Relationship Between Time & Longitude

Ordinarily, we use mean solar time, which is measured by the motion ofthe mean Sun around the Earth. Let’s suppose your ship is on longitude60°W. When the Sun is on your longitude or meridian, it is noon. As theSun continues to move west and crosses over longitude 61°W, it is noonthere and the time on your meridian is later. In fact it is the timeequivalent of 1° later. But you can’t measure 1° on your watch; you mustconvert this 1° of arc to units of time.To have a standard reference point, every celestial observation is timedaccording to the time at the Greenwich meridian. Usually this isdetermined by means of the chronometer which is set to GMT. To clarifythe relationship between time and arc, let’s consider a situation in whichyou know your longitude exactly at noon, and you want to find out thetime in Greenwich.Arc to TimeWhen the Sun is on a particular meridian, it is noon at that meridian. Inother words, when the Sun is on the Greenwich meridian (0°), it is noonby Greenwich time. To make the problem easier, let’s say you’re in 90°Wlongitude. It’s noon where you are, so the Sun must also be in 90°Wlongitude. So, since leaving Greenwich, the Sun has traveled through 90°of arc. Because it was 1200 (noon) Greenwich time when the Sun was at0°, the time at Greenwich now must be 1200 plus the time required forthe Sun to travel through 90° of arc.The following information provides all the elements of a problem forconverting arc to time. If you know that it takes 24 hours for the Sun totravel 360° or one complete revolution, it should be easy to find how longit takes it to go 90°. If the Sun goes 360° in 24 hours, it must go 15° in1 hour. If it goes 15° in 1 hour, it must go 1° in 4 minutes. Then, to go90°, it takes 90 x 4 minutes, or 360 minutes, which is the same as 6hours. Six hours ago it was 1200 Greenwich time; therefore, the time atGreenwich now must be 1800. You actually have converted 90° of arc to6 hours of time. In doing so, you discovered the basic relationshipbetween arc and time. This relationship is stated as 15° of longitude (arc)equals 1 hour of time.Your problem could be converting time to arc--the reverse of the one weworked out. Tables for converting either way are in The NauticalAlmanac and in Bowditch, but if you acquire the following easy methodsof converting, you won’t have to refer to publications. First, you mustmemorize the values for arc and time.

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