Nautical Astronomy
The sun is the center of the solar system, with all the planets,
including the earth, revolving around it, some with orbits greater and
others less than that of the earth. The planets in some instances have
satellites revolving in turn around them, as the moon in the case of
the earth.
The movements of the earth will be, perhaps, more readily understood by
assuming a position at the North Pole; here beneath the observer the
earth is rotating left-handed--against the hands of a watch, once each
day; while at the same time it is speeding onward through space in a
left-handed curve, which in the course of a year resolves itself into a
complete revolution around the sun.
The sun and stars are considered to be stationary for all navigational
purposes, the _apparent_ movements of these bodies being entirely due
to the motions of the earth. The result of our daily rotation from
west to east is, that the heavenly bodies march past our meridian in
a majestic procession for 24 hours, after which the performance is
repeated. The uninitiated are here forewarned against becoming confused
by the assumption used for convenience by navigators that the heavens
revolve around the earth.
The planets and moon join the sun and stars in the daily parade
past our meridian, but their apparent movements are not entirely an
illusion, for they have motions of their own that somewhat affect the
precision of their daily revolution. This is readily observed in the
moon’s hour of rising, which is very perceptibly later each evening.
Her actual revolution around the earth, being from west to east, is
contrary to the apparent diurnal motion and thereby each evening finds
her farther to the eastward and consequently rising later. As a result
of this change in the time of rising, the moon must of necessity rise
in every hour of both day and night in the course of a month--the time
she requires to revolve around the earth.
The onward movement of the earth in its orbit as we face the sun in
latitudes north of the tropics, is toward our right, and this causes
the sun to apparently move slowly eastward or to the left among the
stars, corresponding exactly to our movement westward. This movement is
opposite to his daily course across the heavens. As a year is required
for the earth to accomplish our revolution around the sun, it follows
that this same length of time is consumed by the sun in making its
_apparent_ eastward revolution of the heavens.
The movements of the planets are more complex. They all revolve around
the sun in the same direction as the earth, but as their orbits are
of vastly different sizes, they will be found in various positions
relative to the sun; they overhaul and pass each other, but owing to
their uniform direction of revolution they never meet. The planetary
system is like the horse race at a county fair; the pole horse has the
advantage, but the varying speeds of the contestants soon place them at
various parts of the track.
From the earth the movements of the planets, aside from the diurnal
movement, are composed of their own actual movement around the sun,
combined with an apparent motion, due to the earth’s onward movement
precisely as described above in the case of the sun. The combined
movement of a planet may be noted by reference to the fixed stars
beyond it.
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.
There are three systems of circles, each designed to fulfil a different
requirement.
The first system depends upon the position of the observer and changes
its whole imaginary structure to correspond with his movements. The
plumb-line, if extended to the heavens overhead, will determine the
zenith, the point of origin of this system on the celestial sphere.
The corresponding point directly beneath us is known as the nadir.
The great circle of the celestial sphere everywhere equally distant
from both the zenith and the nadir is the horizon. It is plain that
a new zenith and new horizon are created with every movement of the
observer. The facts that man is on the surface and not at the center of
the earth, and that his eye is elevated above its surface, each creates
another horizon.
The rational horizon is marked by a plane, perpendicular to a
plumb-line and passing through the earth’s center; while the sensible
horizon is determined by a plane, also perpendicular to the plumb-line,
but passing through the eye of the observer. It will therefore be
seen that these two parallel horizons are some 4000 miles apart, the
semi-diameter of the earth; but this distance when projected on the
celestial sphere becomes insignificant when compared with the infinite
distance of this sphere from the earth, and the rational and sensible
horizons shrink into a single line so far as we can perceive.
While this statement is true when dealing with the stars, it needs
modifying when dealing with the sun and moon, and in very accurate
observations of planets, as their distances are insufficient to
eliminate the angle formed between the line from the body to the center
of the earth, and that from the body to the observer. This is allowed
for when observing these bodies by applying the correction of parallax
to the observed altitude.
