Solar Calculator Solar Quotes

Le Verrier—without leaving his study, without even looking at the sky—had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen!

I felt like a calculator with someone's finger over the solar panel - fading in and out, threatening to shut off altogether.

His laws changed all of physics and astronomy. His laws made it possible to calculate the mass of the sun and planets. The way it's done is immensely beautiful. If you know the orbital period of any planet, say, Jupiter or the Earth and you know its distance to the Sun; you can calculate the mass of the Sun. Doesn't this sound like magic? We can carry this one step further - if you know the orbital period of one of Jupiter's bright moons, discovered by Galileo in 1609, and you know the distance between Jupiter and that moon, you can calculate the mass of Jupiter. Therefore, if you know the orbital period of the moon around the Earth (it's 27.32 days), and you know the mean distance between the Earth and the moon (it's about 200,039 miles), then you can calculate to a high degree of accuracy the mass of the Earth. … But Newton's laws reach far beyond our solar system. They dictate and explain the motion of stars, binary stars, star clusters, galaxies and even clusters of galaxies. And Newton's laws deserve credit for the 20th century discovery of what we call dark matter. His laws are beautiful. Breathtakingly simple and incredibly powerful at the same time. They explain so much and the range of phenomena they clarify is mind boggling. By bringing together the physics of motion, of interaction between objects and of planetary movements, Newton brought a new kind of order to astronomical measurements, showing how, what had been a jumble of confused observations made through the centuries were all interconnected.

I felt like a calculator with someone’s finger over the solar panel—fading in and out, threatening to shut off altogether.

Twenty minutes later, Three Body’s Von Neumann architecture human-formation computer had begun full operations under the Qin 1.0 operating system. “Run solar orbit computation software ‘Three Body 1.0’!” Newton screamed at the top of his lungs. “Start the master computing module! Load the differential calculus module! Load the finite element analysis module! Load the spectral method module! Enter initial condition parameters … and begin calculation!” The motherboard sparkled as the display formation flashed with indicators in every color. The human-formation computer began the long computation.

Time, said Austerlitz in the observation room in Greenwich, was by far the most artificial of all our inventions, and in being bound to the planet turning on its own axis was no less arbitrary than would be, say, a calculation based on the growth of trees or the duration required for a piece of limestone to disintegrate, quite apart from the fact that the solar day which we take as our guideline does not provide any precise measurement, so that in order to reckon time we have to devise an imaginary, average sun which has an invariable speed of movement and does not incline towards the equator in its orbit.

The Julian calendar, which it replaced, computed the period of the earth’s orbit around the sun at 365.25 days. Pope Gregory XIII’s reform substituted a finer and more accurate calculation: 365.2425 days. Thanks to scientific advances since 1582 we now know that the exact length of the solar year is 365.2422 days.

Once the solar parallax is known,' they told me, 'once the necessary Degrees are measur'd, and the size and weight and shape of the Earth are calculated inescapably at last, all this will vanish. We will have to seek another Space.' No one explain'd what that meant, however ...? 'Perhaps some of us will try living upon thy own Surface. I am not sure that everyone can adjust from a concave space to a convex one. Here have we been sheltered, nearly everywhere we look is no Sky, but only more Earth. -- How many of us, I wonder, could live the other way, the way you People do, so exposed to the Outer Darkness? Those terrible Lights, great and small? And wherever you may stand, given the Convexity, each of you is slight pointed away from everybody else, all the time, out into that Void that most of you seldom notice. Here in the Earth Concave, everyone is pointed at everyone else, -- ev'rybody's axes converge, -- forc'd at least thus to acknowledge one another,-- an entirely different set of rules for how to behave.

When Dad wasn’t telling us about all the amazing things he had already done, he was telling us about the wondrous things he was going to do. Like build the Glass Castle. All of Dad’s engineering skills and mathematical genius were coming together in one special project: a great big house he was going to build for us in the desert. It would have a glass ceiling and thick glass walls and even a glass staircase. The Glass Castle would have solar cells on the top that would catch the sun’s rays and convert them into electricity for heating and cooling and running all the appliances. It would even have its own water-purification system. Dad had worked out the architecture and the floor plans and most of the mathematical calculations. He carried around the blueprints for the Glass Castle wherever we went, and sometimes he’d pull them out and let us work on the design for our rooms. All we had to do was find gold, Dad said, and we were on the verge of that. Once he finished the Prospector and we struck it rich, he’d start work on our Glass Castle.

