Local Space, Horizon and Declination Equivalents: Eight Views Explained

A point appearing at 90° on a wheel need not mean the same thing in every view. The value may come from a horizon direction, the celestial equator or a rule converting declination into longitude. Identify which quantity you are reading before comparing it with the source chart.

Beyond Normal and Heliocentric, Hermes lists eight coordinate/view options: five entries in the local-sky menu group and three declination equivalents. Sharing a menu group does not make them the same geometrical measurement: right ascension, for example, is not horizon azimuth.

Where does azimuth start, and what does altitude measure?

For north-origin azimuth, use north 0°, east 90°, south 180° and west 270°. The NASA/JPL Horizons AZ–EL definition uses this order. Altitude measures the angle above or below the horizon; it is a separate quantity.

The Swiss Ephemeris swe_azalt documentation measures azimuth from south towards west. Hermes converts it to a north origin by adding 180° and normalising. Check the zero direction before comparing values labelled “azimuth” in different tables.

For altitude, this path uses the call’s true-altitude field, rather than its refracted apparent-altitude field. The geographic height passed to this calculation is 0 metres. Match refraction and observer-height assumptions when comparing an actual observation; do not treat the view itself as a visibility forecast.

Two points can share an azimuth and have different altitudes. At the exact zenith, the horizontal bearing is undefined; a numerical azimuth there should not be read as a definite compass direction.

How do Local Space, Horizon and Azimuth–Altitude differ?

With A for north-origin azimuth, Hermes’s wheel angles are:

• Horizon: normalize(90° − A).
• Local Space and Azimuth–Altitude: normalize(270° − A).

normalize returns an angle from 0° inclusive to 360° exclusive. The two formulas give answers 180° apart for the same point. A change in the heading’s orientation does not imply that a different celestial body position has been calculated.

A wheel angle need not equal compass azimuth or source zodiacal longitude. Read the view’s directional reference even if an angle is displayed with a sign name.

Local Space and Azimuth–Altitude are separate menu entries, but Hermes supplies the same wheel angle for both and stores altitude separately.

These directions belong to a particular instant and location. Changing either changes the horizon calculation. A Local Space wheel is not an astrocartography map: a directional angle at one place is not automatically a planetary line or geographic longitude on a world map.

Why is right ascension different from zodiacal longitude?

Right ascension (RA) is measured eastwards along the celestial equator from the equinox. Declination (δ) measures angular distance north or south of that equator. The USNO astronomical glossary defines the two coordinates together.

RA may be expressed in hours: 24 hours = 360°, and 1 hour = 15°. For example, 6h30m RA = 97°30′. The hours here express an angle, rather than a birth time.

Hermes uses RA in degrees as its wheel angle. An RA value of 97°30′ does not give the planet an ecliptic longitude of 97°30′. The equator and ecliptic are different planes.

When comparing an external table, match the reference equator and equinox/epoch as well as the unit. The USNO geocentric data page, for example, defines its apparent positions against the true equator and equinox of date. That service definition is not a numerical acceptance test against Hermes.

How does the Prime Vertical projection work?

The prime vertical passes through the east and west horizon points, zenith and nadir. The Hermes Mundoscope, Prime Vertical calculation uses a point’s eastward and upward components. With north-origin azimuth A and altitude h:

east = cos(h) × sin(A)
up = sin(h)
wheel angle = normalize(atan 2(up, east))

Use consistent angular units for the trigonometric operations and convert the atan 2 result into degrees. This projection references east at 0°, zenith at 90°, west at 180° and nadir at 270°.

For an example direction due east and 30° above the horizon, A = 90° and h = 30°. Its eastward component is cos(30°), its upward component sin(30°), and its result 30°. Its Horizon wheel angle is 0°. One refers to an azimuth axis; the other uses an east–up projection.

At exactly north or south on the horizon, both projection components vanish and the prime-vertical angle is undefined. A programming language returning a number for a zero vector does not give that number a physical direction.

Why can declination yield two candidate longitudes?

Longitude Equivalent derives a position from declination. It does not simply rename a planet’s source longitude.

For a point with zero ecliptic latitude, sin(δ) = sin(ε) × sin(L), where ε is the obliquity of the ecliptic and L the equivalent longitude. When |δ| ≤ ε, there are generally two longitudes with that declination: normalize(a) and normalize(180° − a), where a = arcsin(sin(δ)/sin(ε)).

For arithmetic only, choose ε = 23.5° and δ = +10°. The candidates are approximately 25.82° and 154.18°. These are not planetary results for a specific date; 23.5° is not proposed as a fixed obliquity for all dates.

Hermes first looks for a candidate in the same 90° quadrant as the source longitude. If neither qualifies, it chooses the closer candidate by short circular distance. Here a source longitude of 40° selects 25.82°, while 140° selects 154.18°. Recording δ alone may therefore be insufficient to reproduce the branch choice.

Declinations beyond the ecliptic limit need another distinction. For |δ| > ε, no point on the ecliptic has the same declination. Hermes reflects the magnitude at the obliquity limit, repeating if necessary, before calculating the equivalent. For ε = 23.5° and δ = +30°, the magnitude used becomes 17°. The result does not preserve the original +30° declination on the ecliptic.

Record the original δ, the ε used, source longitude and selected equivalent together. Keep this boundary rule distinct from an observed measurement.

Is equivalent-longitude antiscia the same as source-longitude antiscia?

The reflection formula is similar, but its input differs:

In the example above, let source λ = 40° and selected L ≈ 25.82°. Equivalent-longitude antiscia gives 154.18°, and contra-antiscia 334.18°. Reflecting the source longitude directly gives 140° instead.

The shared word “antiscia” therefore does not establish a shared starting quantity. When comparing the three equivalent modes, first check the base L used, then check that the two reflected results are opposite each other.

In what order should you compare these views in Hermes?

Use the proposed synthetic data 20 March 2000, 12:00:00 UTC, 41° north, 29° east; Gregorian calendar. Convert the time appropriately if the form expects local time. Use this as an exercise and record your own calculated result.

1. Record the source chart. Begin with the tropical zodiac, Placidus, Normal cusp setting, Normal coordinates and Normal zodiac transformation. Take one planet’s longitude, RA and declination.
2. Try the three horizon options. At the same time and place, record north-origin azimuth, altitude and wheel angle separately. Check the 180° difference between Horizon and Local Space, rather than reading it as an altitude change.
3. Compare the RA view. Convert the value to the external table’s unit. Do not read 6h30m as 6.30°.
4. Inspect the Mundoscope. Distinguish its wheel angle from azimuth; record altitude and projection axes too. Treat directions close to undefined cases separately.
5. Compare the three declination equivalents. Record δ, ε, source longitude and selected L. Note the boundary reflection separately for declinations outside the limit.
6. Separate time and location trials. First keep the place fixed and change the instant; then keep UTC fixed and change the place. This lets you track differences arising from the horizon reference.

The calculation produces a flag requesting hidden house numbers and a projection note for alternative views. Return to source zodiacal longitude for classical house, rulership and dignity readings. Sign-like labels on another projection do not make it the same measurement.

When an alternative coordinate view is requested with a sidereal ayanamsha in this path, the sidereal shift is not applied and a settings warning is produced. Zodiac transformations such as D12 are likewise applied only in the Normal geocentric longitude path. Leave additional transformations off for your first trial.

Keep the full view code, instant/UTC/location, source longitude, RA unit/reference, δ, ε, azimuth zero and increasing direction, true/apparent altitude distinction, result and program version in your archive.

For saving settings and distinguishing them from new-chart defaults, see the Hermes Chart Settings guide. The most useful first note says which angle the number measures.