Marcq st hilaire lrg

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


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.


The Geographical The Geographical Position (GP)Position (GP)

Star PositionDeclinationGreenwich Hour Angle

Geographical PositionLatitudeLongitude


Altitude of Star 90Altitude of Star 90oo

Observer in the Star’s GP

Alt



GP

Alt

Zenith


Star at Infinite Star at Infinite DistanceDistance

GP

Alt

Alt

Zenith


Circle of Equal AltitudeCircle of Equal Altitude

50o 50o

50o

50o


Position Circle on SpherePosition Circle on Sphere

Light from star at infinite distance

Geographical Position

Alt Alt


Altitude & Zenith DistanceAltitude & Zenith Distance

Celestial Horizon

Zenith

90o90o

Altitude

Zenith Distance

Zenith Distance =

90o - Altitude


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


The Zenith DistanceThe Zenith Distance

Geographical Position

ZZ’

XTrue Zenith Distance

Calculated Zenith Distance

A J

Radius ofPosn Circle

U


Position Circles from GPPosition Circles from GP

Radii of circles of Equal Altitude

Position Circle of True Altitude

GPPosition Circle of Calculated Altitude

Intercept


Position Position Circle on Circle on Mercator Mercator

ChartChart

0

15

30

45

60

0153045

GP

1560

15

30

75


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.


Geometry of TangentsGeometry of Tangents

Tangent

Point ofTangency

Radius to point of tangencyRight Angle


Plotting the Intercept Plotting the Intercept TowardsTowards

Bearing of Star & GP

DR

Intercept

Position Line


Plotting the Intercept Plotting the Intercept AwayAway

Bearing of Star & GPDRIntercept

Position Line


Intercept in 3DIntercept in 3DP

P’

Z

XJAzimuth

Intercept

Position Line


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


Simultaneous Sights Simultaneous Sights (2)(2)

Ship’s Track


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


Sun- run - SunSun- run - Sun

DR

EP


Any Questions?Any Questions?

Marcq st hilaire lrg

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