Since the declination gives us the “latitude” of the heavenly body we must now find it’s “longitude”. We do this by measuring the angle between the celestial meridian passing through the body and that running through the observer’s position. The hour angle is defined as “the angle between the meridian running through the observer’s position and that passing through the celestial body”. It is always measured westwards from the observer’s meridian (from 0° to 360°) at the celestial pole. Since the earth rotates, the hour angle of the heavenly body, the position of which is fixed in the celestial sphere, will increase from 0° when the body is on the observer’s meridian to 360° when it returns to the observer’s meridian. It increases steadily throughout the day.
Hour angle.
ON is the observer’s meridian while XN is the meridian passing through the body. Angle ONX is the hour angle
Greenwich Hour Angle (GHA).
When the observer is on the Greenwich meridian, the hour angle of a heavenly body is known as the GHA. The GHA is tabulated for every hour of GMT in the nautical almanac. For the value between these times, the interpolation tables at the back of the almanac must be used. If you substitute “G’” for “O” in the above sketch then angle GNX is the GHA.
Local Hour Angle (LHA).
The hour angle measured from the observer’s meridian is known as the LHA and can be obtained by looking up the GHA for the particular time (remember that the GHA is tabulated in GMT and that if LMT is used or stated, it must first be converted to GMT) and by applying the longitude to produce the LHA.
Local hour angle (LHA).
GN is the meridian passing through Greenwich, ON is the observer’s meridian (to the west of Greenwich), O2N is the observer’s meridian (to the east of Greenwich) and XN is the meridian passing through the body. Angle GNX is the GHA, angle GNO is the observer’s longitude and angles ONXand O2NX are the LHA’s.
(a) In the case of the observer being to the west of Greenwich (at O):
GHA = GNX (measured clockwise)
Long = GNO (measured clockwise)
LHA = [ONX (measured clockwise)]
= GNX – GNO
= GHA – long
(If [GHA – long] results in a negative value then 360° must be added to the result).
(b) In the case of the observer being to the east of Greenwich (at O2):
GHA = GNX (measured clockwise)
Long = GNO2(measuredanti-clockwise)
LHA = O2NX (measured clockwise)
= GNX + GNO
= GHA + long
(If the sum is greater than 360, then 360° must be deducted from the result).
The positions of the meridians relative to one another can cause confusion so as a standing rule, the following is to be adhered to in the circumstances indicated:
(a) When the longitude is west, you will always subtract it from the GHA. If you end up with a negative result, add 360°.
(b) When the longitude is east, you will always add it to the GHA. If the result is greater than 360°, subtract 360°.