Celestial Navigation
Theory, Navigational Astronomy,
The Practice
R. Bruce Jones
February 17, 2014
What is the theory?
• The basic theory behind Celestial
Navigation is that we find our unknown
position from a known position.
• If we have some information we can
deduce the rest.
Find the sun
• Imagine the sun is
directly overhead at a
particular time.
• Look in the Nautical
Almanac to find out
where the sun is.
• That is where we are!
How do we know?
• How do we know that
the sun is directly
overhead?
• The sextant tells us.
• It measures the angle
form the horizon.
• In this case the angle
would be 90°
BUT!, The sun is not overhead!
• But what if the sun were 1° from
overhead (sextant reads 89°)?
• Then we would be somewhere
on a circle 60 miles (60 nm= 1°)
from where the Nautical Almanac
said the sun was.
• This is a circular line of position
(LOP).
Actual Position
• An actual position occurs where
two lines of position (LOP’s)
cross.
• For example: your plotted track
on a chart intersects a circular
LOP.
Second LOP
• If we look at the sun later in the
day, we would get a second
circle.
• Our position would be at one of
the intersections of the two
circles.
• If you still do not know your
position, do a third sight to get a
third circle.
Navigational Astronomy
Just four things to remember!
#1 Ptolemy was right!
• Celestial navigation’s view of the
heavens is pre-Copernican.
• We look at an earth-centric system
in which the sun, moon, planets,
and stars revolve around it.
• It is a what you see is what you
get system.
#2 Einstein was right!
• Space and time are a continuum. In
navigational astronomy time = distance.
• Longitude is measured in degrees where
15° = 1 hour.
• 360° = 24 hours = Earth’s rotation
• 1 second in time = ¼ nautical mile at the
equator
• An error in time is an error in longitude
#3 The Coordinate System
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Earths Coordinates
Celestial Coordinates
Observers/Horizon Coordinates
Ecliptic Coordinate
Earths Coordinates
• Latitude lines running parallel
to earth’s equator at 90° to 0°
at the poles.
• Longitude lines running around
the earth thru each pole.
• Longitude lines start at 0° at
the Greenwich Meridian and
run 180° east and west for a
total of 360°
• 1° = 60 minutes
• 1minute = 60 seconds
• 1° = 3600 seconds
Celestial Coordinates
• Celestial Equator: Earth’s equator
extended into space.
• Declination: Earth’s latitude lines
extended into space, going from
the celestial equator, 90°, north
and south to the celestial poles.
• Hour circles: Earth’s longitude lines
extended into space, this can be
measured two ways.
• The Sidereal Hour Angle (SHA) or
right ascension angle, zero starts
at the first point of Aries or vernal
equinox and travel's west to 360°.
If the Greenwich celestial meridian
is used this measurement is called
the Greenwich Hour Angle (GHA).
Observers/Horizon Coordinates
• Completely
dependent on
observer.
• You measure hs to
start the process of
finding your location
Ecliptic Coordinate System
• The Ecliptic is the
path that the sun
appears to take
among the stars.
• Our navigational
measurement of SHA
start at the first point
of Aries or vernal
equinox.
How they compare
Earth (Terrestrial)
Celestial Equator
Horizon
Ecliptic
equator
celestial equator
horizon
ecliptic
poles
celestial poles
zenith/nadir
ecliptic poles
meridians
hour circles/celestial
meridians
vertical circles
circles of latitude
prime meridian
hour circle of Aries
principle/prime
vertical circle
circle of Aries latitude
parallels
parallels of
declination
parallels of altitude
parallels of latitude
latitude
declination
altitude
celestial altitude
co-altitude
polar distance
zenith distance
celestial co-altitudes
longitude
sha/ra/gha/lha/t
azimuth/azimuth
angle/amplitude
celestial longitude
#4 Hour Angles
• It all starts with Geographic Position (GP).
Imagine a string that stretches from the
center of the earth to the center of the
celestial body. GP is the point the line
passes thru the earths surface. This point
has a location that can be referenced
several ways…
Hour Angle
Remember time = distance
• M – Observers Meridian
• G – Greenwich Meridian
• SHA – Angular distance of a
body westward from the first
point of Aries (0-360)
• RA – Angular distance of body
eastward from the first point of
Aries: in time units (0-24 hrs.)
