PHY115: Professional Skills in Physics and Astronomy

Positional Astronomy: Session 2

We have previously discussed the equatorial co-ordinate system (RA and Dec). One of the great advantages of the equatorial system is that the RA and Dec of a star do not change with time, at least over short timescales. This makes the equatorial co-ordinate system excellent for keeping star catalogues.

Over longer timescales however, the RA and Dec of a star does change, due to a combination of effects. We'll look at them in more detail here.


The Earth's spin axis is not fixed in space, but instead precesses slowly due to the gravitational pulls of the Sun and Moon on the non-spherical Earth. The phenomenon is completely analogous to the precession of a child's spinning top. The Earth's precession period is 25,770 years and precession causes the north celestial pole (NCP) to make a slow circle around the heavens. Although Polaris is currently less than 1° away from the NCP, in 13,000 years it will be nearly 47° away. The same effect causes the celestial equator to move. As a result, the first point of Aries is moving westwards along the ecliptic by around 50"/year. In fact, the first point of Aries is currently in the constellation of Pisces! This effect is known as precession of the equinoxes. It means that the RA and Dec of stars are slowly changing in time.

To get around this, star catalogues specify the equinox (or reference date) when listing the RA and Dec of a star. For an example, and equinox of 2000.0, tells you that the RA and Dec of a star are given relative to the position of the NCP and first point of Aries at noon in Greenwich on January 1st 2000. Although precession is a slow phenomenon, we can measure the positions of stars to such accuracy that all positional measurements must be corrected for precession. Approximate expressions for the changes in the RA (α) and Dec (δ) since equinox 2000.0 are

Δα = M + N sinα tanδ
Δδ = N cosα

where M and N are given by

M = 1°.2812323 T + 0°.0003879 T2 + 0°.0000101 T3
N = 0°.5567530 T - 0°.0001185 T2 + 0°.0000116 T3

and T is defined as

T = (t-2000.0)/100

where t is the current date, specified in fractions of a year.

Proper Motion

Precession will change the RA and Dec of a star even it is not moving through space. However, stars do indeed move, and we cannot neglect stellar motion over moderate timescales. A star's motion through space is called its proper motion, and given the symbol μ. For a star with significant proper motion we must specify, in addition to the RA, Dec and equinox, the star's proper motion, and when the position was measured (known as the epoch). If no epoch is given, it is assumed to be the same as the equinox for an entry. The figure below shows a typical set of entries in a star catalogue.

Entries from a typical star catalogue
Beyond Earth-defined coordinates (optional)

The equatorial co-ordinate system, as discussed so far, relies on us knowing where on the sky the NCP and first point of Aries actually are at any given time. As long as these are defined by the rotation axis of the Earth, we will be reliant on our models of the Earth's rotation and precession to know where the NCP actually is, at any given time.

Therefore, in modern astronomy, we have defined a set of reference objects, which have set right ascensions and declinations. These reference objects and their co-ordinates define the celestial co-ordinate system. This co-ordinate system is called the International Celestial Reference System (ICRS), and is defined by the positions of a specific set of extragalactic objects, which are assumed to have no proper motions. Modern positions are usually quoted in the ICRS system, but the ICRS axes are consistent to better than 0.1 arcseconds with the equinox of 2000.0 defined by the dynamics of the Earth.

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