Orbital Motion and Weightlessness |
Imagine that you are standing on the top of a hill. If you throw a rock straight off the top of the hill, it will move forward and down at the same time. It goes forward because of the initial force that you apply to it, and it moves downward because gravity is pulling on it. (Another force -- friction -- also slows down the rock, but let's ignore that for the moment.)
What if you threw the rock with a greater force? Naturally it would go farther before it fell back to Earth. Newton imagined (Section 2.3) something similar with a cannon firing a cannonball off the top of a hill.
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Ignoring air friction, and the probability of running into a mountain or tall building, Newton imagined a cannon firing cannonballs straight out from the top of a hill.
1) With just a little powder, the cannon ball would go only a short distance before the force of gravity pulled it back to Earth (Gravity always pulls downward, toward the center of the Earth). 2) With more powder (that is, more initial force or impulse ), the cannonball goes farther, perhaps even out of sight and over the horizon. 3) Newton realized that by giving the cannonball a greater push in the beginning, it could travel thousands of miles before the Earth's own gravity pulled it down to the surface. By Newton's time, the size of the Earth was reasonably established, so he knew that if the cannonball could be given enough impulse that it would travel 25,000 miles, it would... 4) ...come back to the place it started -- it would have made a complete circuit around the world. And with just a little more impulse, it would continue around and around, over and over -- it would be orbiting in the same way the Moon orbits Earth! |
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Newton realized that a cannonball would orbit Earth, if it could be pushed far enough forward such that by the time it had fallen one foot toward Earth (because of gravity), the Earth had curved out from under it by one foot. In effect, the cannonball would fall around Earth, but would never get any closer because the Earth curved out from under it at the same rate. This is called free-fall , and it is the situation in which astronauts experience weightlessness . In weightlessness, everything seems to float freely because everything is falling at the same rate.
You have experienced weightlessness, perhaps without even knowing it. Have you ever been on a trampoline? Or have you ever just jumped? It seems strange to think of it as weightlessness, but the floating sensation you have for that very short period of time is weightlessness. Even the sensation you feel when going down in an elevator, or when the "bottom drops out" in an airplane or roller coaster, is partial weightlessness. You see, weightlessness is really just a sensation, a perception, rather than a true physical state. While you are weightless, you are still under the influence of gravitational forces, but since their is nothing to stop your fall, you don't feel gravity. (When you are on solid ground , the force of gravity is pulling you against the surface and hence you feel it. When astronauts are in orbit, there is nothing to stop their fall because everything else is falling at the same rate. Hence they feel no weight. The same is true when you are in the middle of a jump, and even partially true when going down in a fast elevator.)
Have you ever seen the movie, "Apollo 13"? The scenes in which the actors appear weightless seem so realistic because the actors are weightless! No, they were not actually in space, but the interior set of the spacecraft actually was the interior of a large airplane called the "Vomit Comet." This plane climbed up at a steep angle and then pitched over into a steep dive. For a few seconds at the top of the curve, the plane and everything in it (including the actors and sets) were falling at the same rate in the same direction -- hence they experienced "weightlessness" To complete the movie, the airplane had to perform the maneuver hundreds of times!
So, what is weight anyway? Weight is the sensation you experience when gravity pulls you against something such as the surface of the the Earth. If you are not being pulled against anything (as when you are in the middle of a jump), then you do not experience weight.
The concept of weight is not a precise one. Your weight varies according to the strength of the gravitational field you are in. For instance, on other planets or the Moon, your weight would be different from what it is on Earth. Try this:
Your Weight on Other PlanetsIf your browser isn't JAVASCRIPT capable, you will not see the form above. This script was last modified on . |
Since weight varies so much, physicists, astronomers and other scientists usually refer to mass instead. Mass is a measure of the amount of matter in a body. For instance, a one-cubit-foot sphere of iron is much more massive than a sphere of Styrofoam the same size. The force of gravity will pull more strongly on the iron sphere than on the Styrofoam sphere, so the iron sphere weighs more. The catch is that the weight of both spheres depends on the strength of gravity, so if we are discussing the weight of the spheres on different planets, it can get quite confusing.
On the other hand, mass does not vary. The iron sphere will have the same mass on Mars or the Moon as it does on the Earth (The concept of mass is discussed in section 2.4 in your book). For more about gravity, click here: Newton's Law of Universal Gravitation.
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