Ecliptic coordinates

**{Note:** If your browser does not distinguish between
"a,b" and "α, β" (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 ε).

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 β)

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 λ)

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(δ) = sin(α) tan(ε),

where (α, δ) are the object's Right Ascension and declination,

and ε is the obliquity of the ecliptic.

Click here for the answer.