Because the earth rotates on its axis and revolves around the sun, the exact time (which includes the date and hour of day) is necessary to understanding the locations and movements of the sun, stars, and planets and using them to determine your location on the earth. The revolution of the earth around the sun comes into play and causes what is known as the sun’s right ascension to change throughout the year. In a practical sense, if you watched the sun rise every day over the course of a year, it would rise in a slightly different spot each morning and eventually return to its original position after a full year.
These differences in time and longitude are how celestial navigators determine their longitudes. They have an accurate clock, which tells them exactly what time it is in Greenwich, England and they use the stars above them to determine their local time for the given date. For instance, they know from an almanac when a certain star should be in a certain location on a certain day of the year and they already know the date. So, they measure the location of the star or sun, and are then able to determine their local time. From comparing the local time to the time on their clock, or chronometer, they can determine their longitude.
Inaccuracies in both the measurement of the star’s location and the time of day can cause major errors in the determination of one’s longitude. When doing celestial navigation, there is always going to be a small amount of measurement error associated with taking star fixes using a sextant. To keep the amount of error small, navigators take numerous fixes of the same star repeatedly to make sure they are getting an accurate read. In terms of time, the only way to make sure the error is small to have an incredibly accurate clock or chronometer and make sure it is perfectly on time.
To give an idea of how much the accuracy of time affects the determination of longitude, if your chronometer is off by 4 seconds – your longitude will be off by 1 nautical mile at the equator. A clock that is off by 4 minutes will put the navigator’s location off by 60 nautical miles at the equator! Therefore, it's imperative that an accurate clock be tuned precisely to Greenwich Mean Time to successfully use celestial navigation.
In the same vein, the day of the year affects the calculations of longitude because the Sun’s right ascension is used to help determine the local time (which is then compared to a Greenwich Mean Time clock). The Sun’s right ascension changes (due to the Earth’s revolution around it) at a rate of 2 hours per month, or 4 minutes every day. These 4 minutes of change per day also equate, as above, to 60 nautical miles in longitude difference at the equator. So, if you use a different day in your calculations than it really is, your longitude will be off by 60 nautical miles for every day you are off of the real date.
NEXT: An example of a similar calculation...
