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Variant, v. 1, issue 3, September 1947
Page 34
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a reasonable amount. This means velocities which you measure in terms of miles per second. The second reason is more technical. Let us imagine we are situated on tip of a high mountain, shooting in a horizontal direction with a cannon. As any fool can plainly see, the greater the muzzle velocity of the cannon, the farther away the projectile is going to land. Even with muzzle velocities of a few thousand feet per second, the shell is going to land beyond the horizon, and as you raise the speed, the shell reaches farther and farther around the curvature of the earth. (See figure 1) It can be calculated that at about five miles per second the shell will go all the way around the earth and come up on you from behind. That's what they call the circular velocity. If you send the shell off at a slightly higher velocity it will take on an elliptical orbit, and will proceed to move permanently around the earth. (See figure 2) The greater the velocity the more elongated will be the orbit, until finally at about seven miles per second the shell won't come back at all. And that is what they call the escape velocity. The same general situation holds if you send the shell straight up in the air. At seven miles per second the shell will keep on going and never come back. (This incidentally, happens to be the velocity which a body would have if it fell to the earth from an extremely great distance. You can see the possibilities that this presents. If you could give a space ship the escape velocity, pointed in the proper direction,it would keep coasting along in space until it reached a destination. Now while it is impractical to give the ship that great velocity at one blow, it certainly should be possible to take a number of minutes or hours to attain seven miles per second using an acceleration which human beings could withstand. [[illustration text]] Figure 1. ELLIPTIC ORBIT 5 TO 7 MILE PER SECOND Figure 2. [[end illustration text]] (34)
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a reasonable amount. This means velocities which you measure in terms of miles per second. The second reason is more technical. Let us imagine we are situated on tip of a high mountain, shooting in a horizontal direction with a cannon. As any fool can plainly see, the greater the muzzle velocity of the cannon, the farther away the projectile is going to land. Even with muzzle velocities of a few thousand feet per second, the shell is going to land beyond the horizon, and as you raise the speed, the shell reaches farther and farther around the curvature of the earth. (See figure 1) It can be calculated that at about five miles per second the shell will go all the way around the earth and come up on you from behind. That's what they call the circular velocity. If you send the shell off at a slightly higher velocity it will take on an elliptical orbit, and will proceed to move permanently around the earth. (See figure 2) The greater the velocity the more elongated will be the orbit, until finally at about seven miles per second the shell won't come back at all. And that is what they call the escape velocity. The same general situation holds if you send the shell straight up in the air. At seven miles per second the shell will keep on going and never come back. (This incidentally, happens to be the velocity which a body would have if it fell to the earth from an extremely great distance. You can see the possibilities that this presents. If you could give a space ship the escape velocity, pointed in the proper direction,it would keep coasting along in space until it reached a destination. Now while it is impractical to give the ship that great velocity at one blow, it certainly should be possible to take a number of minutes or hours to attain seven miles per second using an acceleration which human beings could withstand. [[illustration text]] Figure 1. ELLIPTIC ORBIT 5 TO 7 MILE PER SECOND Figure 2. [[end illustration text]] (34)
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