Relation Between Longitude and Time

INTRODUCTION TO ASTRONOMY

DEFINITION OF TERMS

 Celestial sphere – a hollow sphere/imaginary globe of infinite radius of which the earth is the center  Celestial poles – are the points where the earth’s axis prolonged pierces the celestial sphere  Zenith – the point where a vertical line pierces the celestial sphere above the head of the observer  Nadir – the corresponding point in the opposite hemisphere, directly below the observer  Celestial equator – is the great circle formed by the intersection of the earth’s equatorial plane with the surface of the celestial sphere  Declination of any celestial body – is the angular distance of the body above or below the celestial equator  Polar distance or codeclination of any celestial body – is p = 90° -   Latitude of a place – may be defined as the angular distance of the place above or below the equator  Longitude of a place – is defined as the angular distance measured along the arc of the equator between a reference meridian and the meridian circle passing through the station  Primary meridian – is the reference meridian  The right ascension of the sun or any star is the angular distance measured along the celestial equator between the vernal equinox and the hour circle through the body  Azimuth of a celestial body – is the angular distance measured along the horizon in a clockwise direction from the meridian to the vertical circle through the body  Altitude of a celestial body – is the angular distance measured along a vertical circle, from the horizon to the body  Zenith distance or coaltitude – is the angular distance from the zenith to the celestial body measured along a vertical circle  Civil time – has the same meaning as the mean solar time or mean time  Local civil time – is the time at the meridian of the observer  Greenwich civil time – civil time of the prime meridian at Greenwich  Apparent solar time (at any place) – is given by the hour angle of the true sun plus 12h. Also called, apparent time  Local apparent time – is the apparent time for the meridian of the observer  Greenwich apparent time – apparent time at Greenwich  Mean solar time (at any place) – is given by the hour angle of the mean sun plus 12h  Sidereal time (at any place) – is the hour angle of the vernal equinox at that place RELATIONS AMONG LATITUDE, ALTITUDE, AND DECLINATION

 Figure 10.7 represents a section of the earth through the pole and the station of an observer  The latitude of the observer is given by the angle  between the equator and a vertical line through the observer’s station, the angle being measured in the plane of the meridian  Figure 10.8 represents a section of the celestial sphere through the celestial poles and the observer’s zenith  As shown

< QOZ =

 Hence, the latitude of a place is given by the angular distance NP, which is the altitude of the pole, or by the angular distance QZ, which is the zenith distance or coaltitude of the equator  The angular distance from the pole to the zenith is 90 -  = c, which is the colatitude of the place  In the northern latitude, if any heavenly body S having declination  is on the meridian and south of the zenith, then from Figure 10.8,

 = (90 - h) +  = z +  RELATION BETWEEN LONGITUDE AND TIME

 As the sun apparently makes a completer revolution (360) about the earth in one solar day (24 h), and as the longitudes of the earth range from 0 to 360, it follows that in 1 hour the sun apparently traverses 360/24 = 15 of longitude  It follows that, the difference in local time between two places, whether the time under consideration be sidereal, mean solar, or apparent solar, is equal to the difference in longitude between the two places, expressed in hours  Some solar ephemeredes are for the meridian of Greenwich, and a frequent problem is to find the local time corresponding to a given instant of Greenwich time or vice versa  The local time (L.T.) of a place at a given instant is obtained by adding or subtracting from the Greenwich time (G.T.) the difference in longitude (), expressed in hours, between the two places  If the place is east of Greenwich, the difference in longitude is added; if the place is west; the difference in longitude is subtracted

Relationship between Time and Longitude  In these problems concerning time intervals and longitude, conversion from angular units to units of time or the reverse frequently is necessary  These conversion can be accomplished by the following relationships

Time Arc Arc Time 24h = 360 360 = 24h 1h = 15 1 = 4m 1m = 15’ 1’ = 4s 1s = 15” 1” = 0.067s