# Declinations

You can define the positions of a planet or other point in several ways. In the drawing of your chart you will see the longitude, which is the position on the ecliptic. But planets are not always exactly positioned on the ecliptic but a bit above or underneath it. The difference is the latitude.

Instead of using longitude you can define a planetary position also in right ascension. That is the position on the heavenly equator. And in that case there is also a deviation which we call declination.

We do not use right ascension directly in astrology; it is mainly an aid for some calculations. But the declination has always been an important factor in the delineation. Think about parallel aspects, the use of declinations in archaeo-astronomy and the system defined by Kt Boehrer. By Tfr000 (talk) 15:34, 15 June 2012 (UTC) (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia CommonsIn the diagram you see the equator defined in green. The position as measured alongside the equator, starting at the point 0 degrees Aries, is the right ascension. You define the declination of the shown star by measuring the distance from the equator to that star alongside a circle that is perpendicular to the equator (an hour circle).
To calculate the value for the declination you need to know the longitude and the latitude and also Epsilon, the angle between equator and ecliptic. (See Oblique angle of the ecliptic).

A special situation occurs if the point for which you want to calculate the declination does not have any latitude. In that case you only need to know the longitude and Epsilon. This situation will occur for the Sun, the nodes and the cusps of the houses.

## The formula without latitude

If the position you want to calculate does not have latitude:

`sin D = sin E . sin L`

In the formula we use the following terms:

D for declination
E for the oblique angle of the ecliptic (Epsilon)
L for the longitude measured from 0 degees Aries

## The formula including latitude

`sin D = cos B . sin L . sin E + sin B . cos E`

This formula uses the same terms as the previous formula but also the term B for latitude.

## Example calculation without latitude

We use the following values:

```L: 10° 53' 04'' Scorpio

E: 23° 26′ 13.56586091''```

Convert to decimal degrees:

```L : 220.884444444444

E: 23.437101628```

Substitute in the formula:

```sin D = sin E . sin L

sind D = sin 23.437101628 . sin 220.884444444444```

Calculate sine:

`sin D = 0.397742095267 . -0.654535578646`

Simplify:

`sin D = -0.260336352473`

Calculate D:

`D = -15.09002104`

Convert to degrees. minutes and seconds:

`D = -15° 5' 24.08''`

## Example calculation including latitude

We use the following values:

```L: 15°08'30'' Sagittarius

E: 23° 26′ 13.56586091''

B: + 05°02'```

Convert to decimal degrees:

```L: 255.141666666667

E: 23.437101628

B: 5.0333333333333```

Substitute in the formula:

```sin D = cos B . sin L . sin E + sin B . cos E

sin D = cos 5.0333333333333 . sin 255.141666666667 . sin 23.437101628 + sin 5.0333333333333 . cos 23.437101628```

Calculate sine and cosine:

`sin D = 0.996143824351 . -0.966562816012 . 0.397742095267 + 0.0877352905478 . 0.917497261932`

Simplify:

```sin D = -0.382960240986 + 0.0804968888451

sin D = -0.30246335214```

Calculate D:

`D = -17.6056180014`

Convert to degrees. minutes and seconds:

`D = 17° 36' 20.22''`

## References

• Kampherbeek, Jan: Declinaties. In Spica jg. 2, nr. 2. Enschede, juni 1978. (Dutch)
• Meeus, Jean: Astronomical Algorithms. Second edition. Richmond, Virginia, 1998.
• Wikipedia: https://en.wikipedia.org/wiki/Declination