Now the driver’s line of gaze had to deviate a whole ninety degrees from the road to engage with his passenger, sometimes for seconds on end, during which time, by Beard’s calculation, they traveled several hundred meters. You don’t have to look at me to talk to me, he wanted to say as he watched the traffic ahead, trying to predict the moment when he might seize the wheel. But even Beard found it difficult to criticize a man who was giving him a lift—his host, in effect. Rather die or spend a life as a morose quadriplegic than be impolite.

At some point in the future, new stars will cease being born. Slowly but surely, the stars of our universe are winking out. A day will come when the night sky will be totally black, and the day sky will be totally black as well. Solar systems will become planets orbiting dead stars. According to astrophysical calculations, in about a million billion years, plus or minus, even those dead solar systems will be disrupted from chance gravitational encounters with other stars. In about ten billion billion years, even galaxies will be disrupted, the cold spheres that were once stars flung out to coast solo through empty space.

A major challenge in constructing theories and models is to identify the important quantities that capture the essential dynamics at each organizational level of a system. For instance, in thinking about the solar system, the masses of the planets and the sun are clearly of central importance in determining the motion of the planets, but their color (Mars red, the Earth mottled blue, Venus white, etc.) is irrelevant: the color of the planets is irrelevant for calculating the details of their motion. Similarly, we don’t need to know the color of the satellites that allow us to communicate on our cell phones when calculating their detailed motion.

Nine months later, on September 1, 1939, Oppenheimer and a different collaborator—yet another student, Hartland Snyder—published a paper titled “On Continued Gravitational Contraction.” Historically, of course, the date is best known for Hitler’s invasion of Poland and the start of World War II. But in its quiet way, this publication was also a momentous event. The physicist and science historian Jeremy Bernstein calls it “one of the great papers in twentieth-century physics.” At the time, it attracted little attention. Only decades later would physicists understand that in 1939 Oppenheimer and Snyder had opened the door to twenty-first-century physics. They began their paper by asking what would happen to a massive star that has begun to burn itself out, having exhausted its fuel. Their calculations suggested that instead of collapsing into a white dwarf star, a star with a core beyond a certain mass—now believed to be two to three solar masses—would continue to contract indefinitely under the force of its own gravity. Relying on Einstein’s theory of general relativity, they argued that such a star would be crushed with such “singularity” that not even light waves would be able to escape the pull of its all-encompassing gravity. Seen from afar, such a star would literally disappear, closing itself off from the rest of the universe. “Only its gravitation field persists,” Oppenheimer and Snyder wrote. That is, though they themselves did not use the term, it would become a black hole. It was an intriguing but bizarre notion—and the paper was ignored, with its calculations long regarded as a mere mathematical curiosity.

Every year, Earth, and the Solar System with it, move some 500 million km (310 million miles) from where they were the previous year. It has been calculated that even the slightest deviation from celestial bodies' paths could have drastic consequences which might spell the end of the entire system. For example, the consequences of the Earth's deviating from its course by a mere 3 mm have been described in one source as follows: While rotating around the sun, the earth follows such an orbit that, every 18 miles, it only deviates 2.8 millimetres from a direct course. The orbit followed by the earth never changes, because even a deviation of 3 millimetres would cause catastrophic disasters: If the deviation were 2.5 mm instead of 2.8 mm, then the orbit would be very large, and all of us would freeze. If the deviation were 3.1 mm, we would be scorched to death.

The establishment of a precise calendar was necessary for tax collection, the development of irrigation works, fixing the times of sowing and harvest, and so for determining when a war could be waged. (At the center of this, the problem of intercalation: the lunar calendar determined the months, but, since the twelve lunar months did not completely fill the solar year, there was a constant gap which was made up for gradually, and then in one go, with the intercalation of a thirteenth month.) At the level of an extended empire, these calculations and the decisions which followed from them could only be centralized. Cosmo- or theogonic knowledge was also linked to political power. [...] Linked to political power and the State apparatus in these two ways, knowledge is quite naturally located in the hands of functionaries: knowledge is a State service and political instrument. Hence its necessary secret character. It does not have to circulate or be widespread. It is linked directly to the possession of power.

