Finding your longitude

The trickier part of celestial navigation

The problem of finding longitude at sea was particularly vexing

Latitude was easy

• Altitude of celestial pole

• Declination of a star at the zenith

• You can also use the sun, but you need to know the declination of the sun at the time

But latitude alone was not always enough

Longitude is harder

• Arbitrary starting point• Longitude 0 degrees

at Greenwich, England

Calculating your longitude

• You can use stars or you can use the Sun

• But in addition to making observations you need to know the time for some location of known longitude, local time alone is not enough

On Land One could observe Natural clocks

• Motion of the moon against the background of the stars

• Motions of the moons of Jupiter

• But these were hard to observe from a ship, although they could be observed from land

The problem of finding longitude at sea

• To the middle of the 18th century, no mechanical clock would keep accurate time in a sea-tossed ship

Odd Solutions

• Anchor a series of ships across the ocean that would shoot off flares and guns at set times

• Telepathic connection between animals on ship and those ashore

Harrison’s chronometer

• John Harrison (1693-1776) invented clocks that would keep good time at sea

Watch out for the difference between local time and local mean time

• The Equation of Time

Finding local time

• “Culmination” of the Sun at noon

• RA of a star on the meridian at a given time of night

• Let’s see how both ways would work

Sextant

Culmination of the Sun

• Set your chronometer to some known time, say Eastern Standard Time, before you set sail

Observe the time of local noon

• You see that the sun has transited the meridian – it is local noon

• Your chronometer reads 8 pm EST

• You make your correction for the equation of time (an important detail but one we won’t include in our calculation)

Getting the longitude

• Find the difference in times:

12 noon minus 8pm = 8 hours

Since the EST clock is the later time, you are 8 hours west of the prime meridian for Eastern Standard Time (75 degrees west of Greenwich)

8 x 15 = 120 degrees

You are at a longitude of 120 + 75 = 195 degrees west of Greenwich, England, which is also 165 degrees east of Greenwich

Using a star

• It is Jan. 21 and you see a star of right ascension = 2 hours on your meridian. You will use this observation to calculate your local time.

• Your chronometer, still set at EST, reads 1am.

Find the difference in the time

• LST = 2 hours. On Jan 21 the LST at local midnight is 2 x 4 = 8 hours. At 1am (the EST given by your chronometer) the LST would be about 9 hours. You are 7 hours earlier. You must be located 7 hours west of the standard longitude for the Eastern Time Zone.

• You are at 7 x 15 = 105 degrees + 75 degrees west of Greenwich, England. You are 180 degrees west (= 180 degrees east) of Greenwich.

You get promoted to admiral