Orbital Motion and Weightlessness |
(Think about these carefully before you consult the answers below)
QUESTIONS
1) If you went down deep underground in a mine, would your weight increase or decrease? <answer>
2) The speed required for a circular orbit of the Earth at 160 km (100 miles) altitude is about 7800 meters per second (roughly 17,500 miles per hour). If you launched a rocket straight up with that speed, would it orbit Earth? <answer>
3) At 35,900 km (22,300 miles) above the Equator, a 1000 kilogram weather satellite orbits in 24 hours, making it a geosynchronous satellite. (That is, because its orbital period is the same as the rotational period for Earth, the satellite stays over one place all the time as if hovering.) What would be the orbital period of a smaller, 500 kilogram satellite at the same altitude? <answer>
4) Imagine that you are an astronaut heading for the Moon, floating weightlessly about the cabin. Suddenly Mission Control calls and tells you the spacecraft is not moving fast enough toward the Moon. You must fire your rocket engine again. When you do, an errant cup comes flying across the cabin and beans you on the head! Ouch! At the same time, every object not stowed or otherwise secured flies backwards as if pulled by gravity. However, you know that the Earth's gravity is actually weakening at this point. What gives? <answer>
5) If you are a fan of science fiction, not doubt you have seen many sci-fi movies and TV shows in which the actors neither float nor have any trouble moving about, even when in deep space. The typical answer is that they are using "artificial gravity." Is "artificial gravity" even possible, and if so, how? <answer>
ANSWERS
1) It would decrease. As you move downward in the mine, your distance to the center of the Earth decreases. Considering this fact alone, and plugging it into Newton's Law of Universal Gravitation, you would immediately think that your weight would be greater because the force of gravity should be greater the closer you get to the center. But that isn't the whole picture. As you move downward in the Earth, the effective mass of the Earth changes, as Newton showed, because you can consider only the Earth from whatever your depth is down to the center of the planet. The mass of Earth above you attracts you, too, except that it pulls you upward! The result is that your weight is less as you go down in a mine. (If you could reach the exact center of Earth and survive, you would have no weight at all, just as if you were weightless in space. Why? It is because at the center of the Earth, the gravity of all overlying areas would be pulling you equally in all directions -- thus there would be no net force of gravity and you would feel weightless.
2) If you launched the rocket straight up without the influence of any outside forces other than gravity, the answer is no . If you launched it without any sideways motion, it would simply go up until its fuel ran out, and then fall back to Earth under the force of gravity. In order to orbit, there has to be sideways motion so that the rocket or satellite can fall around the curvature of Earth.
If on the other hand, you launched it with a speed of about 11,080 meters per second (6.89 miles per second), it would escape forever the Earth's gravitational pull, regardless of the direction.
3) Uh oh! This is kind of a trick question. As long as the mass of the satellites are small compared the the mass of the Earth, their masses don't enter into the consideration. All satellites at 35,900 km above the Equator, orbiting from West to East (the direction of the Earth's turning), will orbit at the same speed and have the same period of 24 hours. At any given height, any satellite in a circular orbit will have the same speed and period as any other at that height. (You can find out more in Section 2.7 of your text.)
4) In Section 2.2 you can read about inertia, which is a property of matter that causes it to resist changes in motion. Thus any objects that were not secured to the spacecraft would not want to accelerate with the rest of the spacecraft. They wouldn't immediately get the same push forward that the rest of the spacecraft got from the rocket. The result is that the spacecraft would move forward faster than those floating objects, and the difference in motions would cause them to appear to fall in the direction opposite of the motion of the spacecraft. The astronaut would feel "G" forces just as if he or she were in the presence of a strong gravitational field. Both Galileo and Newton had a lot to say about inertia, and nearly 300 years after Newton, Albert Einstein declared in his "Principle of Equivalence" that in the absence of any other clues, you can't tell the difference between true gravity and the sensation of acceleration.
5) As generally portrayed on "Star Trek" and "Star Wars" and a myriad other sci-fi shows, "artificial gravity" will be possible through some kind of electronic or "force field" mechanism. However, at present there does not seem to be any reason to believe that this kind of artificial gravity on is achievable or even possible . Certainly there is no known mechanism whereby artificial gravity as portrayed in these programs could be produced, nor does it even seem likely at this point that one will ever be found.
On the other hand, one form of "artificial gravity" is possible and will in fact be employed on the International Space Station. You have sensed it every time you've been on a roller coaster or encountered a sudden updraft in an airplane. It is a product of inertia. Any time you are being accelerated (or decelerated), your body wants to resist the changes in motion. Your body feels pushed in the opposite direction, as in the answer to #4 above.
To create "artificial gravity" in a space station, all that needs to be done is to rotate it. The angular acceleration caused by the rotation will push objects to the outer edge of the space station, a sensation which will feel to humans just like gravity. (This effect is well illustrated in the space station scenes from the classic, "2001: A Space Odyssey."
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