Celestial mechanics: The insurmountable velocity required to breach the sun's gravitational hold

“ Man has an instinct for travel and speed. To travel a couple of months is a sufficient reward for a thousand toilful days. He earnestly desires speed, develops race horses and bicycles to surpass them, yachts, and engines. Not satisfied with this, he harnesses lightning that takes his mind, his thought, to the ends of the earth in a twinkling. But he is stopped there. How he yearns to go to the moon, the sun, and stars! But he could not take his present body through the temperatures of space three or four hundred degrees below zero. ”

“ Well, the projectile is the carriage of the future, and, to speak the truth, planets are only projectiles, simple cannon-balls hurled by the hand of the Creator. But to return to our vehicle. Some of you, gentlemen, may think that the speed it will travel at is excessive—nothing of the kind. All the planets go faster, and the earth itself in its movement round the sun carries us along three times as fast. Here are some examples. Only I ask your permission to express myself in leagues, for American measures are not very familiar to me, and I fear getting muddled in my calculations. ”

“ Man began by walking on all-fours; then, one fine day, on two feet; then in a carriage; then in a stage-coach; and lastly by railway. Well, the projectile is the vehicle of the future, and the planets themselves are nothing else! Now some of you, gentlemen, may imagine that the velocity we propose to impart to it is extravagant. It is nothing of the kind. All the stars exceed it in rapidity, and the earth herself is at this moment carrying us round the sun at three times as rapid a rate, and yet she is a mere lounger on the way compared with many others of the planets! ”

“ Travelling with the speed of an express train flung into space at 40 miles an hour towards the nearest star without any stoppage or any slowing down, we should not arrive at our destination until after an uninterrupted flight of 75 million years.
Travelling with the speed of the swiftest projectile which the most ingenious man-killers have yet constructed, a speed which we can reckon as double that of sound, or 2,200 feet per second, we should yet require a million and a half years to cover that distance. ”

“ The sun apparently turns about us, rising every morning, setting at night; the earth where we are seems to be motionless: but the contrary is the truth. We live on a whirling projectile, thrown into space with a speed seventy-five times as great as that which carries a cannon-ball. ”

“ Who can contemplate the power which produced the solar system, at once so magnificent, beautiful, and delightful, without astonishment and admiration? The planets are kept in a regular motion, and retained in an invariable course round the sun, by the power of this luminary’s attraction or gravity. These bodies have a projectile force, being propelled forwards in a right line, which is the nature of all simple motion; but the sun’s attraction combining with their own projectile force, withdraws them from their rectilineal courses, and preserves the most perfect harmony in the system. ”

“ He is flying through space at the rate of not less than a hundred and sixty millions of miles in a year, and the earth and her sister planets are his fellow voyagers, which, obeying his overpowering attraction, circle about him as he advances. In other words, if we could take up a position in open space in advance of the sun, we should see him rushing toward us at the rate of some 450,000 miles a day, chased by his whole family of shining worlds and the vast swarms of meteoric bodies which obey his attraction. ”

“ The projectile from the planet, as it quits the neighbourhood of the parent globe, becomes appreciably affected by the attraction of the sun, and as its distance from the planet increases, the attraction of that planet dwindles to evanescence, while the attraction of the sun becomes the predominating influence by which the movement is guided. ”

“ If we look up at the clock, and as we watch the pendulum recall that we have moved about nineteen miles at every beat, or in less than three minutes, over a distance greater than that which divides New York from Liverpool, we still probably but very imperfectly realize the fact that (dropping all metaphor) the earth is really a great projectile, heavier than the heaviest of her surface rocks, and traversing space with a velocity of over sixty times that of the cannon-ball. ”

“ What inhabitant of the earth perceives its speed, which, however, is at the rate of 68,000 miles per hour? Motion under such conditions is "felt" no more than repose; and when a body is in repose it will remain so as long as no strange force displaces it; if moving, it will not stop unless an obstacle comes in its way. This indifference to motion or repose is called inertia.
Barbicane and his companions might have believed themselves perfectly stationary, being shut up in the projectile ”

“ The Earth is sustained by nothing material. What maintains her in equilibrium is the ethereal void; an immaterial force; gravitation. The [Pg 22] Sun attracts her, and if she did not revolve, she would drop into him; but rotating round him, at a speed of 107,000 kilometers [2] (about 66,000 miles) per hour, she produces a centrifugal force, like that of a stone in a sling, that is precisely equivalent, and of contrary sign, to its gravitation toward the central orb, and these two equilibrated forces keep her at the same medium distance. ”

“ The earth, for example, as it swings around the sun, tends to fly away from the center of its orbit. This tendency of the earth—its centrifugal force—keeps it from being drawn into the sun by the powerful pull of the sun's gravitation. At the same time it is this gravitation of the sun that keeps the earth from [pg 75] flying off into space, where we should all be frozen to icicles and lost in everlasting night. For if the sun's pull stopped, the earth would fly off as does a stone whirled from the end of a string, when you let go of the string. ”

“ The problem before us is how to communicate an initial force of 12,000 yards per second to a shell of 108 inches in diameter, weighing 20,000 lbs. Now when a projectile is launched into space, what happens to it? It is acted upon by three independent forces, the resistance of the air, the attraction of the earth, and the force of impulsion with which it is endowed. ”

“ We all recollect Jules Verne's voyage to the moon, in which he described the Columbiad, an imaginary cannon, capable of shooting out a projectile with a velocity of six or seven miles a second. This is the critical velocity for the earth. If we could imagine the air removed, then a cannon of seven-mile power would project a body upwards which would never fall down. ”

