Decide
Your corrected altitude is 47°45.8′. How far are you from the body's GP?
The lesson in plain words
- Your own sky
- The zenith is the point directly above you; the nadir is directly below.
- The celestial horizon is the great circle 90° from your zenith.
- Its plane passes through the Earth's centre, perpendicular to your vertical.
- Your observer's meridian runs through the poles and your zenith.
- Sextant altitudes are corrected to the celestial horizon (Celestial: the sextant).
- Altitude and azimuth
- A body's altitude (H) is its angle above the celestial horizon, 0° to 90°.
- Its zenith distance (ZD) is 90° − altitude.
- Its azimuth (Zn) is its true bearing, 000° to 360° clockwise from true north.
- At meridian passage it bears north or south, unless overhead, when azimuth is undefined.
- Upper passage has LHA 0°; lower passage has LHA 180°.
- Pole height = latitudeThe elevated celestial pole, the one on your side of the equator, stands above your horizon at an altitude equal to your latitude. At 40°N it is 40° up.
- The circle of equal altitude
- The angle between your zenith and the body equals the angle at the Earth's centre between you and the GP.
- Each 1′ of arc is 1 nautical mile.
- So everyone who measures the same altitude at the same instant stands on one circle around the GP: the circle of equal altitude.
- Its radius is the zenith distance in minutes, in miles.
- From circle to position line
- An altitude of 47°45.8′ gives a ZD of 42°14.2′: a circle of about 2,534 M radius.
- Your dead-reckoning (DR) position is estimated from a known position using course and distance travelled.
- Near it, a short arc of the circle is almost straight, at right angles to the azimuth: your position line.
- Time each sight: the GP moves about 15′ of longitude a minute, up to about 15 M.
Key data
- Zenith distance
- ZD = 90° − altitude
- 1′ of arc
- 1 nautical mile on the Earth's surface
- Circle radius
- ZD in minutes = miles from the GP
- Elevated pole
- Its altitude equals your latitude
- GP motion
- 15′ of longitude a minute (up to 15 M)
- Spanish terms
- Cenit, horizonte, altura, azimut, distancia cenital
Key points
- Altitude above the celestial horizon; zenith distance = 90° − altitude.
- Azimuth Zn is the body's true bearing, 000°–360°.
- The elevated pole's altitude equals your latitude.
- Same altitude, same instant: you are on a circle of equal altitude around the GP.
- Near your DR the circle is a straight position line at right angles to the azimuth.
Check what you have read
At 35°N, what is the altitude of the north celestial pole?
True or false?
Decide each statement before you see the answer.
Azimuth Zn is the body's true bearing, 000°–360°.
The elevated pole's altitude equals your latitude.
A few seconds of error in time do not matter for a sight.
A position line runs towards the body, along its bearing.
Practice case & exam keys
Situation
You observe the Sun at an altitude of 47°45.8′ (corrected). A crew member asks: 'So where are we?' Explain what that single altitude tells you.
Show the answer
ZD = 90° − 47°45.8′ = 42°14.2′, about 2,534 M. You are somewhere on a circle of about 2,534 M radius around the Sun's GP at that instant. Near your DR, that circle is almost a straight position line at right angles to the Sun's bearing. A fix needs two nonparallel position lines referred to the same time.
Exam keys
- Altitude from the celestial horizon; ZD = 90° − altitude; azimuth is true bearing.
- Altitude of the elevated pole = latitude.
- Circle of equal altitude: centre the GP, radius ZD with 1′ = 1 M.
- Position line: at right angles to the azimuth, near the DR.