Altitude (astronomy)

“ By using stars of both high and low altitudes, a greater exactness can be obtained, but, after all, the method only gives a first approximation, as its weakness lies in the very slow change of altitude as the meridian is approached. ”

“ The Moon’s inhabitants on the side next the Earth may as easily find the longitude of their places as we can find the latitude of ours. For the Earth keeping constantly, or very nearly so, over one Meridian of the Moon, the east or west distances of places from that Meridian are as easily found, as we can find our distance from the Equator by the Altitude of our celestial Poles. ”

“ In addition to these, other imaginary circles are drawn parallel to the horizon and becoming smaller and smaller 14until the uppermost one may run close round the zenith, which is the common centre of the entire set. These are called altitude circles, because each one throughout its 15whole extent is at an unvarying height, or altitude, above the horizon. Such circles may be drawn anywhere we please, so as to pass through any chosen star or stars. If two stars in different quarters of the sky are found to lie on the same circle, then we know that both have the same altitude. ”

“ 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. ”

“ Since the apparent course of the sun through the sky is a curve, rising from the eastern horizon, attaining its greatest elevation where it meets the meridian, and thence declining to the western horizon, it is evident that the length of the shadow must be least when the sun is on the meridian, or at its maximum altitude. ”

“ In astronomy it is the vertical height of any point or body above the horizon. It is measured or estimated by the angle subtended between the object and the plane of the horizon, and may be either true or apparent. The apparent altitude is that which is obtained immediately from observation; the true altitude, that which results from correcting the apparent altitude, by making allowance for parallax, refraction, &c. Altitude is one of the main determining influences of local climate. Its increase has the same effect on temperature as an increase of distance north or south of the equator. ”

“ Having measured the altitude and the azimuth we have the two co-ordinates which are needed to indicate accurately the place of a star in the sky. But, as we shall see in a moment, other co-ordinates beside altitude and azimuth are needed for a complete description of the places of the stars on the celestial sphere. Owing to the apparent revolution of the heavens round the earth, the altitudes and azimuths of the celestial bodies are continually changing. We shall now study the causes of these changes.
5. The Apparent Motion of the Heavens. We have likened the earth to a rotating school globe. ”

“ The student who has studied elementary geometry should be able to demonstrate that at the mean of the two recorded times the sun's altitude was equal to one half of the angle measured in the figure.
Fig. 4.—Taking the sun's altitude.
When the board is turned edgewise toward the sun so that its shadow is as thin as possible, rule a pencil line alongside it on the horizon plane. The angle which this line makes with a line pointing due south is called the sun's azimuth. When the sun is south, its azimuth is zero; when west, it is 90° ”

“ From this table it will be seen that at the height of 35 miles the air is one thousand times rarer than at the surface of the earth; and that, supposing the same rate of decrease to continue, at the height of 140 miles the rarity would be one trillion times greater. The atmosphere, however, is not unlimited. When it becomes so rare that the force of repulsion between its particles is counterbalanced by the earth's attraction, no further expansion is possible. To determine the altitude of its superior surface is a problem at once difficult and interesting. ”

“ When a planet is on the right or east side of the Meridional line, and is moving forward along the signs, without increase of declination, its altitude will be less on the second occasion than on the first at the moment when the altitude of the fixed star is the same as before. ”

“ No doubt the intensity of the attraction becomes weaker with every increase in the altitude, but that action would still exist to some extent, however lofty might be the elevation which had been attained. ”

“ I have been enabled to distinguish his ring several times before sun-set, with a power of 65; but his great southern declination, and consequent low altitude, at the periods when these observations were made, 483 were unfavourable for determining the degree of his visibility in day-light; for a planet or a star is always more distinctly perceptible in a high than in a low altitude, on account of the superior purity of the atmosphere through which a celestial object is seen when at a high elevation above the horizon. ”

“ If the convergence is measured, the exact distance from either station can be calculated, and if the angle between the cloud-point and the horizon beneath it is noted, it is a simple matter to deduce the actual altitude of the cloud. ”

“ In fact, this element becomes so unreliable in low altitudes that it is not advisable to observe a body when less than 10° or 13° above the horizon. This in no way concerns bearings taken of bodies in the horizon for amplitude, as refraction affects the altitude and not the azimuth of a body.
Dip
It is a well-known fact to every seaman that by going aloft, he can pick up a light sooner than on deck ”