“ According to that philosopher, if a cannon was pointed vertically, and the projectile was discharged with a speed of seven miles a second it would soar aloft, and whether it went to the moon or not, it would at all events not return to the earth except by such a marvellous series of coincidences as those which he has described. But the story will at all events serve to illustrate the fact that for each particular globe there is a certain speed with which if a body leaves the globe it will not return. ”

“ The greater the body the greater in general must be the initial speed which will enable the projectile to forsake for ever the globe from [Pg 104] which it has been discharged. As we have already indicated, this speed is about seven miles per second on the earth. It would be three on the planet Mercury, three and a half on Mars, twenty-two on Saturn, and thirty-seven on Jupiter; while for a missile to depart from the sun without prospect of return, it must leave the brilliant surface at a speed not less than 391 miles per second. ”

“ From this illustration it will be plain that it is necessary to take into account both the mass of a globe and its dimensions when we would determine the height to which a projectile can ascend.
Let us consider the case of a great cannon placed on a globe of comparatively small mass, the density of that globe being about the same as the average density of the worlds which we find in the solar system. It is plain that as the object goes aloft a lessened attractive force will be exerted to check its upward movement, and consequently the speed will but slowly abate. ”

“ If, however, we were performing our experiments on some of the smaller globes belonging to the solar system, then a speed considerably less than that of seven miles a second would suffice to discharge the missile finally from the vicinity of the globe on which it was placed. A cannon, for instance, which was strong enough to impart to the projectiles that issued from it a velocity double as great as that which our missiles receive here, would send the body entirely away from the moon. On globes still smaller a speed correspondingly less would suffice. ”

“ Let us now pass to the attraction of the earth—that is to say, to the weight of the projectile. We know that that weight diminishes in an inverse ratio to the square of distances—in fact, this is what physics teach us: when a body left to itself falls on the surface of the earth, it falls 15 feet in the first second, and if the same body had to fall 257,542 miles—that is to say, the distance between the earth and the moon—its fall would be reduced to half a line in the first second. ”

“ If the earth had been alone in space, if the other celestial bodies had been suddenly annihilated, the projectile, according to Newton's laws, would weigh less as it got farther from the earth, but without ever losing its weight entirely, for the terrestrial attraction would always have made itself felt, at whatever distance. ”

“ Now, since the power of gravity and the resistance of the air will always be greater than any force of projection we can give a body, the latter must be gradually overcome, and the body brought to the ground; but the stronger the projectile force, the longer will those powers be in subduing it, and the farther will the body go before it falls. ”

“ You forget that every man upon this earth is continually moving at the rate of about sixty thousand miles an hour, this being the speed at which the earth revolves about the sun, and yet we find means to breathe comfortably. ”

“ The speed of the earth as it moves round the sun is more than eighteen miles a second—that is to say, it is three and a half times the critical speed of five miles. In virtue of this speed the earth has a corresponding quantity of energy. To find the equivalent of that energy it must, as already explained, be remembered that the energy of a moving body is proportional to the square of its velocity ”

“ The sun also, with its family of worlds and their satellites, is plunging through space at the rate of 8.5 mi. per second; moreover, there are swarms of huge suns, many larger than ours, moving in straight-lines like a universe on a journey, and countless millions of suns in swiftest flight through the skies, whose orbits and rates of motion must all be calculated and controlled by a mind of amazing power and intelligence. ”

“ All these millions, these thousands of millions, of suns hasten through boundless space with a speed which attains a velocity of two, three, and even four thousand metres a second. Motion maintains the equilibrium of the universe, and constitutes its organization, energy, and life. ”

“ Travelling thus continually, in twenty-four hours you would leave the last member of the solar system behind you, and begin your plunge into the depths of space. How long would it be before you encountered another object? A month, should you guess? Twenty years you must journey with that prodigious speed before you reach the nearest star, and then another twenty years before you reach another. At these awful distances from one another the stars are scattered in space, and were they not brilliantly self-luminous and glowing like our sun, they would be hopelessly invisible. ”

“ Just so it is with the planets: the attractive or centripetal force of the sun being equal to that of the projectile or centrifugal force of the planets, they are by attraction prevented moving on in a strait line, and, as it were, drawn towards the sun; and by the projectile force from being overcome by attraction. ”

“ For, if the Sun moves about the Earth, the Earth’s attractive power must draw the Sun towards it from the line of projection so, as to bend it’s motion into a curve; and the Earth being at least 169 thousand times lighter than the Sun, by being so much less as to it’s quantity of matter, must move 169 thousand times faster toward the Sun than the Sun does toward the Earth; and consequently would fall to the Sun in a short time if it had not a very strong projectile motion to carry it off. ”

“ A lesser speed would make the weight predominate, and would lead to the Earth's falling into the Sun; a greater speed, on the contrary, would progressively and infinitely send our planet away from [268] its life-giving focus. But at the speed resulting from gravitation, our wandering home remains suspended in permanent stability, just as the Moon is upheld in space by the force of the Earth's gravity, which makes it circulate about the Earth with the speed requisite to maintain it constantly at the same mean distance. ”

“ If the orbital speed of the earth were a mile less per hour, or even a foot less, then the earth would wind up around the sun as a dog gets wound up with his chain around a tree. If this speed were a mile more per hour, then the earth would wind out, each year getting farther and farther away, until finally it would be lost. When the speed is exactly proportional to the pull—that is, when it is as 1.6 is to 2,—the result is a circular orbit, the eccentricity of which is caused by certain fluctuations in the attraction and repulsion. ”