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J. Perelman
"Entertaining physics". Book 1.
Chapter 2. Gravity and weight. A lever. Pressure

FROM THE CANNON TO THE MOON

In 1865 - 1870 appeared in France fiction novel by Jules Verne “From a cannon to the moon”, which made an extraordinary idea: to send to the moon giant cannon projectile-wagon with real people! Jules Verne presented his project in such a believable way that most readers, probably, the question arose: is it possible to actually implement this idea? About this interesting visit [Now, after launching an artificial Earth satellites and space rockets, we can say that space travel will be used rockets, not missiles. However, the motion of a rocket after it worked the last stage, is subject to the same laws as the movement of the artillery shell. Therefore, the text of the author is not out of date. (Approx. as amended)].

First consider whether you can - at least theoretically - fire the gun so that the bullet never fell back to Earth. The theory allows for such a possibility. In fact, why the projectile, thrown horizontally gun, eventually falls to the Ground? Because the Earth, pulling the projectile, curves his way: he's not flying in a straight line and on a curve towards the Earth, and therefore sooner or later meets with soil. The surface, however, is also curved, but the path of the projectile curves are much steeper. If the curvature of the path of the projectile to weaken and make it identical with the curvature of the surface of the globe, then the projectile will never be able to fall to the Ground! He will move in a curve concentric with the circumference of the globe; in other words, will become his companion, like a second Moon.

But how to ensure that the projectile is thrown cannon went on his way, less curved than the earth's surface? For this purpose it is necessary only to inform him enough speed. Note on the picture representing the cut part of the globe.


The calculation speed of the projectile, which has to ever leave the Ground.

It remains to compute the line segment AB, i.e., the path traveled by the projectile in a second horizontal direction; then we learn how second speed is necessary for our purpose to throw the projectile from the vent of a cannon. To calculate it, it is easy from the triangle AOW, where OA is the radius of the globe (about 6 370 000 m); OS = OA, VS = 5 m; hence, 0V = 6 370 005 m Hence, by the Pythagorean theorem we have: (AB)2 = (6 370 005)2 - (6 370 000)2.

Making the calculation, we find that the path AB is approximately 8 km

Now, if it were not for air, which greatly hindered by the rapid motion, the projectile is thrown horizontally from a cannon with a speed of 8 km/sec, would never have fell to the Ground, and always swirled around it would like a companion.

And if you throw a projectile from a gun with greater speed, where he will fly? In celestial mechanics it is proved that at a speed of 8, 9, even 10 km/s projectile, flying from the vent of the gun must describe around the globe ellipse, the more elongated, more than the initial velocity. When the speed of the projectile 11.2 km/sec instead of the ellipse will describe non-closed curve is a parabola, forever moving away from the Earth.


The fate of the cannon shell fired with an initial speed of 8 km/sec and more.

We see, therefore, that it is theoretically possible to go to the moon within a projectile thrown with enough speed.

(The previous reasoning is meant an atmosphere which does not impede the movement of projectiles. In real conditions the presence of a resisting atmosphere is extremely difficult to obtain such high speeds, and maybe would make them completely inaccessible.)

Entertaining physics J. Perelman

 




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