Celestial Machine

Celestial Machine

Gravity

Suppose we had a magic gravity machine – a device with which we could control the Earth’s gravity, perhaps by turning a dial… Initially the dial is set at 1 g and everything behaves as we have grown up to expect.

1 g is the acceleration experienced by falling objects on the Earth, almost 10 meters per second every second. A falling rock will reach a speed of 10 meters per second after one second of all, 20 meters per second after two seconds, and so on until it strikes the ground or is slowed by friction with the air. On a world where the gravitational acceleration was much greater, falling bodies would increase their speed by correspondingly greater amounts. On a world with 10 g acceleration, a rock would travel 10×10 m/sec. or almost 100 m/sec after the first second, 200m/sec after the next second, and so on. A slight stumble could be fatal.

The acceleration due to gravity should always be written with a lowercase g, to distinguish it from the Newtonian gravitation constant, G, which is a measure of the strength of gravity everywhere in the universe, not merely on whatever world or sun we are discussing. The Newtonian relationship of the two quantities is F = mg = GM/r2, where F is the gravitational force, M is the mass of the planet or star, m is the mass of the falling object, and r is the distance from the falling object to the center of the planet or star.

The cosmic Cheshire cat has vanished; only its gravitational grin remains… Image: © Elena

The animals and plants on Earth and the structures of our buildings are all evolved and designed for 1g. If the gravity were much less, there might be tall, spindly shapes that would not be tumbled or crushed by their own weight. If the gravity were much more, plants and animals and architecture would have to be short and squat and sturdy on order not to collapse. But even in a fairly strong gravity field, light would travel in a straight line, as it does, of course, in everyday life.

Consider a possibly typical group of Earth beings at the tea party from Alice in Wonderland. As we lower the gravity, things weigh less. Near 0 g the slightest motion sends our friend floating and tumbling up in the air. Spilled tea – or and other liquid – forms throbbing spherical globs in the air: the surface tension of the liquid overwhelms gravity. Balls of tea are everywhere. If now we dial 1g again, we make a rain of tea. When we increase the gravity a little – from 1 g to, say, 3 or 4 g’s – everyone becomes immobilized: even moving a paw requires enormous effort.

As a kindness we remove our friends from the domain of the gravity machine before we dial higher gravities still. The beam from a lantern travels in a perfectly straight line (as nearly as we can see) at a few g’s, as it does at 0 g. At 1000 g’s, the beam is still straight, but trees have become squashed and flattened; at 100,000 g’s rocks are crushed by their own weight. Eventually, nothing at all survives except, through a special dispensation, the Cheshire cat.

When the gravity approaches a billion g’s, something still more strange happens. The beam of light, which has until now been heading straight up into the sky, if beginning to bend. Under extremely strong gravitational accelerations, even light is affected. If we increase the gravity still more, the light is pulled back to the ground near us.

When the gravity approaches a billion g’s the cosmic Cheshire cat will vanish and nothing will be as it has been before. Illustration by Elena.

Magnetism and Gravity

Magnetism is, of course, not the same as gravity, but Kepler’s fundamental innovation here is nothing short of breathtaking: he proposed that quantitative physical laws that apply to the Earth are also the underpinnings of quantitative physical laws that govern the heavens. It was the first nonmystical explanation of motion in the heavens; it made the Earth a province of the Cosmos. “Astronomy”, Kepler said, “is part of physics”. Kepler stood at a cusp in history; the last scientific astrologer was the first astrophysicist.

Johannes Kepler: My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork…, insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force, as in the case of clockwork, where all motions are caused by a simple weight.

Within the symphony of voices, Kepler believed that the speed of each planet correspond to certain notes in the Latinate musical scale popular in his day – do, re, mi, fa, sol, la, ti, do. He claimed that in the harmony of the spheres, the tones of Earth are fa and mi, that the Earth is forever humming fa and mi, and that they stand in a straightforward way for the Latin word for famine. He argued, not unsuccessfully, that the Earth was best described by that single doleful word.

By changing our perspective we can figure how world work. Image: Megan Jorgensen (Elena)

Exactly eight days after Kepler’s discovery of his third law of nature, the incident that unleashed the Thirty Years’ War transpired in Prague. The war’s convulsions shattered the lives of millions, Kepler among them. He lost his wife and son to an epidemic carried by the soldiery, his royal patron was deposed, and he was excommunicated by the Lutheran Church for his uncompromising individualism on matters of doctrine. Kepler was a refugee once again. The conflict, portrayed by both the Catholics and the Protestants as a holy war, was more an exploitation of religious fanaticism by those hungry for land and power. In the past, war had tended to be resolved when the belligerent princes had exhausted their resources. But now organized pillage was introduced as a means of keeping armies in the field. The savaged population of Europe stood helpless as plowshares and pruning hooks were literally beaten into swords and spears (some examples of these arms are still to be seen in the Graz armory).

Waves or rumor and paranoia swept through the countryside, enveloping especially the powerless. Among the many scapegoats chosen were elderly women living alone, who were charged with witchcraft: Kepler’s mother was carried away in the middle of night in a laundry chest. In Kepler’s little hometown of Weil des Stadt, roughly three women were tortured and killed as witches every year between 1615 and 1629. And Katharina Kepler was a cantankerous old woman. She engaged in disputes that annoyed the local nobility, and she sold soporific and perhaps hallucinogenic drugs as do contemporary Mexican curanderas. Poor Kepler believed that he himself had contributed to her arrest.