Meridian Angle The meridian angle, like the LHA, is measured between
the observer’s celestial meridian and the hour circle
of the observed body. The meridian angle, however, is measured east or west from
the celestial meridian to the hour circle, through a maximum of 180°, instead
of being measured always to the west, as done for the LHA, through 360°.
Polar Distance
The polar distance of a heavenly body at a given instant is simply the
complement of its declination at that instant; that is, polar distance amounts
to 90° minus the body’s declination. The conventional symbol used to indicate
polar distance is the letter p.
Altitude and Altitude Corrections
The angle measured at the observer’s position from the horizon to a
celestial object along the vertical circle through the object is the altitude of
the object. Altitudes are measured from 0° on the horizon to 90° at the
zenith. The complement of the altitude is the zenith distance, which is often
more convenient to measure and to use in calculations. Your horizontal plane at
the instant of observation is, of course, tangent to the earth’s surface at
the point of observation; however, the altitude value used in computations is
related to a plane parallel to this one but passing through the center of the
earth. The difference between the surfaceplane altitude value and the
centeroftheearthplane altitude value is the parallax
correction.
Because of the vast distance between the earth and the
fixed stars, the difference between the surfaceplane altitude and the
centeroftheearthplane altitude is small enough to be ignored. For the sun
and for planets, however, a correction for parallax must be applied to the
observed altitude (symbol h_{o}) to get the true altitude (h_{a}). A second altitude
correction is the correction for
refraction– a
phenomenon that causes a slight curve in light rays traveling to the observer
from a body observed at low altitude.
A third altitude correction,
applying to only the sun and moon, is semidiameter correction. The stars and the
planets Venus, Mars, Jupiter, and Saturn, are pinpoint in observable size. The
sun and moon, however, show sizable disks. The true altitude of either of these
is the altitude of the center of the disk; but you
cannot line the horizontal cross hair accurately on the center. To get an
accurate setting, you must line the cross hair on either the lower edge (called
the lower limb) or the upper edge (called the upper limb). In either case you
must apply a correction to get the altitude of the center.
A combined parallax and refraction correction for the
sun and planets and a refraction correction for stars keyed to observed
altitudes are given in the two inside cover pages in the Nautical Almanac.
Semidiameter corrections for the sun and moon are given in the daily pages of
the almanac. If you observe the lower limb, you add the semidiameter correction
to the observed altitude; if you observe the upper limb, you subtract it. The
correction appears at the foot of the Sun or Moon column, beside the letters S.D.
Zenith Distance
The zenith distance of
an observed body amounts, simply,
to 90° minus the true (or corrected) altitude of the
body. The letter z is
the conventional symbol used to represent
zenith distance.
DETERMINING LATITUDE
To determine the true azimuth of a line on the ground from a celestial
observation, you must know the latitude of the point from which the celestial
observation is made. If you can locate the point of observation precisely on an
accurate map, such as a U.S. Geological Survey (USGS) quadrangle map, you can
determine the latitude from the marginal latitude scale. If no such map is
available, you can determine the latitude through a
meridian observation of
a heavenly body.
Latitude by Meridian Altitude Observation
In a meridian observation you determine the altitude of
the body at the instant it crosses your celestial meridian.
At this instant the body will be at the maximum
altitude observable from your position. When you are applying a meridian
altitude to get the latitude, there are three possible situations, each
illustrated in figure 1512 and explained in the following paragraphs.
CASE I. When the body observed is toward the equator
from the zenith, you can use the following formula
to get the latitude:
Figure 1512.Three possible situations in determining latitude by
meridian altitude observation.
where:
F = latitude of place
d = declination of observed body
h = corrected observed altitude
CASE II. When the body observed is toward the pole
from the zenith, which is the case for circumpolar stars,
you can get the latitude of the place of observation by
using the following formulas:
F
= h
± p Use this formula only for circumpolar (90° 
d).
CASE III. When the equator is between the body observed
and the zenith, use the following formula to get
the latitude:
In the above situations, always remember that d
and F
arc positive when they are located north of the equator and
negative when south of it.
