Transcript Finding your longitude - MSU Department of Physics and

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 (16931776) 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