Celestial Ships

Celestial Ships

Tycho Brahe, like Johannes Kepler, was far from hostile to astrology, although he carefully distinguished his own secret version of astrology from the more common variants of his time, which he thought conducive to superstition. In his book Astronomiae Instauratae Mechanica, published in 1598, he argued that astrology is “really more reliable than one would think” if charts of the position of the stars were properly improved. Brahe wrote: “I have been occupied in alchemy, as much as by the celestial studies, from my 23rd year.” But both of these pseudosciences, he felt, had secrets far too dangerous for the general populace (although entirely safe, he though, in the hand of those princes and kings from whom he sought support). Brahe continued the long and truly dangerous tradition of some scientists who believe that only they and the temporal and ecclesiastical powers can be trusted with arcane knowledge: “It serves no useful purpose and is unreasonable, to make such things generally known”.

Kepler, on the other hand, lectured on astronomy in schools, published extensively and often at his own expense, and wrote science fiction, which was certainly not intended primarily for his scientific peers. He may not have been a popular writer of science in the modern sense, but the transition in attitudes in the single generation that separated Tycho and Kepler is telling.

I prefer the hard truth to my dearest illusions. Image: As Stars Shine Bright by © Elena

But it was a Thirty Years’ War epoch. As soon as Kepler learned about his mother’s fate, in the midst of other grave personal problems, hi rushed to Würtemberg to find his seventy-four-year-old mother chained in a Protestant secular dungeon and threatened, like Galileo in a Catholic dungeon, with torture. He set about, as a scientist naturally would, to find natural explanations for the various events that had precipitated the accusations of witchcraft, including minor physical ailments that the burghers of Württemberg had attributed to her spells. The research was successful, a triumph, as was much of the rest of his life, of reason over superstition. His mother was exiled, with a sentence of death passed on her should she ever return to Wüttemberg; and Kepler’s spirited defense apparently led to a decree by the Duke forbidding further trials for witchcraft on such splender evidence.

The upheavals of the war deprived Kepler of much of his financial support, and the end of his life was spent fitfully, pleading for money and sponsors. He cast horoscopes for the Duke of Wallenstein, as he had done for Rudolf II, and spent his final years in a Silesian town controlled by Wallenstein and called Sagan.

Kepler’s epitaph, which he himself composed, was: “I measured the skies, now the shadows I measure. Sky-bound was the mind, Earth-bound the body rests”. The Thirty Years’ War obliterated his grave. If a marker were to be erected today, it might read, in homage to his scientific courage: “He preferred the hard truth to his dearest illusions”.

Johannes Kepler believed that there would one day be “celestial ships with sails adapted to the winds of heaven” navigation the sky, filled with explorers “who would not fear the vastness” of space. And today those explorers, human and robot, employ as unerring guides on their voyages through the vastness of space the three laws of planetary motion that Kepler uncovered during a lifetime of personal travail and ecstatic discovery.

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.

Stars Are Born in Batches

Stars Are Born in Batches

Two protons and two neutrons are the nucleus of a helium atom, which turns out to be very stable. Three helium nuclei make a carbon nucleus; four, oxygen; five, neon; six, magnesium; seven, silicon; eight, sulfur; and so on. Every time we add one or more protons and enough neutrons to keep the nucleus together, we make a new chemical element. If we subtract one proton and three neutrons from mercury, we make gold, the dream of the ancient alchemists. Beyond uranium there are other elements that do not naturally occur on Earth. They are synthesized by human beings and in most cases promptly fall to pieces. One of them, Element 94, is called plutonium and is one of the most toxic substances known. Unfortunately, it falls to pieces slowly.

Where do the naturally occurring elements come from? We might contemplate a separate creation of each atomic species. But the universe, all of it, almost everywhere, is 99 percent hydrogen and helium, the two simplest elements. Helium, in fact, was detected on the Sun before it was found on the Earth – hence its name (from Helios, one of the Greek sun gods).

Supernova explosions are the death of stars. Image: © Elena

But the Earth is an exception, because our primordial hydrogen, only weakly bound by our planet’s comparatively feeble gravitation attraction, has by now largely escaped to space. Jupiter, with its more massive gravity, has retained at least much of its original complement of the lightest element.

Might the other chemical elements have somehow evolved from hydrogen and helium? To balance the electrical repulsion, pieces of nuclear matter would have to be brought very close together so that the short range nuclear forces are engaged. This can happen only at very high temperatures where the particles are moving so fast that the repulsive force does not have time to act –temperatures of tens of millions of degrees. In nature, such high temperatures and attendant high pressures are common only in the insides of the stars.

In the direction of the star Deneb, in the constellation of Cygnus the Swan, is an enormous gloving superbubble of extremely hot gas, probably produced by supernova explosions, the death of stars, near the center of the bubble. At the periphery, interstellar matter is compressed by the supernova shock wave, triggering new generations of cloud collapse and star formation. In this sense, stars have parents; and, as is sometimes also true for humans, a parent may die in the birth of the child.

