# Proper motion (astronomy)

It shows the relationship between proper motion and the heliocentric speed components radial speed and tangential speed of an object.
If the object is at a distance d from the sun and moves transversely to the sun's line of sight at a tangential velocity v t , the angular velocity is μ = v t / d .

As a proper motion is referred to in the astronomy of spatial movements on celestial bodies based, slow change in position on the imaginary celestial sphere . In astrometry it is given in two spherical components (north and east) and is usually less than 1 per year for objects outside the solar system . Together with the radial velocity it gives the spatial movement of the object.

In contrast to the annual parallax, there is a progressive change in the star locations during proper motion .

The term peculiar movement (from the Latin peculiaris = own) is rarely used for proper movement , but it is misleading because it can be confused with the peculiar speed , which has a completely different meaning.

## Proper movement and speed

The proper movement indicates an angular velocity . The speed component perpendicular to the connection between earth and star (tangential speed) is calculated from this by multiplying it by the distance. For example, a proper movement of one arc second per year at a distance of one parsec corresponds to a speed of one  AU per year or about 4.75 km / s. For the relative speed to the sun, the (heliocentric) radial speed must also be taken into account.

## Magnitude

The star with the highest self-motion measured so far is Barnard's Arrow Star , which moves at 10.34 "per year and is only six  light-years away from Earth. The Kapteyns star moves second fastest on the imaginary celestial sphere, although its actual tangential velocity is higher because of its greater distance.

The Triangle Nebula , a neighboring galaxy, is one of the few extra-galactic objects whose proper motion could be measured. This amounts to around 50 micro-arc seconds per year.

## Directional information

In order to indicate the apparent direction of the proper motion on the celestial sphere in addition to the angular difference per year , two systems are used:

• In addition to the total own movement per year, a position angle is also noted as a deviation from the north direction. North is 0 °, east 90 °, south 180 ° and west 270 °. For the example of Barnard's arrow star, the position angle of 355.8 ° is specified in addition to μ = 10.34 ″ / a.
• The total natural movement per year is broken down into two components μ (RA) ( right ascension ) and μ (Dec) ( declination ). For Barnard's Arrow Star, the values ​​are:
μ (RA) = −0.757 "/ a
µ (Dec) = 10.31 "/ a.

## Discovery story

Self motions were only recognized by James Bradley in 1728 , because they take place very slowly because of the great distances between the stars; up until then, fixed stars were generally spoken of. They are measured in arc seconds per year , unit ″ / a, and usually have the symbol  μ. In 1777 Christian Mayer proposed a method to study proper motion using stars that are close together. In his further observations in 1779, he distinguished between possible physical and only optical double stars .

In 1783, Wilhelm Herschel examined the proper motion of 14 stars and found that eleven stars move to a common point near the star Lambda Herculis . From this he concluded that the solar system was in absolute motion. He ascribed a real movement of their own to the three stars whose movement was not aligned with this point. This investigation was repeated by Argelander in 1838–1840 using almost 600 stars. Argelander's investigation confirmed Herschel's result. Thus, starting in 1840, it was possible to trace back the proper movement to an absolute movement of the solar system and a real movement of the fixed stars.

## Other movements on the celestial sphere

A distinction must be made between apparent movements on the celestial sphere that are caused in other ways:

• The yearly movement of the earth around the sun causes a parallax, i. That is, nearby stars shift slightly against the background of much more distant stars due to the different viewing angle.
• The fluctuations in the earth's axis , essentially precession and nutation , lead to a uniform displacement of the entire celestial sphere.
• The finite speed of light , together with the earth's movement, leads to aberration (deflection) of starlight, as the earth moves under the incident light.

## Individual evidence

1. ^ Andreas Brunthaler, Mark J. Reid, Heino Falcke, Lincoln J. Greenhill, Christian Henkel ,: The Geometric Distance and Proper Motion of the Triangulum Galaxy (M33) . In: Science . 307, No. 5714, 2005, pp. 1440-1443. doi : 10.1126 / science.1108342 .

## literature

• Christian Mayer, Thorough defense of new observations of fixed star satellites which took place in Mannheim on the electoral prince. Observatory were discovered, Mannheim 1778