Things have becone even more mysterious. We have recently discovered that when we make observations at still larger scales, corresponding to billions of light-years, the equations of general relativity are not satisfied even when the dark matter is added in. The expansion of the universe, set in motion by the big bang some 13.7 billion years ago, appears to be accelerating, whereas, given the observed matter plus the calculated amount of dark matter, it should be doing the opposite-decelerating. Again there are two possible explanations. General relativity could simply be wrong. It has been verified precisely only within our solar system and nearby systems in our own galaxy. Perhaps when one gets to a scale comparable to the size of the whole universe, general relativity is simply no longer applicable. Or there is a new form of matter-or energy (recall Einstein's famous equation E=mc^2, showing the equivalence of energy and mass)-that becomes relevant on these very large scales: That is, this new form of energy affects only the expansion of the universe. To do this, it cannot clump around galaxies or even clusters of galaxies. This strange new energy, which we have postulated to fit the data, is called the dark energy.

The assessment will be guided by insights from research in particle physics, astrophysics, and cosmology that allow us to predict how the universe will unfold over epochs that dwarf the timeline back to the bang. There are significant uncertainties, of course, and like most scientists I live for the possibility that nature will slap down our hubris and reveal surprises we can’t yet fathom. But focusing on what we’ve measured, on what we’ve observed, and on what we’ve calculated, what we’ll find, as laid out in chapters 9 and 10, is not heartening. Planets and stars and solar systems and galaxies and even black holes are transitory. The end of each is driven by its own distinctive combination of physical processes, spanning quantum mechanics through general relativity, ultimately yielding a mist of particles drifting through a cold and quiet cosmos. How will conscious thought fare in a universe experiencing such transformation? The language for asking and answering this question is provided once again by entropy. And by following the entropic trail we will encounter the all-too-real possibility that the very act of thinking, undertaken by any entity of any kind anywhere, may be thwarted by an unavoidable buildup of environmental waste: in the distant future, anything that thinks may burn up in the heat generated by its own thoughts. Thought itself may become physically impossible. While the case against endless thought will be based on a conservative set of assumptions, we will also consider alternatives, possible futures more conducive to life and thinking. But the most straightforward reading suggests that life, and intelligent life in particular, is ephemeral. The interval on the cosmic timeline in which conditions allow for the existence of self-reflective beings may well be extremely narrow. Take a cursory glance at the whole shebang, and you might miss life entirely. Nabokov’s description of a human life as a “brief crack of light between two eternities of darkness”6 may apply to the phenomenon of life itself. We mourn our transience and take comfort in a symbolic transcendence, the legacy of having participated in the journey at all. You and I won’t be here, but others will, and what you and I do, what you and I create, what you and I leave behind contributes to what will be and how future life will live. But in a universe that will ultimately be devoid of life and consciousness, even a symbolic legacy—a whisper intended for our distant descendants—will disappear into the void. Where, then, does that leave us?

Nuclear energy is green. Renewables are not green.” His argument was based on footprint analysis. “As a Green,” he wrote, “I care intensely about land-sparing, about leaving land for Nature…. Considered in watts per square meter, nuclear has astronomical advantages over its competitors.” The solar energy equivalent of a 1-gigawatt nuclear reactor, he projected—with his own variation on Saul Griffith’s and Gwyneth Cravens’s calculations—would require 150 square kilometers (58 square miles); the wind power equivalent, 770 square kilometers (298 square miles); the corn biofuel equivalent, 2,500 square kilometers (965 square miles).

Dynamically speaking, a globular cluster is a big many-body problem. The two-body problem is easy. Newton solved it completely. Each body—the earth and the moon, for example—travels in a perfect ellipse around the system’s joint center of gravity. Add just one more gravitational object, however, and everything changes. The three-body problem is hard, and worse than hard. As Poincaré discovered, it is most often impossible. The orbits can be calculated numerically for a while, and with powerful computers they can be tracked for a long while before uncertainties begin to take over. But the equations cannot be solved analytically, which means that long-term questions about a three-body system cannot be answered. Is the solar system stable? It certainly appears to be, in the short term, but even today no one knows for sure that some planetary orbits could not become more and more eccentric until the planets fly off from the system forever.

