The meridian angle, like the LHA, is measuredbetween 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°.
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 letterp.
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 surface-plane altitude value and the center-of-the-earth-plane altitude value is theparallax correction.
Because of the vast distance between the earth andthe fixed stars, the difference between the surface-plane altitude and the center-of-the-earth-plane 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 ho) to get the true altitude (ha). 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.
Thezenith 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.
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 ameridian observation of a heavenly body.
Latitude by Meridian Altitude Observation
In a meridian observation you determine the altitudeof 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 15-12 and explained in the following paragraphs.
CASE I. When the body observed is toward theequator from the zenith, you can use the following formula to get the latitude:
Figure 15-12.-Three possible situations in determining latitudeby meridian altitude observation.
F = latitude of place
d = declination of observed body
h = corrected observed altitude
CASE II. When the body observed is toward thepole 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.