The visible horizon is the boundary seen between the sea and sky. If
the observer’s eye were at the level of the sea, his visible horizon
would coincide with the sensible horizon, defined above; but the
elevation above the surface from which sights are taken causes the line
of vision, tangent to the sea, to be depressed below the plane of the
sensible horizon making an angle with it called the dip of the horizon.
In practice all altitudes of heavenly bodies taken from a vessel are
measured to the visible horizon and corrected for the dip to reduce
them to the sensible horizon, then again corrected for parallax to
obtain the true altitude of the body above the rational horizon; or
what is the same thing, the altitude as observed at the center of the
earth.
From the zenith, an infinite number of great circles, known as
vertical circles, sweep around the celestial sphere, cutting the
horizon at right angles and passing through the nadir. The one which
cuts the north and south points is called the celestial meridian, and
is evidently a projection of the terrestrial meridian. The vertical
circle passing through the east and west points is called the prime
vertical, and has a distinction above other vertical circles by virtue
of its being the most favorable position for a body in observations
for longitude. The heavens are further swept by an infinite number of
parallels of altitude which are, as their name implies, parallel to the
horizon.
The azimuth of a body is its angular distance from the north or south
points of the horizon, determined by the angle formed at the zenith,
or by the arc of the horizon between the meridian of the observer and
the vertical circle passing through the body. Amplitude is the angle
at the zenith formed by the prime vertical and the vertical circle
passing through the body or it is the angular distance from the east or
west points, measured on the horizon, and is measured similarly to the
azimuth.
The system of laying off the heavens just described is well enough for
the momentary locating of a body, which is a very important feature in
navigation, but for some purposes a more stable point than the zenith,
which on shipboard is ever changing, is needed, from which to form a
system that is constant the world over. To meet this demand we take
the point in the sky penetrated by the prolongation of the earth’s
northern axis--the celestial pole--and from this point meridians and
parallels are developed upon the celestial sphere as has been done on
the earth. In fact, it is as though these terrestrial coordinates were
projected to the heavens where they hold the same relative positions
as upon the earth. The northern celestial pole is in the zenith at our
north pole. The same is true of the south pole. The celestial equator,
or equinoctial, is a great circle, which is midway between the poles
and everywhere 90° from them. It marks the termination of the plane of
our equator extended to the celestial sphere, or in other words, it is
always directly over our equator.
The parallels of the celestial sphere evolved by this system,
corresponding to those of latitude upon the earth are called parallels
of declination, while the celestial meridians having as their point of
origin the prolongation of the earth’s axis, are known as hour circles.
The particular hour circle passing through the zenith is one and the
same with the celestial meridian. It will be seen that this circle must
pass through the zenith, nadir and the poles. The angle formed at the
pole by the hour circle passing through a body and a local meridian is
the hour angle of that body, and is measured westward through 24 hours,
although A.M. hour angles of the sun are reckoned eastward through 12
hours.
At the north pole where the zenith is identical with the celestial
pole, the vertical circles, parallels of altitude and rational horizon
are coincident with the hour circles, parallels of declination and the
equator, respectively; but departing from this point they form angles
with each other corresponding to the degrees of latitude from the pole;
at the equator the angle reaches 90°.
The system of circles described above is by far the most extensively
used, and positions determined by its coordinates are comparatively
constant, but there is still a third system of circles which was used
and handed down to us by the ancients. In the place of the celestial
equator, a similar great circle is used, known as the ecliptic. This
circle is determined by the extension of the plane of the earth’s
orbit to the celestial sphere. The poles of the ecliptic everywhere
90° from this circle are the points from which meridians depart as
upon the earth. The prime meridian of this system passes through the
intersection of the celestial equator, and the ecliptic--the vernal
equinox or First Point of Aries. Celestial latitude and longitude are
the coordinates used with this system, but navigators universally
prefer to use the well-known declination and right ascension. Hence the
path of usefulness of the former seldom leads beyond the observatories.