Specifies the east-west position using an angular measure
Ranges from \(0^\circ\) at the prime meridian
to \(180^\circ\) at the international date line (with
positive value to the east and negative values to the
west)
Denoted by \(\lambda\)
Day:
The amount of time it takes for the Earth to rotate
around it's axis one time
Divided into 24 (equally-sized) hours
Implications
Some Basic Math:
Since the Earth rotates \(360^\circ\)
in 24 hours, it rotates \(360/24 = 15^\circ\)
per hour (i.e., \(1^\circ\) in 4 minutes)
An "Obvious" Conclusion:
The longitude of a given location can be determined
by measuring differences between times
Some History
150 BC:
Hipparchus proposed using a prime meridian through Rhodes
and lunar eclipses (visible "everywhere") to determine
time differences, unfortunately clocks were unavailable
1500s-1600s:
Clocks began to improve but were not reliable enough to
use at sea
1700s:
The English Parliament offered a prize of £20 000
to anyone who could determine longitude at sea to within
0.5 degrees (i.e., to build a clock that was accurate at sea to
two minutes)
John Harrison built such a chronograph (on his fourth attempt)
around 1760
Determining the Local Time
Local Noon Defined:
The time when the sun is at its zenith (i.e., the highest
point in the sky)
Measuring Local Noon:
In principle, a gnomon can be used to determine when
the sun is at its zenith
In practice, the arc is flat near the zenith so
identifying it is difficult and an average is often used
(e.g., of the angles at sunrise and sunset)
Local Time:
Is then defined relative to local noon
Determining Longitude Using Lunar Eclipses
Data Collection:
An observer at the undetermined location measures the local
time of the lunar eclipse
An observer at the prime meridian measures the local time
of the same lunar eclipse
Communication:
The observer at the prime meridian transmits their observation
to the observer at the undetermined location
Calculation:
The observer at the undetermined location uses the difference
in local times calculate their longitude
Determining Longitude Using Lunar Eclipses (cont.)
An Example Eclipse (August 21, 2017):
Measured Start at the Prime Meridian: 15:46
Measured Start in Harrisonburg, VA: 10:31
Calculations:
Time difference: 5 hours and 15 minutes (i.e., 5.25 hr)
Longitude of Harrisonburg: 5.25 hr \(\cdot\)
15 deg/hr = 78.75 deg (which is pretty close to the
absolute value of -78.8689, the actual longitude)
Determining Longitude Using an Accurate Clock
Preparation:
The clock is set to 12:00 at local noon at the prime
meridian (or some other known longitude)
Determining Longitude of an Undetermined Location:
At local noon at the undetermined location, noon is subtracted
from the time on the clock to get the time difference
The longitude is calculated from the time difference
Determining Longitude Using an Accurate Clock (cont.)
Example Data:
The HMS Beagle sailed with 22 chronometers to provide
redundancy and error correction
In June of 1837, the chronometers were set to 12:00 at
local noon at the prime meridian
On November 15, 1837, the average time on the working chronometers
was 19:45
Calculations:
Time Difference: 7 hours and 45 minutes (i.e., 7.75 hr)