“ The sun's altitude being known, and the edges of the projections of cloud shadows being parallel to the sun's rays: if we have a map of the country round the station, and mark on it the spots where the sun‘s rays strike through clouds, or where the shadows of clouds fall, the determination of the height of the cloud stratum is effected by plane trigonometry, if we observe the altitude of the precise points in the cloud. ”

“ Aloft we have no association to guide us, and their insulation in the expanse of the sky leads us rather to undervalue than to over-rate their apparent magnitudes. Actual measurement with a proper instrument corrects our error, without, however, dispelling our illusion. By this we learn that the sun, when just on the horizon, subtends at our eyes almost exactly the same, and the moon a materially less, angle than when seen at a greater altitude in the sky, owing to its greater distance from us in the former situation as compared with the latter.—Sir John Herschel’s Outlines. ”

“ Place your ship between Trenco and the sun. Enter the atmosphere exactly fifteen G-P minutes from ... check ... at twenty degrees after meridian, as nearly as possible on the ecliptic, which is also our equator. Go inert as you enter atmosphere; for a free landing upon this planet is impossible. Synchronize with our rotation, which is twenty-six point two G-P hours. Descend vertically until the atmospheric pressure is seven hundred millimeters of mercury, which will be at an altitude of approximately one thousand meters. ”

“ This deficit increases as the gauges are higher above the ground in proportion approximately to the square root of the altitude, provided that they are fully exposed to the increase of wind that prevails at those altitudes. It is evident that even for altitudes of 5 or 10 ft. ”

“ It may likewise be made to serve as a theodolite for surveying land and taking horizontal angles—as a Quadrant for taking angles of altitude—as a level—as an equal altitude instrument—an azimuth instrument for ascertaining the sun’s distance from the north or south points of the horizon—and as an accurate Universal Sun Dial, for finding the exact mean or true time, on any occasion when the sun is visible. ”

“ But if in any country the sun should be both in its perigee and nearer to the perpendicular at the same time, it must necessarily give out more heat than in a country where it is also in perigee, but situated more obliquely; so that the comparative altitude of the planets should be observed, and their approach to or declination from the perpendicular in different countries. ”

“ Another very important point to bear in mind when observing a body with the view of computing its hour angle, is its azimuth. When the bearing is nearly east or west, on the prime vertical, the body is rising or falling faster than at any other time, and an error in altitude or latitude will produce the least error in the resulting longitude. ”

“ Next, apply the altitude correction. Find the altitude correction table on the inside front cover of the Nautical Almanac next to the dip table. The altitude correction varies as a function of both the type of body sighted (Sun, star, or planet) and the body’s apparent altitude. ”

“ Because it is found, by experiment and observation, that the air becomes less dense in proportion to its altitude from the earth's surface. The gradual decrease of atmospheric density observed in ascending a mountain, or in a balloon, supplies sufficient data to enable us to calculate the height at which the atmosphere would probably altogether cease. ”

“ The choice of altitude is yours—whether to accept this current or mount higher and go with another. You may mount above the clouds, where one breathes oxygen from tubes, while the earth, in the last glimpse you had of it, seems to spin beneath you, and you lose all bearings; or you may descend and scud along the surface, aided by your guide rope and a dipperful of ballast to leap over trees and houses—giant leaps made without effort. ”

“ When the navigator is directly east or west, the altitude, corrected for the time of observation, gives its longitude.
If the horizon is invisible, owing to fogs or unsuitable clouds, it may be replaced by means of a spirit level; but great care should be taken in making such observations, since a spirit level on an aëroplane or airship is not wholly reliable, unless the craft is proceeding in an absolutely straight direction, and without sway of any kind.
All methods of navigation by Astronomical Observation fail when the sky is obscured by clouds and the heavenly bodies cannot be seen. ”

“ A star reaches its greatest altitude when on the part of the meridional circle between the south point of the horizon, S, and the north pole, P. A star seen between the north pole and the north point on the horizon, that is, on the arc PN, must obviously be a circum-polar star and would have its highest altitude when between the pole and the zenith, or on the arc PZ. When a star reaches the meridian in its course across the celestial sphere it is said to culminate or reach its culmination. ”

“ FLYING ALTITUDE.—It is doubtful whether the disturbed condition of the atmosphere, due to the contour of the earth's surface, reaches higher than 500 feet. Over a level area it is certain that it is much less, but in some sections of the country, where the hill ranges extend for many miles, at altitudes of three and four hundred feet, the upper atmosphere may be affected for a thousand feet above. ”