A major challenge in constructing theories and models is to identify the important quantities that capture the essential dynamics at each organizational level of a system. For instance, in thinking about the solar system, the masses of the planets and the sun are clearly of central importance in determining the motion of the planets, but their color (Mars red, the Earth mottled blue, Venus white, etc.) is irrelevant: the color of the planets is irrelevant for calculating the details of their motion. Similarly, we don’t need to know the color of the satellites that allow us to communicate on our cell phones when calculating their detailed motion. However, this is clearly a scale-dependent statement in that if we look at the Earth from a very close distance of, say, just a few miles above its surface rather than from millions of miles away in space, then what was perceived as its color is now revealed as a manifestation of the huge diversity of the Earth’s surface phenomena, which include everything from mountains and rivers to lions, oceans, cities, forests, and us. So what was irrelevant at one scale can become dominant at another. The challenge at every level of observation is to abstract the important variables that determine the dominant behavior of the system.

The Aryabhatiya covers arithmetic, squares, cubes, square roots, cube roots, triangles, the properties of a circle, algebra, fractions, quadratic equations and sines, and it utilises the decimal system with place value. It contains a very close approximation of the value of pi – 3.1416 – and perfected the ‘rule of three’ still used to compute ratios. It also deals with spherical trigonometry. The ease of making calculations using this system had direct implications for astronomy and allowed Aryabhata to calculate the movements of the planet, eclipses, the size of the earth and, astonishingly, the exact length of the solar year to an accuracy of seven decimal points.

Calculated globally, human society consumes the equivalent of 400 years' worth of ancient solar energy (expressed in terms of the net primary productivity of plants during previous geological eras) each year through our use of fossil fuels.

The most commonly quoted mass for the vacuum is 1094 grams per centimeter cubed (g/cm3) as calculated by John Wheeler who was quoted above.11 We will calculate later that the energy of the vacuum is 1095 g/cm3 by a slightly different method, so that value will be used from here on. As we will see, one order of magnitude difference is not that significant at this point in our discussions. Energy is related to mass by the well-known relation E=mc2. For comparison water has a mass density of 1 g/cm3 by definition. It is impossible for most normal people to grasp just how big a difference in energy there is between the zero-point field and water, so perhaps a simple illustrative example will help. Let’s start with the clichéd drop in a bucket. If the drop is one milliliter (1 ml) and the bucket 100 liters (72.5 gallons), then that gives us a factor of 105. If instead we consider a drop in all the Earth’s oceans, then we have a factor of 1024. That is a lot bigger than a bucket but nowhere close to how insignificant the mass of the drop of water is when compared to zero-point energy. To continue, what if the ocean was the size of the sun? That gives us a ratio on the order of 1041, which is still a long way off. If the ocean was the size of the solar system we get a ratio on the order of 1050. Now if we expand the ocean to the size of the galaxy we get ~1076 and we are still not anywhere close. What if the ocean is the size of the known visible universe? Assuming a radius of 7.4 x 1026 meters the mass ratio is 5 x 1095. There we go. So, the density of water compared to the energy of the vacuum is equivalent to five 1 ml drops of water in an ocean the size of the visible universe. Since we are mostly water and have a similar density to water, the vacuum fluctuations inside our body are like having all the mass-energy of an ocean of water the size of the universe inside each little part of us. Wow, we are pretty insignificant in the big scheme of things and so is any other body of solid matter or any amount of energy associated with it. This zero-point energy is all around us and all throughout us. We are lucky that zero-point energy is not detectable or anything we did would be undetectable noise to any sensor we could possibly make. Even worse, if we could absorb even a small fraction of that energy, we would be vaporized in an instant. Or, if all that energy participated in a gravitational force, the universe would be crushed to a speck.

Aristarchus’s observations led him to propose a completely new model of the universe and solar system, based on the hypothesis that the planets revolved around the sun and that the earth itself revolved every twenty-four hours around its axis. Aristarchus was also a formidable mathematician, who made calculations of the distance from the earth to the sun and the diameter of the sun based on solar eclipses.

Well, Scaliger (partially) solved the problem by turning his attention to the three basic units upon which virtually all workable calendars are based, namely, the Solar Cycle, the Metonic Cycle and the Roman Indiction. In simple terms, the Solar Cycle is completed every 28 years, the Metonic Cycle every 19 years, and the Roman Indiction every 15 years. Scaliger realised that there must obviously be points in time when all three cycles begin and end together, so, noting carefully the age of each cycle at the moment when he began his calculations, he counted the years backwards until he came to that year when all three cycles began together. And that was the year 4713 BC.

