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A formula first derived by Newton, giving (1+z) a, the result of raising 1 + z to an arbitrary power a, as a sequence of form
(1+z) a = 1 + A1z + A2z 2 + A3z 3 + ....
where the terms Ai (i = 1,2,3...) are given by the formula and where a can be positive, negative, fractional or whole. When the magnitude of z is less than 1, the higher powers get smaller and smaller and the formula can be made as precise as one wishes by including enough of them (for z of small magnitude, 1-2 terms are sufficient), although the result is never exact. For magnitudes of z equal to 1 or more, the formula only holds for values of a which are positive whole numbers. In that case, for any z, the result is exact and the sum of terms with powers of z does not go on arbitrarily but ends with z a.
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light or other electromagnetic radiation emitted due to heat by a solid, liquid or dense gas, with no color of its own (hence "black"). Distinguished by a continuous distribution of spectral color, with its peak of emission shifting towards shorter wavelengths as the temperature increases--e.g. infra-red for a warm hand, red for a hot iron bar, yellow for the glowing filament in a lightbulb.
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an extremely compact object, collapsed by gravity which has overcome electric and nuclear forces. It is believed that stars appreciably larger than the Sun, once they have exhausted all their nuclear fuel, collapse to form black holes: they are "black" because no light escapes their intense gravity. Material attracted to a black hole, though, gains enormous energy and can radiate part of it before being swallowed up. Some astronomers believe that enormously massive black holes exist in the center of our galaxy and of other galaxies.
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A fundamental law in the behavior of ideal gases: if temperature is kept constant, the density D of a gas varies proportionally to its pressure P. Actual gases usually approximate ideal ones pretty well as long as the temperature is far above their boiling point, e.g. nitrogen and oxygen in ordinary air.
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The extra extension of the Earth's equator, caused by the centrifugal force of the Earth's rotation, which slightly flattens the spherical shape of the Earth. The Earth's bulge causes the planes of satellite orbits inclined to the equator (but not polar) to slowly rotate around the Earth's axis.
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The lifting force acting in a fluid on bodies and regions less dense than their surroundings. The buoyancy of hot air--the force that also lifts hot-air balloons--is the main cause of weather-related flows in the Earth's atmosphere. Also see convection.
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