**Coordinating the Heavens**

A thousand generations ago, people had no quantitative concept of the sky. In the past few millennia, we have refined astronomical measurement as a science and an art. Mathematics, and geometry in particular, has made this possible.

**Points On A Sphere**

It is natural to imagine the sky as a dome or sphere at the center of which we, the observers, are situated. This notion has always been, and still is, used by astronomers to define the positions of objects in the heavens. It’s not easy to specify the locations of points on a sphere by mathematical means. We can’t wrap a piece of quadrille paper around a globe and make a rectangular coordinate scheme work neatly with a sphere. However, there are ways to uniquely define points on a sphere and, by extension, points in the sky.

**Meridians And Parallels**

You’ve seen globes that show lines of *longitude* and *latitude* on Earth. Every point has a unique latitude and a unique longitude. These lines are actually half circles or full circles that run around Earth.

The lines of longitude, also called *meridians* , are half circles with centers that coincide with the physical center of Earth (Fig. 1-1 *A* ). The ends of these arcs all come together at two points, one at the *north geographic pole* and the other at the *south geographic pole.* Every point on Earth’s surface, except for the north pole and the south pole, can be assigned a unique longitude.

The lines of latitude, also called *parallels* , are all full circles, with two exceptions: the north and south poles. All the parallels have centers that lie somewhere along Earth’s *axis of rotation* (Fig. 1-1 *B* ), the line connecting the north and south poles. The *equator* is the largest parallel; above and below it, the parallels get smaller and smaller. Near the north and south poles, the circles of latitude are tiny. At the poles, the circles vanish to points.

All the meridians and parallels are defined in units called *degrees* and are assigned values with strict upper and lower limits.

**Degrees, Minutes, Seconds**

There are 360 degrees in a complete circle. Why 360 and not 100 or 1000, which are “rounder” numbers, or 256 or 512, which can be divided repeatedly in half all the way down to 1?

No doubt ancient people noticed that there are about 360 days in a year and that the stellar patterns in the sky are repeated every year. A year is like a circle. Various familiar patterns repeat from year to year: the general nature of the weather, the Sun’s way of moving across the sky, the lengths of the days, the positions of the stars at sunset. Maybe some guru decided that 360, being close to the number of days in a year, was a natural number to use when dividing up a circle into units for angular measurement. Then people could say that the stars shift in the sky by 1 degree, more or less, every night. Whether this story is true or not doesn’t matter; different cultures came up with different ideas anyway. The fact is that we’re stuck with degrees that represent 1/360 of a circle (Fig. 1-2), whether we like it or not.

For astronomical measurements, the degree is not always exact enough. The same is true in geography. On Earth’s surface, 1 degree of latitude represents about 112 kilometers or 70 miles. This is okay for locating general regions but not for pinpointing small towns or city blocks or individual houses. In astronomy, the degree may be good enough for locating the Sun or the Moon or a particular bright star, but for dim stars, distant galaxies, nebulae, and quasars, smaller units are needed. Degrees are broken into *minutes of arc* or *arc minutes* , where 1 minute is equal to of a degree. Minutes, in turn, are broken into *seconds of arc* or *arc seconds* , where 1 second is equal to of a minute. When units smaller than 1 second of arc are needed, decimal fractions are used.

Let’s take a close look at how latitude and longitude coordinates are defined on the surface of Earth. It will help if you use a globe as a visual aid.

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