Celestial Latitude and Longitude Help
Introduction to Celestial Latitude and Longitude—The Stars
Suppose that a star is at x degrees north celestial latitude and y degrees west celestial longitude. If you stand at the point on the surface corresponding to x °N and y °W, then a straight, infinitely long geometric ray originating at the center of Earth and passing right between your eyes will shoot up into space in the direction of the star (Fig. 1-3).
As you might guess, any star that happens to be at the zenith will stay there for only a little while unless you happen to be standing at either of the geographic poles (not likely). Earth rotates with respect to the stars, completing a full circle approximately every 23 hours and 56 minutes. In a few minutes, a star that is straight overhead will move noticeably down toward the western horizon. This effect is exaggerated when you look through a telescope. The greater the magnification, the more vividly apparent is the rotation of Earth.
The next time you get a chance, set up a telescope and point it at some star that is overhead. Use the shortest focal-length eyepiece that the telescope has so that the magnification is high. Center the star in the field of view. If that star is exactly overhead, then its celestial latitude and longitude correspond to yours. For example, if you’re on the shore of Lake Tahoe, your approximate latitude is 39°N and your approximate longitude is 120°W. If you have a telescope pointing straight up and a star is centered in the field of view, then that star’s celestial coordinates are close to 39°N, 120°W. However, this won’t be the case for long. You will be able to watch the star drift out of the field of view. Theoretically, a star stays exactly at a given celestial longitude coordinate ( x, y ) for an infinitely short length of time—in essence, for no time at all. However, the celestial latitude of each and every star remains constant, moment after moment, hour after hour, day after day. (With the passage of centuries, the celestial latitudes of the stars change gradually because Earth’s axis wobbles slowly. However, this effect doesn’t change things noticeably to the average observer over the span of a lifetime.)
What’s The Use?
The celestial longitude of any natural object in the sky (except those at the north and south geographic poles) revolves around Earth as the planet rotates on its axis. No wonder people thought for so many centuries that Earth must be the center of the universe! This makes the celestial latitude/longitude scheme seem useless for the purpose of locating stars independently of time. What good can such a coordinate scheme be if its values have meaning only for zero-length micromoments that recur every 23 hours and 56 minutes? This might be okay for the theoretician, but what about people concerned with reality?
It turns out that the celestial latitude/longitude coordinate system is anything but useless. Understanding it will help you understand the more substantial coordinate schemes described in the next sections. And in fact, there is one important set of objects in the sky, a truly nuts-and-bolts group of hardware items, all of which stay at the same celestial latitude and longitude as viewed from any fixed location. These are the geostationary satellites, which lie in a human-made ring around our planet. These satellites orbit several thousand kilometers above the equator, and they revolve right along with Earth’s rotation (Fig. 1-4).
When it is necessary to point a dish antenna, such as the sort you might use to receive digital television or broadband Internet signals, at a geostationary “bird,” the satellite’s celestial coordinates must be known, in addition to your own geographic latitude and longitude, with great accuracy. The celestial latitude and longitude of a geostationary satellite are constant for any given place on Earth. If a satellite is in a geostationary orbit precisely above Quito, Ecuador, then that is where the “bird” will stay, moment after moment, hour after hour, day after day.
An Internet user fond of broadband and living in the remote South American equatorial jungle might use a dish antenna to transmit and receive data to and from a “bird” straight overhead. The dish could be set to point at the zenith and then left there. (It would need a hole near the bottom to keep it from collecting rain water!) A second user on the shore of Lake Tahoe, in the western United States, would point her dish at some spot in the southern sky. A third user in Tierra del Fuego, at the tip of South America, would point his dish at some spot in the northern sky (Fig. 1-5). None of the three dishes, once positioned, would ever have to be moved and, in fact, should never be moved.
If you’re astute, you’ll notice that although the geostationary satellite is directly above the equator, its celestial latitude is zero only with respect to observers located at the equator. If viewed from north of the equator, the satellite shifts a little bit into the southern celestial hemisphere; when observed from south of the equator, the satellite shifts slightly into the northern celestial hemisphere. The reason for this is parallax . The satellite is only a few thousand kilometers away, whereas the stars, whose celestial latitudes remain fixed, are trillions and quadrillions of kilometers distant. This is why the signal paths in Fig. 1-5 aren’t exactly parallel. On a small scale, the phenomenon of parallax allows us to perceive depth with binocular vision. On a large scale, parallax is used to measure the distance to the Sun, the Moon, the other planets in the solar system, and even a few of the nearer stars.
Practice problems of this concept can be found at: Coordinating the Heavens Practice Problems