the scale is compressed, moving a pointer to read your weight. Consider yourself in an elevator with a scale inside it. When the elevator is at rest, the scale reads your weight. If the elevator moves up, the spring in the scale will compress more, reading a heavier weight. If the elevator moves down, the spring will compress less, reading a lighter weight. If the elevator cable snaps and you free fall in the elevator, the scale will read no weight at all. Are you really weightless?
Mouse Over to View AnimationThe weight of an object is the force it exerts on the supporting floor, or scale. So if the elevator is in free fall, you are exerting no force on the scale and feeling no weight! You are weightless. However, there is still a gravitational force acting on you, it just isn't felt as weight. Consider an astronaut in orbit around the earth. The astronaut is weightless. According to Newton, the astronaut is freely falling around the earth. When you are in free fall, you are weightless. If the astronaut were in a spaceship that was accelerating, even if the ship was far away from all gravitational sources, the astronaut would fell weight. So weight and gravity don't have to go together.
Seafarers have always known that the moon and tides were related. Newton showed that this is because the moon is pulling with a stronger gravitational force on one side of the earth than the other. Consider a ball of Jell-O. If you pull with the same force on all parts of the ball, the ball will remain spherical as it moves. But if you exert a greater force on one side of the ball, the Jell-O will become elongated as it moves. The same thing happens with the earth and the moon. The earth is elongated, mostly in its oceans. Bulges are produced at fixed places (with respect to the moon.) there are two high tide bulges and two low tide bulges. Since the earth rotates once per day, a point on the earth will pass through all of these bulges. So there are two high tides and two low tides per day.
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The sun has a gravitational force 180 times as strong as the moon. So why doesn't the sun produce huge tides? Newton deduced the reason for this, too. The sun is so far from the earth that it doesn't pull much stronger on one side of the earth than the other. Newton discovered that the tidal force between two objects is inversely proportional to the distance between them cubed, or Ft~1/d3. So the tidal force decreases faster than the gravitational force. The sun does contribute a little bit to tides. When the sun and the moon are lined up there is an abnormally high high tide and an abnormally low low tide. These are called spring tides. When the sun and the moon are at right angles to each other there is a high low tide and a low high tide. This is called neap tides.
t Tides are also formed in our atmosphere and in the earth's magnetic field. There are tides on the moon and tides on the sun. Gravity is everywhere.