Run solar orbit computation software ‘Three Body 1.0’!” Newton screamed at the top of his lungs. “Start the master computing module! Load the differential calculus module! Load the finite element analysis module! Load the spectral method module! Enter initial condition parameters … and begin calculation!” The motherboard sparkled as the display formation flashed with indicators in every color. The human-formation computer began the long computation. “This is really interesting,” Qin Shi Huang said, pointing to the spectacular sight. “Each individual’s behavior is so simple, yet together, they can produce such a complex, great whole! Europeans criticize me for my tyrannical rule, claiming that I suppress creativity. But in reality, a large number of men yoked by severe discipline can also produce great wisdom when bound together as one.” “Great First Emperor, this is just the mechanical operation of a machine, not wisdom. Each of these lowly individuals is just a zero. Only when someone like you is added to the front as a one can the whole have any meaning.” Newton’s smile was ingratiating. “Disgusting philosophy!” Von Neumann said as he glanced at Newton. “If, in the end, the results computed in accordance with your theory and mathematical model don’t match reality, then you and I aren’t even zeroes.” “Indeed. If that turns out to be the case, you will be nothing!” Qin Shi Huang turned and left the scene.

In the 8th Century, the Greek philosopher Homer thought that the Earth was flat. Many of the less educated people in the 15th Century still held on to that concept when Columbus set sail, following the setting sun west. The less informed warned Columbus and his crew of the danger of sailing right off the edge of the Earth. However, navigators and mathematicians knew better, since Greek philosophers in the 5th Century such as Parmenides, Empedocles and Pythagoras had already proved, by using various scientific methods, that the Earth was round. In about 200 BC Eratosthenes, who lived along the Nile near Alexandria, Egypt, calculated the circumference of the Earth to within a very close tolerance. Later in Prussia, Copernicus presented his concept that the Sun was the center of the Solar system and theorized that the planets revolved around it. It was not coincidental that Copernicus did this shortly after Columbus discovered the new continent. Although the ancients did not have radio and television, they could communicate by various means, and definitely knew what was going on. However there were those who remained superstitious, believing that there were monstrous sea creatures near the edge of the Earth. But Columbus and other relatively educated people knew better!

The years in which a month is added are referred to as “pregnant” years. This calculation, however, is not totally accurate. If we average out the length of the Hebrew year, it is slightly longer than the solar year. The difference is only one of minutes, but over a very long period the difference accumulates, each time making Passover start a little later on the average. Over a very long time, this can, eventually, in theory, result in Passover taking place in the summer.

In recent years there have been many proposals for geoengineering through solar radiation management. Some involve literally making the earth whiter (say, by using white roofs and roads). Perhaps the easiest to visualize is putting millions of little mirror-like particles 20 miles above the earth. For example, we might artificially increase sulfate aerosols in the stratosphere above background levels. This would increase the planetary albedo or whiteness and reduce incoming solar radiation. Climate scientists have calculated that reflecting about 2 percent of solar output could offset the warming effect of a doubling of CO2. The right number of particles in the right place could reduce solar radiation and cool the earth by the desired amount.

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Texas Instruments (TI) fell into the irrelevance trap in calculators and watches. By relentlessly building volume, driving down costs, and lowering prices, TI achieved leading market share in both products. Retail prices for watches and calculators plunged below $15, and TI dominated the volume channels, including supermarkets and discount stores. Casio, Sharp, and Seiko—all Japanese companies—followed TI’s lead in pursuing volume by slashing prices and designing costs out of the products and their manufacturing. But, as prices sank, the Japanese companies introduced new products with many more features than TI’s offerings. Prices were so low, consumers were willing to pay a few dollars extra for features such as solar power, more mathematical functions for calculators, and styling features for watches. Before long, TI’s relentless pursuit of higher volumes and lower costs became irrelevant to consumers, and the Japanese companies took over the categories. If you have not examined your costs, in detail, within the past five years—or if you believe your competitors have not—it is very likely that there exists, lurking somewhere in your cost structure, a major opportunity to improve your profits, weaken your competitor, and expand your influence. There are limits to cost-raising strategy. As important as price is to your customers, they care about other things as well, including product features, quality, time, and status. So, even as you pursue this hardball strategy with gusto, remember the mortal words of Dirty Harry: “A man’s got to know his limitations.”2