**Point Z represents the zenith of the observer’s position. **

**Point X represents the position of the celestial body and this point, if projected onto the Earth’s surface, would correspond to the Geographical position of the body.**

**P and P1 are the north and south poles respectively.**

** ****The Zenith Distance****.** The zenith distance is the angular distance ZX that is subtended by the angle XOZ and is measured along the vertical circle that passes through the celestial body.

**Relationship Between Zenith Distance And The Nautical Mile**. An angle of 1 minute at the earth’s centre will subtend an arc of length 1 n.m on the earth’s surface. Therefore if the angle XOZ is 30^{o} (the arc ZX) will be equal to 30 x 60 = 1800 arc minutes at the earth’s surface and so the zenith distance will be equal to 1800 nautical miles.

** ****The Altitude.**** **Altitude is the angle AOX, that is the angle from the celestial horizon to the celestial body and is measured along the same vertical circle as the zenith distance.

**Relationship between Altitude and Zenith Distance **Since the celestial meridian is another vertical circle and is therefore, also perpendicular to the celestial horizon, it follows that angle AOZ is a right angle and angles AOX and XOZ are complementary angles. From this we can deduce that:

**Zenith Distance = 90 ^{o} – Altitude**

and **Altitude = 90 ^{o} – Zenith Distance**

**Azimuth. **The angle PZX is the azimuth of the celestial body and is the angular distance between the observer’s celestial meridian and the direction of the position of the body.

** ****The Role Of Altitude, Azimuth And Zenith Distance In Astro Navigation. **It can be seen that by measuring the altitude of a celestial body, we are able to easily calculate the zenith distance which will give us the distance in nautical miles from the observer’s position to the geographical position of the body. The azimuth will give us the direction of the GP from the observer’s position. This explains why measuring the altitude and azimuth are the first steps in determining our position in astro navigation.

(A thorough treatment of this topic can be found in the book Astro Navigation Demystified).

**Where to buy books of the Astro Navigation Demystified series:**

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk