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Grunt Productions 2007
Simple Astronomical Simple Astronomical PrinciplesPrinciples
(The Essence of Marcq St Hilaire)(The Essence of Marcq St Hilaire)
A brief by Lance GrindleyA brief by Lance Grindley
Grunt Productions 2007
Covering:Covering:
The Geographical Position.The Geographical Position. Zenith Distance and Position circlesZenith Distance and Position circles The intercept and position line.The intercept and position line. Simultaneous sights and running position Simultaneous sights and running position
lines on or back.lines on or back. Sun sights and transferred position lines. Sun sights and transferred position lines.
Grunt Productions 2007
The Geographical The Geographical Position (GP)Position (GP)
Star PositionDeclinationGreenwich Hour Angle
Geographical PositionLatitudeLongitude
Grunt Productions 2007
Altitude of Star 90Altitude of Star 90oo
Observer in the Star’s GP
Alt
Grunt Productions 2007
Altitude of Star 60Altitude of Star 60oo
GP
Alt
Zenith
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Altitude of Star 30Altitude of Star 30oo
GP
Alt
Zenith
Grunt Productions 2007
Star at Infinite Star at Infinite DistanceDistance
GP
Alt
Alt
Zenith
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Circle of Equal AltitudeCircle of Equal Altitude
50o 50o
50o
50o
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Position Circle on SpherePosition Circle on Sphere
Light from star at infinite distance
Geographical Position
Alt Alt
Grunt Productions 2007
Altitude & Zenith DistanceAltitude & Zenith Distance
Celestial Horizon
Zenith
90o90o
Altitude
Zenith Distance
Zenith Distance =
90o - Altitude
Grunt Productions 2007
Sextant to True AltitudeSextant to True Altitude
Sextant altitude must be corrected to true Sextant altitude must be corrected to true altitude.altitude.
True zenith distance (ZD) the radius of the True zenith distance (ZD) the radius of the position circle is 90º - true altitude.position circle is 90º - true altitude.
Sextant altitude is corrected for the Sextant altitude is corrected for the following following
Sextant index errorSextant index error Height of eye (dip)Height of eye (dip) Refraction and semi-diameterRefraction and semi-diameter
Grunt Productions 2007
The Zenith DistanceThe Zenith Distance
Geographical Position
ZZ’
XTrue Zenith Distance
Calculated Zenith Distance
A J
Radius ofPosn Circle
U
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Position Circles from GPPosition Circles from GP
Radii of circles of Equal Altitude
Position Circle of True Altitude
GPPosition Circle of Calculated Altitude
Intercept
Grunt Productions 2007
Position Position Circle on Circle on Mercator Mercator
ChartChart
0
15
30
45
60
0153045
GP
1560
15
30
75
Grunt Productions 2007
Relationship of AltitudesRelationship of Altitudes
Calculated zenith distance of a star provides the Calculated zenith distance of a star provides the Great Circle distance between the GP and the chosen Great Circle distance between the GP and the chosen Latitude & Longitude.Latitude & Longitude.
True zenith distance of the star, the angular distance True zenith distance of the star, the angular distance between the zenith and the star, is found from the between the zenith and the star, is found from the altitude measured with the sextant.altitude measured with the sextant.
Difference is called the intercept.Difference is called the intercept. Although theoretically we compare the zenith Although theoretically we compare the zenith
distances, the same value can be derived from distances, the same value can be derived from comparison of true and calculated altitudes. comparison of true and calculated altitudes.
Grunt Productions 2007
Geometry of TangentsGeometry of Tangents
Tangent
Point ofTangency
Radius to point of tangencyRight Angle
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Plotting the Intercept Plotting the Intercept TowardsTowards
Bearing of Star & GP
DR
Intercept
Position Line
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Plotting the Intercept Plotting the Intercept AwayAway
Bearing of Star & GPDRIntercept
Position Line
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Intercept in 3DIntercept in 3DP
P’
Z
XJAzimuth
Intercept
Position Line
Grunt Productions 2007
Simultaneous Sights Simultaneous Sights (1)(1)
Sights taken at Morning or Evening Civil Sights taken at Morning or Evening Civil Twilight allow a series of observations Twilight allow a series of observations within a period of 10-15 minutes.within a period of 10-15 minutes.
Sights must be corrected for the ship’s Sights must be corrected for the ship’s movement so that the position lines all movement so that the position lines all relate to a common time.relate to a common time.
Distance is small and therefore DR errors Distance is small and therefore DR errors are minimal - called simultaneous sightsare minimal - called simultaneous sights
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Simultaneous Sights Simultaneous Sights (2)(2)
Ship’s Track
Grunt Productions 2007
Sun-run-SunSun-run-Sun
In principle there is no difference in In principle there is no difference in running a position line over three running a position line over three minutes or three hoursminutes or three hours
In practice a Sun-run-Sun becomes In practice a Sun-run-Sun becomes inaccurate because the positional inaccurate because the positional errors in DR increase with timeerrors in DR increase with time
Grunt Productions 2007
Sun- run - SunSun- run - Sun
DR
EP
Grunt Productions 2007
Any Questions?Any Questions?
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