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

• 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. Observed altitude of the Body above the celestial horizon. Measure it with a sextant (hs), and then apply relevant corrections to get Ho.

2. Latitude and longitude of your assumed position (AP).

3. Precise time of the sextant altitude measurement, in order to calculate Hc and Zn for the nearby assumed position (AP).

4. Computed altitude (Hc) of the Body as if observed from the AP at the time of the sextant sight. Requires Almanac ephemerides.

5. 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 • 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

• 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