Types of aberration

Types of aberration[edit]

There are a number of types of aberration, caused by the differing components of the Earth's and observed object's motion:

• Annual aberration is due to the orbital revolution of the Earth around the Sun.
• Planetary aberration is the combination of aberration and light-time correction.
• Diurnal aberration is due to the rotation of the Earth about its own axis.
• Secular aberration is due to the motion of the Sun and Solar System relative to other stars in our Galaxy.

Annual aberration[edit]

Stars at the ecliptic poles appear to move in circles, stars exactly in the ecliptic plane move in lines, and stars at intermediate angles move in ellipses. Shown here are the apparent motions of stars with the ecliptic latitudes corresponding to these cases, and with ecliptic longitude of 270°.

The direction of aberration of a star at the northern ecliptic pole differs at different times of the year

See also: Stellar parallax

Annual aberration is caused by the motion of an observer on Earth as the planet revolves around the Sun. Due to orbital eccentricity, the orbital velocity  of Earth (in the Sun's rest frame) varies periodically during the year as the planet traverses its elliptic orbit and consequently the aberration also varies periodically, typically causing stars to appear to move in small ellipses.

Approximating Earth's orbit as circular, the maximum displacement of a star due to annual aberration is known as the constant of aberration, conventionally represented by . It may be calculated using the relation  substituting the Earth's average speed in the Sun's frame for  and the speed of light . Its accepted value is 20.49552  arcseconds (at J2000).^[8]

Assuming a circular orbit, annual aberration causes stars exactly on the ecliptic (the plane of Earth's orbit) to appear to move back and forth along a straight line, varying by  on either side of their position in the Sun's frame. A star that is precisely at one of the ecliptic poles (at 90° from the ecliptic plane) will appear to move in a circle of radius  about its true position, and stars at intermediate ecliptic latitudes will appear to move along a small ellipse.

For illustration, consider a star at the northern ecliptic pole viewed by an observer at a point on the Arctic Circle. Such an observer will see the star transit at the zenith, once every day (strictly speaking sidereal day). At the time of the March equinox, Earth's orbit carries the observer in a southwards direction, and the star's apparent declination is therefore displaced to the south by an angle of . On the September equinox, the star's position is displaced to the north by an equal and opposite amount. On either solstice, the displacement in declination is 0. Conversely, the amount of displacement in right ascension is 0 on either equinox and at maximum on either solstice.

In actuality, Earth's orbit is slightly elliptic rather than circular, and its speed varies somewhat over the course of its orbit, which means the description above is only approximate. Aberration is more accurately calculated using Earth's instantaneous velocity relative to the barycenter of the Solar System.^[8]

Note that the displacement due to aberration is orthogonal to any displacement due to parallax. If parallax were detectable, the maximum displacement to the south would occur in December, and the maximum displacement to the north in June. It is this apparently anomalous motion that so mystified early astronomers.

Solar annual aberration[edit]

A special case of annual aberration is the nearly constant deflection of the Sun from its position in the Sun's rest frame by  towards the west (as viewed from Earth), opposite to the apparent motion of the Sun along the ecliptic (which is from west to east, as seen from Earth). The deflection thus makes the Sun appear to be behind (or retarded) from its rest-frame position on the ecliptic by a position or angle .

This deflection may equivalently be described as a light-time effect due to motion of the Earth during the 8.3 minutes that it takes light to travel from the Sun to Earth. This is possible since the transit time of sunlight is short relative to the orbital period of the Earth, so the Earth's frame may be approximated as inertial. In the Earth's frame, the Sun moves by a distance  in the time it takes light to reach Earth,  for the orbit of radius . This gives an angular correction  which can be solved to give , the same as the aberrational correction.

Planetary aberration[edit]

See also: Light-time correction

Planetary aberration is the combination of the aberration of light (due to Earth's velocity) and light-time correction (due to the object's motion and distance), as calculated in the rest frame of the Solar System. Both are determined at the instant when the moving object's light reaches the moving observer on Earth. It is so called because it is usually applied to planets and other objects in the Solar System whose motion and distance are accurately known.

Diurnal aberration[edit]

Diurnal aberration is caused by the velocity of the observer on the surface of the rotating Earth. It is therefore dependent not only on the time of the observation, but also the latitudeand longitude of the observer. Its effect is much smaller than that of annual aberration, and is only 0.32 arcseconds in the case of an observer at the Equator, where the rotational velocity is greatest.^[9]

Secular aberration[edit]

The Sun and Solar System are revolving around the center of the Galaxy. Aberration due to this motion is known as secular aberration and affects the apparent positions of distant stars and extragalactic objects. However, since the galactic year is about 230 million years, the aberration varies very slowly and this change is extremely difficult to observe. Therefore, secular aberration is usually ignored when considering the positions of stars. In other words, star maps show the observed apparent positions of the stars, not their calculated true positions after accounting for secular aberration.

For stars significantly less than 230 million light years away, the Solar System may be approximated as an inertial frame and so the effect of secular aberration is equivalent to a light-time correction. This includes stars in the Milky Way, since the Milky Way is about 100,000 light years in diameter. For these stars the true position of the star is then easily computed from its proper motion and its distance.

Secular aberration is typically a small number of arcminutes, for example the stationary star Groombridge 1830 is displaced by approximately 3 arcminutes,^[9] due to secular aberration. This is roughly 8 times the effect of annual aberration, as one would expect since the velocity of the Solar System relative to the center of the Galaxy is about 8 times the velocity of the Earth relative to the Sun.