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J. Perelman
"Entertaining physics". Book 2.
Chapter 5. Journey into the cannon projectile

NEWTONIAN MOUNT

In conclusion, our conversations about the laws of motion and gravity will consider it a fantastic trip to the moon, which is so entertaining described in the novels of Jules Verne's "From the Earth to the moon" and "Around the moon" (English translation-Wovoka entitled: "From a cannon to the moon"). Of course, you remember that the members of the Gun club of Baltimore, doomed to inaction with the end of the American war, decided to cast a giant gun, charge her huge hollow shell and put inside passengers, shot to send the bullet-train to the moon.

Fantastic if this idea? And first of all: is it possible to inform the body such speed that it permanently left the earth's surface?

Let's give a word to the genius of Newton who discovered the law of universal gravitation. In his "Mathematical principles of physics," he writes (here is the place for the sake of easy understanding, in free translation):

"Cast stone under the action of gravity deviates from the straight path and falls to the Ground, describing a curve line. If you throw a stone with greater speed, it will fly away; therefore, it may happen that he will describe an arc in ten, a hundred, a thousand miles, and finally leaves the Earth and will not go back on it more. Let AFB (see figure) represents the surface of the Earth, With its centre, a UD, UE, UF, UG - curves, which describes the body, throw in a horizontal direction with a very high mountain with greater and greater speed. We do not take into account the reluctance of the atmosphere, i.e., we assume that it is completely absent. When youngest of the initial velocity of the body describes a curve UD, and at a faster rate curve UE, at higher speeds - curves UF, UG. At a certain speed, the body will go round the whole Earth and will return to the top of the mountain, from which he was thrown. So as returning to the initial point of the velocity of the body will not be less than at the beginning, the body will continue to move further along the curve.


How should falling stones thrown on top of a mountain with great speed in the horizontal direction.

If this imaginary mountain gun was then thrown out of her shell at a known speed never would have fallen back to Earth, and would be a non-stop whirl around the globe. Through a fairly simple calculation it is easy to determine that it should occur at a speed of about 8 km per second. In other words, the projectile leaving the gun with a speed of eight kilometers per second, permanently leaves the surface of the globe and becomes a satellite of our planet. He will be racing in 17 times faster than any point on the equator, and describe a complete revolution around the planet in 1 hour 24 minutes. If you inform the projectile faster it will rotate around the Earth is not a circle, but more or less elongated ellipse, away from Earth at a great distance. The greater the initial velocity of the projectile has been permanently removed from our planet in outer space. This should occur at the initial speed of about 11 miles per second. (In all these arguments have in mind the shells moving in empty space, not in the air.)

Now let's seewhether you can take a flight to the moon of the tools offered by Jules Verne. Modern guns are reported to the projectile speed is not more than two kilometers in the first second. This is five times less than the speed with which the body can go to the moon. The characters of the novel was thinking that if they build a giant cannon and it will charge a huge amount of explosives, they will be able to get fast enough to send a projectile to the moon.

Entertaining physics J. Perelman

 




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