The Demystified Astro Navigation Course – Unit 3 Part 1

Unit 3 – Altitude and Azimuth – Part 1

 altitude and azimuth mod

Azimuth is a specific type of bearing which measures the direction of an object in relation to true north, in the horizontal plane, clockwise from 0o to 360o.  For example, in terms of azimuth, due east is 090o and due west is 270o.

Azimuth is measured by use of either a magnetic compass or a gyro compass.  A gyro compass is a form of electrically driven gyroscope which measures azimuth in relation to true north.  Such an azimuth measurement is known as true azimuth.  A magnetic compass employs a magnetized needle which is used to measure the azimuth of an object in relation to magnetic north. Magnetic compass readings must be corrected for variation and deviation in order to convert them to true azimuth.

Azimuth Angle.  In astro navigation, when we calculate the azimuth of a celestial body, the result is expressed as an azimuth angle.  Azimuth angle is measured from 0o to 180o either westwards or eastwards from either north or south.  If the observer is in the northern hemisphere, the azimuth is measured from north and if in the southern hemisphere, it is measured from south.

For example, if the true azimuth of an object is 225o, the azimuth angle for an observer in the northern hemisphere will be N135oW but for an observer in the southern hemisphere, it will be S045oW.

The rules for converting azimuth angle to true azimuth are summarised in the following table:

Rules for converting Azimuth Angle (Z) to True Azimuth (Zn)

Lat. North    Lat. South
LHA>180o Zn = Z    Zn =  180o – Z
LHA<180o Zn = 360o-Z    Zn =  180o + Z


If latitude is 225oN, LHA is 145o and azimuth angle is 120o then true azimuth is 360 o – Z  i.e. 360o – 120o = 240o.

If latitude is 25oS, LHA is 245o, and azimuth angle is 075o then true azimuth is 180o – Z i.e. 180o – 075o = 105o.

Altitude.  The altitude of a celestial body is the angular distance between its position in the celestial sphere and the celestial horizon as measured at the observer’s position.

Measuring the Altitude.  To measure the altitude of a celestial body, we use a sextant.

diag 25modAs shown in the diagram, the horizon is viewed directly through the sextant telescope and the celestial body is viewed via two mirrors. The upper mirror is attached to the index bar.  The index bar is moved until it reflects an image of the celestial body into the lower mirror which is fixed.  The position of the index bar is finely adjusted until the image of the celestial body appears to sit on the horizon.  As the index bar is adjusted, it moves a pointer over a graduated scale and when the images are made to coincide, the angle indicated by the pointer is the altitude.

The altitude measured by a sextant is referred to as the Sextant Altitude (Sext. Alt).  

Corrections.  A number of corrections have to be made to the sextant altitude before we arrive at the True Altitude.

Index ErrorNo matter how carefully a sextant is manufactured, there will usually be a very small error in its reading and this is known as index error.

To calculate index error, view a single object through the sextant telescope and through the mirrors; move the index bar until the two images coincide and note the reading.  If the reading is not zero, the actual reading is the index error.

For example, if the reading is 2’ too high, it is said to be 2’  ‘on the arc’ and recorded as:  Index Error – 2’.0.  If the reading is 2’ too low, it is said to be 2’ ‘off the arc and recorded as +2’.0. 

Dip.  A correction has to be made to allow for the height of the observer’s eye above the horizon; this is known as Dip.

nonum diag26

In this diagram, O is an observer’s position on the Earth’s surface and E is the position of his eye.  We can see that, as the observer’s height of eye is raised above sea level, his visible horizon ‘dips’ below the true horizon and so the altitude measured at E becomes greater than that measured at O.  Dip is the error caused by this difference and has to be subtracted from the reading.

Tables of corrections for dip are printed in the Nautical Almanac as shown in the extract below:


For example, if the height of eye is 4.6m. the correction will be 3’.8 (interpolate as necessary). 

Apparent Altitude is found by applying the index error and dip to the sextant altitude.


Sextant Altitude =      48o 15’.2

Index Error =                       +1’.3

Dip   =                                       -5’.3

Apparent Alt. =           48o  11’.2

Effectively, when measuring the altitude the Sun the stars, the Moon and the planets, index error and dip are the only corrections that the navigator has to apply manually.  However, there are a number of additional corrections which are incorporated in the altitude correction tables which must be applied in order to arrive at the true altitude.  The additional corrections are fully explained in ‘Astro Navigation Demystified’ but are briefly described below:

Semi Diameter.  In practice, the altitude that we measure is that of the lower limb; however, what we really need is the altitude of the Sun’s centre and so,we must add a correction for the value of its semi-diameter.

Parallax. The observer measures the altitude in relation to the visible horizon from his position on the Earth’s surface whereas the true altitude is measured from the Earth’s centre and so a correction called parallax must be added to allow for this.

Refraction.  When a ray of light from a celestial body passes through the Earth’s atmosphere, it becomes bent through refraction and causes the apparent altitude to be greater than the true altitude.  Since the sextant measures the apparent altitude, a correction for refraction must be applied to find the true altitude.  Refraction is at its greatest when the altitude is small (i.e. when the celestial body is near the horizon) and becomes less as the altitude increases

Additional correction for temperature and atmospheric pressure.  This may be needed if the temperature and pressure are greatly different to the standard conditions which are assumed to be 10oC, 1010mb.

True Altitude is found by applying the additional corrections for parallax, refraction, semi-diameter, temperature and atmospheric pressure which are incorporated in the altitude correction tables.

The Altitude correction tables will be explained in Unit 3 Part 2.

(Note. This topic is covered in greater depth in the book ‘Astro Navigation Demystified’).

Watch for unit 3 part 2


Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at

Astro Navigation Demystified at

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at

Astronomy for Astro Navigation at