CELESTIAL NAVIGATION

to be useful to the aerial navigator positions located on the celestial sphere must be transferred to the earth the relationship between the observers position on the earth and his Zenith on the celestial sphere has already been demonstrated similarly a relationship exists between a body on the celestial sphere and the point on the earth directly beneath it this point is called the geographical position or GP of the particular celestial body it is the point which at a given instant has that body at its zenith if a body's geographical position is known it's meridian on the earth is also known using this meridian and the Greenwich Meridian which is the zero meridian for longitude the Greenwich our angle or GHA for the particular body can be measured it is the angle at the pole between the meridian of a celestial body and the Greenwich Meridian it is measured to the west through 360 degrees another type of our angle which was discussed in connection with the celestial sphere can also be represented on the earth it is the angle at the pole between the observers Meridian and the Meridian of the celestial body to distinguish it from other types of our angle it is called local our angle or LH a it is found by combining Greenwich our angle and the navigators longitude the air Almanac is consulted to get the Greenwich our angle of the observed celestial body next from his dead reckoning the Navigator determines his longitude fairly accurately the Greenwich our angle of the celestial body represents the longitude of its geographical position and the observers longitude represents his angular distance from the Greenwich Meridian local our angle is obtained when Greenwich our angle and longitude are added or subtracted in the example the navigators longitude is subtracted from the bodies Greenwich our angle in this example the navigators longitude is added to the Greenwich our angle local our angle shows in terms of longitude the relation between the navigator and the body he is observing Zenith distance shows the same relation but differently it is the Great Circle distance from a body's geographical position to the observers position it is an angular distance on the celestial sphere having a corresponding linear value on the earth that is computed from the altitude the angle between the horizon and the line from the center of the earth to the observer Zenith is always 90 degrees since light from a star at an infinite distance always strikes the earth with parallel rays it's altitude or angle with respect to the observer is always the same whether he is above the earth on its surface or theoretically at its center in this particular case the altitude is 60 degrees therefore the angular value of the zenith distance is 30 degrees or the complement of the altitude 90 degrees minus the altitude always equals the zenith distance because there are eighteen hundred minutes in 30 degrees and each minute equals a mile the linear value of the zenith distance in this example is 1800 miles an important conception for the Navigator is the circle of position it is still another way of showing the relationship between the observers position and the geographical position of the celestial body being observed Zenith distance is the radius of this circle this navigational aid can be illustrated easily the top of the pole represents a star under observation the base of the pole represents the geographical position of that star the length of tape along the ground represents the zenith distance to see the top of the pole or the star always at the same angle or altitude the observer must stay on a circle if the radius is lengthened the altitude or angle of observation is decreased if the radius is shortened the altitude is increased the navigators circle of position however is on a much larger scale to repeat its center is the observed celestial bodies geographical position and it's radius is the zenith distance between the geographical position and the observers position obviously an observer at any point on the circle will observe the same celestial body at the same altitude therefore an altitude say of 62 degrees in 33 minutes for a particular celestial body must be secured from any point on a definite circle but the question that confronts the Navigator is at what particular point am I to answer this he constructs another circle of position for another body observed at the same time he can be on both circles at only two points the two intersections of the circles are normally so far apart that one may be disregarded because it is obviously incorrect according to his dead reckoning if globes of suitable size and accuracy could be carried an airplane celestial navigation could be simplified by drawing circles of positions directly on the globe but this is out of the question because the Navigator must work with maps which represent only a fraction of the Earth's surface instead of unwieldy circles of position he uses Manute parts of circles of position so Manute that they are assumed to be straight without appreciable error each of these is called a line of positions or LP and the intersection of two of them gives the Navigator a fix or definite position on a map a third line of position based on a third celestial body may be added to get an additional check formerly the plotting of lines of position dependent upon voltage is fairly lengthy mathematical solution of the astronomical triangle the vertices of this triangle are at the nearer Pole the observed bodies geographical position and the observers position it was solved by substituting assumed values for any three of the five values involved in the triangle today however the labor required to solve this triangle has been tremendously reduced it is now largely a routine procedure involving several index tables of pre computed data from which values are entered on a standardized form in actual practice the Navigator begins with an assumed position this may be the dead reckoning position at which he would be if all factors influencing the flight of his airplane have been compensated for or it may be a position close to and on either side of the dead reckoning position using the greenwich hour angle of the observed body and the longitude of the assumed position navigator determines local hour angle with this value he enters a set of logarithmic tables and computes what the azimuth and altitude of the observed celestial body would be had it been observed from the assumed position let us say that the results of this computation show the Navigator that from the assumed position the azimuth of the observed body is 130 degrees and the altitude 30 degrees this information enables him to draw a line of position however by actual observation he has found the altitude of the same celestial body to be 29 degrees and 54 minutes since the smaller the altitude farther an observer is from the geographical position the observer in this case is farther from the geographical position of the body then his assumed position is this distance is 6 minutes or six nautical miles and is called the intercept the new line of position indicating the navigators position is now drawn parallel to the assumed line of position and six miles from it if the observed altitude should be greater than the calculated altitude the Navigator is closer to the body's geographical position then his assumed position is we have seen how the position of a celestial body is transferred to the earth our Greenwich our angle and local our angle are found and how zenith distance is related to the geographical position of a celestial body and an observer we also know that Zenith distance is the complement of the altitude from this information the circle of position and its Manute part the line of position are constructed this knowledge coupled with the health of time-saving tables highly developed instruments and well-planned navigators compartments makes position finding on the earth a rapid routine procedure whose chief requirement is constant practice