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Naut. Almanac    


Celestial Navigation





Dip of horizon

We know from physics that a ray of light is bent (refraction) when passing from a denser to a rarer medium and vice versa. On the earth’s surface the atmosphere, which is present, is made up of several layers of varying densities, as such a ray of light gets bent due to the above phenomenon. If the earth’s surface were flat, visible and sensible horizon would be identical, however the visible horizon appears several arc minutes below the sensible horizon, which is the result of two opposing effects:

  1. The curvature of the earth’s surface and
  2. The atmospheric refraction.

Atmospheric refraction thus bends light rays passing along the earth’s surface toward the earth, all points on the horizon appear to be elevated, giving rise to a false horizon, and this is termed VISIBLE HORIZON.

The sensible horizon is the actual horizon that the observer would see if the atmosphere was not present or the atmosphere density was uniform as well if the earth were flat and not round.

Thus the visible horizon is some arc minutes below the sensible horizon.


The altitude of the sensible horizon relative to the visible horizon is called dip and is a function of the height of eye,

HE, the vertical distance of the observer’s eye from the earth’s surface:

Dip (in minutes) = 1.76√Height of Eye (in metres)

= 0.97√Height of Eye (in feet)

The above includes the effects of the curvature of the earth’s surface and atmospheric refraction.

If a sextant angle is taken using an artificial horizon then DIP does NOT have to be applied, since the artificial horizon itself is the sensible horizon.

The altitude obtained after applying corrections for index error and dip is also referred to as apparent altitude.

More on Refraction

A ray of light arriving from a heavenly body also is refracted when passing through the atmosphere. But the observer sees the star at a position and sees no bending of the light, the position of the star however as observed by the observer and the actual position differ; the star appears higher in the sky due to refraction.


Atmospheric standard refraction, R0, is 0’ at 90° altitude and increases progressively to approx. 34’ as the apparent altitude approaches 0°:

‘Dip’, ‘refraction’, ‘semi‑diameter’ and ‘parallax’, and their causes

Calculations of celestial navigation refer to the altitude with respect to the earth’s center and the celestial horizon.

But when taking observations the observer is on the surface of the earth.

Parallax in altitude, is the difference in the in the altitude as measured with respect to the sensible horizon and that with the rational horizon. For distant objects it is not so significant since the distance is huge and the angular difference is not much.

This parallax is of importance as a body is closer to the earth like the Moon and the Sun, and to some extent for the planets, it becomes progressively less for distant objects.


It decreases with growing distance between object and earth and is too small to be measured when observing stars. Since the height of eye is several magnitudes smaller than the radius of the earth, the observed parallax refers to the sensible.

When observing sun or moon with a sextant, it is not possible to locate the center of the body with sufficient accuracy. It is therefore common practice to measure the altitude of the upper or lower limb of the body and add or subtract the apparent semi diameter, SD, the angular distance of the respective limb from the center.

The geocentric semi diameters of sun and moon are given on the daily pages of the Nautical Almanac

The SD of the sun is given once for every 3 days – November 3, 4 5 whereas the SD of the Moon is given for each individual day. In this case for all three days the SD is the same.