• GHA – GP’s distance from
Greenwich Meridian (Degree,
Min:Sec)
• LHA – GP’s distance west from
the meridian you are located
on (Degree, Min:Sec)
• The Nautical Almanac gives us the GHA of
the sun and the moon for every day, hour
and minute of the year.
• For the stars it gives the SHA, which we
can then convert, and worksheets help us
figure the LHA by using our longitude.
The Practice
Taking the sight
• Setting up
• Shooting body and noting exact time corrected for watch
error and east or west of Greenwich meridian.
• Correcting for sextant error, height of eye and altitude
giving Observed Altitude.
• Entering body’s data for same time from the Nautical
Almanac, apply corrections.
• Entering tables for sight reduction with:
– Local Hour Angle (LHA)
– Assumed Latitude
– Body's declination (from Almanac) to find the calculated height if
you were where you assumed yourself to be
– This will give you the CALCULATED ALTITUDE as well as the
true bearing of the body
Navigational Triangle aka spherical
trigonometry
• For a given date and time
you know.
– AP - Your assumed position
– GP – Celestials Bodies
position
• Given information that you
have or can drive from
tables or formulas you
determine: Z- Azimuth
angle and Zenith distance.
Plotting Celestial Fix
There are 5 essential pieces of data for reducing a celestial sight
1.
2.
3.
4.
5.
Observed altitude of the Body above the celestial horizon. Measure it with a
sextant (hs), and then apply relevant corrections to get Ho.
Latitude and longitude of your assumed position (AP).
Precise time of the sextant altitude measurement, in order to calculate Hc and
Zn for the nearby assumed position (AP).
Computed altitude (Hc) of the Body as if observed from the AP at the time of
the sextant sight. Requires Almanac ephemerides.
Bearing of the Body (azimuth). Azimuth can only be determined for the AP,
not for the vessel's real position; so the navigator needs to be precise about
the time of the sextant altitude, and have confidence in the AP. Requires
Almanac ephemerides.
#1 comes from the sextant sighting, and Almanac data for the date and time
#2 comes from the DR plotting
#3 comes from a timepiece simultaneous to #1.
#4 and #5 come from calculations to solve the navigational triangle with corners
GP, AP and nearest Pole, using #2, #3 and Almanac data.
Single LOP
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Blue line: dead reckoning course.
Blue half circle/dot: dead reckoning position at
the time you took your sight.
Red solid line: azimuth bearing toward the GP
of the body (southwest).
Red dashed line: extension of the azimuth
bearing "away", because in this case the
calculated sextant altitude for the DR position
was larger than the sextant altitude you
observed.
Green line: the celestial LOP, perpendicular to
the azimuth. Your boat is somewhere on that
green line. This celestial LOP actually is a tiny
segment of the gigantic circle of position around
the GP; at any point on that circle at that precise
moment in time you would find the same sextant
altitude.
Black box: your Estimated Position; also the
intercept.
Advance position to new EP. Start new DR line
from this fix
Timeline of Navigation
Kamal, Astrolabe
Cross-staff, Backstaff
Octant, Sextant
How the sextant works
Measurement without horizon
References
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www.celestialnavigation.net
Jim Thompson MD CCFP(EM) FCPP: www.jimthompson.net
Celestial Navigation for Yachtsman, Mary Blewitt, 1995
Peter Ifland, Ph. D. in Biochemistry (U. of Texas)
Commander in the US Naval Reserve
Author of Taking the Stars: Celestial Navigation from Argonauts to
Astronauts, The Mariners' Museum, Newport News, Virginia, 1998
www.mat.uc.pt/~helios/Mestre/Novemb00/H61iflan.htm
BobGraham@longcamp.com,www.longcamp.com
American Practical Navigator, Bowditch, Defense Mapping Agency
Hydrographic/Topographic Center, 1995
Longitude, Dava Sobel, 1995