Greenwich Hour Angle and Nautical Astronomy

On this page, Greenwich Hour Angle and Nautical Astronomy, we emphasize the significance of understanding Greenwich Hour Angle, a crucial factor in comprehending and calculating the Line of Position (LOP), which constitutes the main objective of this site.

Greenwich Hour Angle : the solar coordinate system involves two key components: Solar Declination (D) and Solar Greenwich Hour Angle (GHA).

Our mathematical formulas, which resolve the spherical triangle, utilize these data, obtained from the Nautical Almanac’s daily pages.

Greenwich Hour Angle and Nautical Astronomy, daily page of the nautical almanac
daily page of the nautical almanac

Boat and sunshine. author image: marneejill

Greenwich Hour Angle and Nautical Astronomy: point PG

Greenwich hour angle image point PG
point PG (Geographical position, also called GP.)

The thread stretching between the sun center and the earth center strikes the earth’s crust at point PG.

Greenwich Hour Angle and Nautical Astronomy, image observed altitude circle
Greenwich Hour Angle and Nautical Astronomy, image GHA = longitude and Declination = latitude

GHA and Declination are simply the coordinates on earth for point PG.

Indeed, it can be concluded that D is equivalent to the latitude and AHvo is equivalent to the longitude of the point PG at that moment

In fact, the declination of the sun (latitude) can never exceed 23° 44′ N or 23° 44′ S.

The point GP is probably too far out and not usable for finding your position on a nautical chart.

However, our mathematical formulas (resolution of the spherical triangle) use the two data points: GHA (Greenwich Hour Angle) and D (Declination) of this point GP.

Greenwich Hour Angle and Nautical Astronomy, image spherical triangle
spherical triangle

Rocky beach at Port Nolloth, Northern Cape, South Africa. Author image: South African Tourisme

Greenwich Hour Angle and Nautical Astronomy: difference between hour angle and longitude

There is a subtle difference in the expression between longitude (G) and GHA but for the same results.

Indeed, the hour angle progresses from 0° to 360° in a westward direction.

Alternatively, when referring to the coordinates on the Earth’s surface, we utilize longitude East (ranging from 0° to 180°) and longitude West (ranging from 0° to 180°).

Greenwich hour angle image difference between GHA and longitude
There is a subtle difference in the expression between longitude (G) and GHA
Greenwich Hour Angle and Nautical Astronomy, image difference between GHA and longitude coordinates
difference in the expression between longitude (G) and GHA

In fact, the manipulation that needs to be performed is handled by the formulas.


A Inuit boat in the fog and in the sea of ice. Author image: patano

Greenwich Hour Angle and Nautical Astronomy:

The nautical almanac
Greenwich Hour Angle and Nautical Astronomy, text importance of the Declination and GHA

While, the nautical almanac gives us for each day and each whole UT hour this Declination and GHA.

Therefore, it is up to us to interpolate to have the Declination and GHA at the exact UT time of the observation

That is to say, to the nearest second !

How to calculate to the nearest second ?