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Celestial navigation

Ephemeris calculation – GHA and declination for any moment

Every celestial position line needs the Greenwich hour angle and the declination of the body. NauticTools2 calculates them for the sun, moon, Venus, Mars, Jupiter, Saturn and 83 stars – to the second, for any date, without looking up and interpolating in the Nautical Almanac.

• GHA
• Declination
• SHA and GHA Aries
• HP and semi-diameter
• Local hour angle
• 83 stars

What is calculated?

• GHA (Greenwich hour angle): the angle from the Greenwich meridian to the body, measured westward from 0° to 360° – for every body.
• Declination: the body's “latitude” in the sky, ±90°.
• SHA and GHA Aries: for stars, the two building blocks of the GHA.
• Semi-diameter (sun) and horizontal parallax HP (moon, Venus, Mars): corrections for the sextant altitude.
• Sun's Greenwich transit: the time the sun crosses the Greenwich meridian.
• Local hour angle: optionally included if you enter your own longitude.

When do you need it?

• Working a position line: GHA and declination are the inputs for computed altitude and azimuth – and so for every celestial position line.
• Replacing or checking the almanac: No more page-turning and interpolating – or check your own almanac working.
• Solving older exercises: Many exercises date from years for which you no longer have an almanac. The calculation works for any date.

Formulas and working

1. Time

   Date and time in UT1, to the second – the sun's GHA grows by 15′ per minute.

2. Sun, moon and planets

   GHA and declination come from a modern astronomy library that runs offline – reliable even far outside 1950 to 2050.

3. Stars

   SHA and declination are brought from epoch 2000.0 to the date (precession, nutation, aberration). The GHA of Aries comes from sidereal time; the sum is the GHA of the star.

4. Local hour angle

   LHA = GHA + λ – add east longitude, subtract west longitude.

Example

Things to watch out for

• To the second: One second of time error is 0.25′ of GHA – a quarter of a mile in the position line. Take the time of the sight carefully.
• UT1 and UTC: The calculation uses UT1, the Earth rotation time. It differs from UTC by at most 0.9 seconds – negligible for navigation.
• Sign of longitude: For the local hour angle add east longitude and subtract west longitude; reduce results above 360° by 360°.
• Small differences from the almanac: The printed almanac is rounded to 0.1′ and interpolated linearly, so differences of one or two tenths of a minute are normal.

How it works in NauticTools2

1. Enter the time

   Date and time (UT1); the current time is filled in.

2. Choose the body

   Sun, moon, one of the planets or a star from the list. The list starts with the 57 navigational stars of the Nautical Almanac with their numbers, then Polaris, then further bright stars in alphabetical order.

3. Local hour angle

   Optionally tick “Calculate local hour angle t” and enter your longitude.

4. Calculate, save, print

   The values appear in the result; inputs can be saved and loaded, the result printed as a record or saved as a PDF.

Frequently asked questions

What is the Greenwich hour angle?

The angle between the Greenwich meridian and the body, measured westward. Together with the declination it fixes the point on Earth directly beneath the body – its geographical position.

Why do you get SHA and GHA Aries for stars?

The stars hardly move relative to each other. So the almanac gives each star only its sidereal hour angle from Aries, plus the GHA of Aries for every hour. Their sum is the GHA of the star – NauticTools2 shows both parts.

Does the tool replace the Nautical Almanac?

It gives the same values for any moment and any year. For exams and as a backup on board, the printed almanac is still worth having.

Related tools

• Fix from 2 or 3 altitudes – from GHA, declination and sextant altitudes to the fix
• Star chart – which stars are up right now
• Rising and setting times – twilight times for star sights