large and beautiful astronomy photographs
Albert Einstein (1879-1955)
Einstein's immense contribution to mankind is his "special theory of relativity that mass and energy are both but different manifestations of the same thing" (his own words). This is what priests and astrologers have been talking about forever. But before you go further, you may want to re-examine exactly what "mass" is, and how it differs from "weight" by clicking here.
Considered by many to be the greatest astrophysicist who ever lived, Albert Einstein (1879-1955) took the next step beyond Newton by postulating that there was an equivalence between all matter and energy in the universe, and that that equivalence is quantifiable by the simple equation e = mc2. In that equation "e" stands for energy, "m" stands for mass, and "c" stands for the speed of light. Thus the amount of energy "e" in any body is equal to its mass "m" (its weight divided by the attractive pull of the body that confers that "feeling of weight") times the speed of light "c" squared (the speed of light times itself). Since light goes 300 million meters per second, the speed of light squared is 9x1016 (90 quadrillion) meters per second, so there's a lot of energy in matter! This is how stars shine, how the universe makes a living, and how atomic and hydrogen bombs are able to liberate as much energy as they do.
Stars shine because they convert matter into energy. At the Sun’s core, for example, the pressure is 250 billion times sea level on Earth, the density more than 150 times that of water, and the temperature is 15.6 million degrees. The pressure is so great at the center of the Sun that there the lightest gas in the universe, hydrogen, is 14 times denser than lead! Under this tremendous pressure ionized—meaning they've lost their electrons due to the great heat—hydrogen atoms (protons) are fused together to form ionized helium. But two protons stuck together have about 7% less mass than two separate protons. This 7% mass loss in fusing two protons together is released as energy to the tune of Einstein's e = mc2; this is where stars get the juice to shine for billions of years.
From e = mc2 we can calculate that the amount of energy in a raisin is equivalent to that released by 10,000 tons of TNT. This is how the Sun is able to emit 386 billion billion (not a typo!) megawatts every second. The entire Earth would need one million years to make that much energy at current production rates. At the center of the Sun 700 million tons of hydrogen are converted by nuclear fusion to about 695 million tons of helium and 5 million tons of gamma ray energy every second. Since its birth 4.6 billion years ago, the Sun has burned up about half of the hydrogen in its core. It will continue to burn as it does now for about another five billion years, during which time it will become twice as bright. Eventually it will run out of hydrogen, undergoing changes that will totally destroy the Earth.
Before Einstein, an unresolved problem that none of Newton's laws (or any other law, for that matter) could explain was the precession of Mercury's orbit by 575" (575 arc seconds or almost 0.1°) per century. Isaac Newton actually predicted stable elliptical orbits only for planets in an idealized two-body system, in this case Mercury and the Sun. In point of fact Mercury is also acted upon gravitationally by Venus and the Earth due to their relative proximity, and by Jupiter because of its great mass. It is very difficult to solve such n-body problems, but by using methods developed by LaGrange and Laplace it has been determined that these planets contribute 532" per century to Mercury's orbital precession. This leaves 43" of Mercury's 575" precession unaccounted for by all of Newton's laws. And this amount is significant, because astronomers are certain their observations of Mercury's orbit cannot be off by more than a fraction of one arc second.
Newton's universal law of gravitational attraction describes the attractive force between all bodies in the universe. If two bodies of mass m1 and m2 are separated by a distance d, the gravitational force F between them is
F = γ m1m2 ⁄ d2
where γ is the gravitational constant. Since d is in the denominator, as the distance d between the two bodies decreases—which it does as Mercury approaches perihelion in its very elliptical orbit—the force between them increases. And as the Sun's force F on Mercury increases, by Newton's second law
F = ma
Mercury's acceleration a also increases; and because acceleration is a change in velocity over time, Mercury's velocity increases as it approaches perihelion. Now here's the clincher. Because Mercury's velocity increases, according to Einstein's general theory of relativity its mass must also increase, the governing equation being
m = m0 ⁄ √ ( 1 - v2/c2 )
where c is the speed of light, m0 is Mercury's rest mass (if it were not moving), and m is its mass at velocity v. Since Mercury's mass increases, by Newton's law of gravitation F = γ m1m2 ⁄ d2, the Sun's force on it increases; it is therefore again accelerated in its orbit, in turn causing the orbit to precess. Einstein calculated this relativistic precession to be 42.92" of arc per century for Mercury, 8.62" for Venus, 3.83" for the Earth, and 1.35" for Mars. Since Venus and the Earth have nearly circular orbits, precisely locating their lines of apsides (the major axes of their elliptical orbits) and thereby precisely pinning down their orbital rates of precession was initially elusive. Once space probes, radar ranging and computer analysis of data became available, however, this and the generally precise measurement of planetary precessions became possible. Astronomical observations today put the balance unaccounted for by Newton's laws in the rates of precession of the four inner planets at 43.1", 8.65", 3.85", and 1.36" per century respectively, in essentially exact agreement with Einstein's calculations in his groundbreaking 1916 paper on general relativity!
deriving the relativistic precession
formulae and data for Mercury and all of the planets of the solar
Einstein closed his 1916 masterpiece with the following words:
"Calculation gives for the planet Mercury a rotation of the orbit of 43" per century, corresponding exactly to the astronomical observation (Leverrier); for the astronomers have discovered in the motion of the perihelion of this planet, after allowing for disturbances by the other planets, an inexplicable remainder of this magnitude."
The following quote is also attributed to Einstein, but the more I think about it the less likely I believe it to be something he said. It's just too perfect and too florid (especially "life-giving elixir"). In any event, here it is: "Astrology is a science in itself and contains an illuminating body of knowledge. It taught me many things, and I am greatly indebted to it. Geophysical evidence reveals the power of the stars and the planets in relation to the terrestrial. In turn, astrology reinforces this power to some extent. This is why astrology is like a life-giving elixir to mankind."—supposedly from Albert Einstein.
This Albert Einstein page and and much of this 550-page resource website are excerpted from You and the Universe.
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© Carl Woebcke: Albert Einstein, Physicist, 1991-2011. All rights reserved.