## Eccentricity

A circle may be big or small, but it is always a circle. Ellipses, on the other hand, vary in shape as well as size—they are more elliptical or less so. When the ellipse represents the path of an orbiting body, the extent to which the ellipse is stretched is known as the eccentricity of the orbit.

Eccentricity can be measured. The two foci and the center of an ellipse all lie along the major axis—the longest straight line that will fit inside the ellipse. Suppose, in the drawing, that the body is orbiting focus

Eccentricity

Eccentricity

F1. The distance from F1 to the center (C) is called the linear eccentricity, denoted by le. Fi lies at the center of one half of the major axis. The length of this line is symbolized by a (the Greek letter alpha). Eccentricity (e) is then given by: e = le /a. This must always be less than 1, because a is invariably larger than le. If the orbit is perfectly circular, so that F1 lies at C, le will equal zero and e = 0. At present the eccentricity of Earth's orbit is 0.017, which is almost circular.

Earth reaches perihelion—the point in its orbit when it is closest to the Sun—in January and aphelion—the point farthest from the Sun—in July. This means that the Sun shines more intensely on the Earth in January than it does in July, but the difference is very small. With an eccentricity of 0.017, the distance between Earth and the Sun is only 3 percent greater at aphelion than it is at perihelion. This is the difference between approximately 95,687,000 miles (153,960,000 km) and 90,113,000 miles (144,991,000 km). It means we receive 7 percent more sunshine in January than we do in July. This hardly seems sufficient to affect global climate, although it means winters in the Northern Hemisphere are milder and summers in the Southern Hemisphere warmer than they would be if the orbit were perfectly circular.

Over a period of about 100,000 years, however, the eccentricity of the Earth's orbit changes from 0.001 to 0.054 and back again. When the eccentricity is almost circular (0.001) there will be almost no difference in the intensity of solar radiation falling on the Earth as a whole through the year, but an eccentricity of 0.054 is enough to make a significant climatic difference.

Planetary orbits are highly predictable. The gravitational fields of other bodies affect them, but these can be calculated. The mathematics is complicated, but Milankovitch was a mathematician, and he worked out the way the eccentricity of the orbit had changed over several hundred thousand years.

## Telescopes Mastery

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