The whys and wherefores of navigation

by Gershom Bradford

The positions of heavenly bodies are determined by two measurements—coordinates—the distance north or south of the celestial equator, called the declination, and the distance east from the prime celestial meridian taken as a reference, called the right ascension, each of which will be subsequently treated at length under its individual heading. The movement of the planets eastward or westward as described, constantly changes their right ascension; and as their orbits are inclined at different angles to the celestial equator, they are always changing their declination.

The planets whose orbits are smaller than that of the earth are called inferior, while those whose orbits are of greater dimensions are known as superior planets. Mercury and Venus are inferior planets and consequently are always nearer the sun; their comparatively close proximity making them appear to us as morning and evening stars. In fact, Mercury is so close that it is unavailable, owing to the brilliancy of the sun, for observation with a sextant; while Venus, on the other hand, a little more remote, is an excellent body to observe, and is always found in the east or west, conveniently near the prime vertical, the most favorable place for a time sight for longitude. The twilight or dawn which usually prevails at the time of a Venus sight gives the navigator a good horizon to observe upon. Mars, Jupiter and Saturn are superior planets and their travels are so extended that they may be found almost anywhere in the heavens within the limits of their declinations.

The earth’s orbit is slightly elliptical, with the sun located a little out of center—a little nearer one end. Should a line or axis be drawn through the long diameter, its intersection with that part of the orbit nearest the sun is called the Perihelion while the opposite point is known as the Aphelion. The former is used as a point of reference from which the earth’s position can be located in terms of angular measurement from time to time. This angle, known as the anomaly, is formed by the line from the sun to the Perihelion and that drawn from the sun to the earth. The latter distance is called the radius vector of the earth. We (the earth), are at the Perihelion about January 1, and consequently this angle at that date is 0°, but from this time on, the angle increases approximately one degree a day throughout the year.

The plane of the earth’s equator makes at all times an angle of about 23° 28´ with the plane of its orbit. This is a highly important angle to mankind, for upon it depends the climate of the world. The axis of the earth, if we can conceive it as represented by a slender imaginary staff, extends through the unlimited distance to a point in the heavens—the celestial pole; this point is in the zenith for a person at our north pole. Since the distance between these points is mathematically infinite, any number of lines parallel to this “staff” will appear to penetrate the sky at the single point of the celestial pole. Thus the parallel positions of the axis corresponding to the earth’s various positions, even those at opposite sides of the orbit, converge into this common point. To be clearer, the parallel lines representing the different positions of the axis during the year according to our geometry form a group of separate points on the heavens, but the distance being beyond all reckoning, our limited conceptions fail to identify the group of points and it resolves into one point.

By the same line of reasoning the plane of the earth’s equator remains parallel in all its positions throughout the yearly cruise around the sun, and its projection marks but one celestial equator upon the sky.

While the direction of the axis and corresponding position of the equator are constant for all practical purposes, there is, nevertheless, an extremely slow circular movement of the axis, called the precession of the equinoxes, a subject which is reserved for subsequent discussion.

Coordinates

In nautical astronomy the earth is assumed to be the center of space with the heavens forming a globular shell around it, known as the celestial sphere. All fixed stars are assumed to lie on its concave surface from the earth regardless of their actual distances. The tracks of all other bodies moving, or appearing to move, across the sky are considered to be on the surface of this sphere.

It is necessary, in order to conveniently define the position of heavenly bodies to mark this celestial sphere with imaginary circles to serve as coordinates, as we mark the earth with meridians of longitude and parallels of latitude.

Before going into the explanation of these coordinates, it may be well to consider a few facts concerning circles. A great circle is of course understood to be one whose plane passes through the center of a sphere, dividing it into two equal parts. There can be an infinite number of these circles whose planes cut the sphere at every possible inclination as long as they pass through its center. A circle may be a great circle of either the celestial sphere, the earth, or even of a baseball. The poles of a great circle are the points on the surface of its sphere, penetrated by the diameter perpendicular to the plane of the great circle. As for example, the poles of the earth are connected by the diameter that is perpendicular to the plane of the equator. An angle at any pole is measured on the great circle which subtends it. For instance, angles at the poles of the earth are measured on the equator; angles at the zenith on the horizon. With these facts well in mind we will proceed, showing the scheme of circles employed in laying off the surface of the heavens.