Ecliptic coordinates

**{Note:** If your browser does not distinguish
between "a,b" and "a,b" (the Greek letters "*alpha, beta*")
then I am afraid you will not be able to make much sense of the
equations on this page.}

All the objects considered so far have been "fixed
stars",

which keep almost constant values of Right Ascension
and declination.

But bodies *within* the Solar System change
their celestial positions.

The most important one to consider is the Sun.

The
Sun's *declination* can be found by measuring its altitude when
it's on the meridian (at midday).

The Sun's *Right Ascension*
can be found by measuring the Local Sidereal Time of meridian
transit.

We find that the Sun's RA increases by approximately 4
minutes a day,

and its declination varies between +23°26' and
-23°26'.

This path apparently followed by Sun is called the
**ecliptic**.

The reason the Sun behaves this way is that the
Earth's axis is tilted to its orbital plane.

The angle of tilt is
+23°26', which is called the **obliquity of the ecliptic **(symbol
e
).

Any two great circles intersect at two **nodes**.

The node where the Sun crosses the equator *from south to north*
(the **ascending** node)

is called the **vernal (or spring)
equinox**.

The Sun passes through this point around March 21st
each year.

This is the point from which R.A. is measured, so here
RA = 0h.

At RA = 12h, the **descending** node is called the
**autumnal equinox;t**he Sun
passes through this point around September 23rd each year.

At both these points, the Sun is on the equator,

and spends 12 hours above horizon and 12 hours below.

("Equinox" means "equal night": night equal to day.)

*The symbols used for the spring and autumn
equinoxes,
and
,are the astrological symbols for Aries and Libra.*

The most northerly point of the ecliptic is called
(in the northern hemisphere)

the **Summer Solstice** (RA =
6h):

the Sun passes through this point around June 21st each
year.

The most southerly point is the **Winter Solstice** (RA =
18h);

the Sun passes through this point around December 21st each
year.

At the northern Summer Solstice, the northern hemisphere of
Earth is tipped towards Sun,

giving longer hours of daylight and
warmer weather

(despite the fact that Earth's slightly elliptical
orbit takes it *furthest *from the Sun in July!)

Thus the Sun's motion is simple when referred to the
ecliptic;

also the Moon and the planets move near to the
ecliptic.

So the **ecliptic system** is sometimes more useful
than the equatorial system for solar-system objects.

**Exercise:**

The Moon’s orbit is tilted
at 5°8' to the ecliptic.

What is the lowest latitude from
which the Moon may never set (the Moon’s “arctic circle”)?

Would the Moon *always *be
circumpolar, at this latitude?

Click here for the answer.

In
the ecliptic system of coordinates,

the *fundamental great
circle *is the **ecliptic**.

The *zero-point* is still
the vernal equinox.

Take K as the northern pole of the ecliptic,
K' as the southern one.

To fix the ecliptic coordinates of an object X on the
celestial sphere,

draw the great circle from K to K' through X.

The **ecliptic **(or **celestial**)** latitude**
of X (symbol b)

is the angular distance from the ecliptic to X,

measured from
-90° at K' to +90° at K.

Any point on the ecliptic has
ecliptic latitude 0°.

The **ecliptic **(or** celestial**)**
longitude** of X (symbol l)

is the angular distance along the ecliptic

from the vernal
equinox to the great circle through X.

It is measured eastwards
(like R.A.), but in degrees, 0°-360°.

To convert between ecliptic and equatorial coordinates, use the spherical triangle KPX.

**Exercise:**

Show that, for any object on
the ecliptic,

tan(d) = sin(a)
tan(e),

where (a,d)
are the object's Right Ascension and declination,

and e
is the obliquity of the ecliptic.

Click here for the answer.

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Galactic coordinates

Next section: The relation between ecliptic
and equatorial coordinates

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