Stars like the Sun are born in batches, in great compressed cloud complexes such as the Orion Nebula. Seen from the outside, such clouds seem dark and gloomy. But inside, they are brilliantly illuminated by the hot newborns stars. Later, the stars wander out of their nursery to seek their fortunes in the Milky Was, stellar adolescents still surrounded by tufts of glowing nebulosity, residues still gravitationally attached of their amniotic gas. The Pleiades are a nearby example. As in the families of humans, the maturing stars journey far from home, and the siblings see little of each other. Somewhere in the Galaxy there are stars – perhaps dozens of them – that are the brothers and sisters of the Sun, formed from the some cloud complex, some 5 billion years ago. But we do not know which stars they are. They may, for all we know, be on the other side of the Milky Way.

Cyg X-1

Cyg X-1

What Cyg X-1 could possibly be?

Cyg X-1 is in precisely the same place in the sky as a hot blue supergiant star, which reveals itself in visible light to have a massive close but unseen companion that gravitationally tugs it furs in one direction then in another. The companion’s mass is about ten times that of the Sun. The supergiant is an unlikely source of X-rays, and it is tempting to identify the companion inferred in visible light with the source detected in X-ray light. But an invisible object weighing ten times more than the Sun and collapsed into a volume the size of an asteroid can only be a black hole. The X-rays are plausible generated by friction in the disk of gas and dust accreted around Cyg X-1 from its supergiant companion. Other stars called V861 Scorpii, GX339-4, SS433, and Circinus X-2 are also candidate black holes. Cassiopeia A is the remnant of a supernova whose light should have reached the Earth in the seventeenth century, when there were a fair number of astronomers. Yet no one reported the explosion. Perhaps, as I. S. Shklovskii has suggested, there is a black hole hiding there, which ate the exploding stellar core and damped the fires of the supernova. Telescopes in space are the means for checking these shards and fragments of data that may be the spoor, the trail, of the legendary black hole.

Cygnus X-1. You would take an infinite amount of time to fall in a Black Hole. Image in public domain

A helpful way to understand black holes is to think about the curvature of space. Consider a flat, flexible, lined two-dimensional surface, like a piece of graph paper made of rubber. If we drop a small mass, the surface is deformed or puckered. A marble rolls around the pucker in an orbit like that of a planet around the Sun. In this interpretation, which we owe to Einstein, gravity is a distortion in the fabric of space. In our example, we see two-dimensional space warped by mass into a third physical dimension. Imagine we live in a three-dimensional universe, locally distorted by matter into a fourth physical dimension that we cannot perceive directly.

The greater the local mass, the more intense the local gravity, and the more severe the pucker, distortion or warp of space. In this analogy, a black hole is a kind of bottomless pit. What happens if you fall in? As seen from the outside, you would take an infinite amount of time to fall in, because all your clocks – mechanical and biological – would be perceived as having stopped. But from your point of view, all your clocks would be ticking away normally.

Gravity and Black Holes

Gravity and Black Holes

When the gravity is sufficiently high, nothing, not even light, can get out. Such a place is called a black hole. Enigmatically indifferent to its surroundings, it is a kind of cosmic Cheshire cat. When the density and gravity become sufficiently high, the black hole winks out and disappears from our universe. That is why it is called black: no light can escape from it. On the inside, because the light is trapped down there, things may be attractively well-lit.

Even if a black hole is invisible from the outside, its gravitational presence can be palpable. If, on an interstellar voyage, you are not paying attention, you can find yourself drawn into a irrevocably, your body stretched unpleasantly into a long, thin thread. But the matter accreting into a disk surrounding the black hole would be sight worth remembering, in the unlikely case that you survived the trip.

Cyg X-1, a mysterious brilliant, blinking source of X-rays, visible over interstellar distances. Image: © Elena

Thermonuclear reactions in the solar interior support the outer layers of the Sun and postpone for billions of years a catastrophic  gravitational collapse. For white dwarfs, the pressure of the electrons, stripped from their nuclei, holds the star up. For neutron stars, the pressure of the neutrons staves off gravity. But for an elderly star left after supernova explosions and other impetuosities with more than several times the Sun’s mass, there are no forces known that can prevent collapse. The star shrinks incredibly, spins, reddens and disappears. A star twenty times the mass of the Sun will shrink until it is the size of greater Los Angeles: the crushing gravity becomes 10(10) g’s, and the star slips through a self-generated crack in the space-time continuum and vanishes from our universe.

Black holes were first thought of by the English astronomer John Mitchell in 1783. But the idea seemed so bizarre that it was generally ignored until quite recently. Then, to the astonishment of many, including many astronomers, evidence was actually found for the existence of black holes in space. The Earth’s atmosphere is opaque to X-rays. To determine whether astronomical objects emit such short wavelengths of light, an X-ray telescope must be carried aloft. The first X-ray observatory was an admirably international effort, orbited by the United States from an Italian launch platform in the Indian Ocean off the coast of Kenya and named Uhuru, the Swajili word for “freedom”.

In 1971, Uhuru discovered a remarkably bright X-ray source in the constellation of Cygnus, the Swan, flickering on and off a thousand times a second. The source, called Cygnus X-1, must therefore be very small. Whatever the reason for the flicker, information on when to turn on and off can cross Cyg X-1, no faster than the speed of light, 300, 000 km/sec. Thus Cyg X-1 can be no larger than 300,000 km/sec X 1/10000 sec = 300 kilometers across. Something the size of an asteroid is a brilliant, blinking source of X-rays, visible over interstellar distances.