# Proper motion

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The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system.[1] It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree.[2] This contrasts with radial velocity, which is the time rate of change in distance toward or away from the viewer, usually measured by Doppler shift of received radiation. The proper motion is not entirely "proper" (that is, intrinsic to the star) because it includes a component due to the motion of the solar system itself.[3]

## Contents

### Introduction

Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major, for example, looks nearly the same now as it did hundreds of years ago. However, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent motion.

This motion is caused by the true movement of the stars relative to the Sun and solar system through space. The Sun travels in a nearly circular orbit (the solar circle) about the center of the Milky Way at a speed of about 220 km/s at a radius of 8 ± 0.65 kpc from the center,[4][5] which can be taken as the rate of rotation of the Milky Way itself at this radius.[6][7]

The proper motion is measured by two quantities: the position angle and the proper motion itself. The first quantity indicates the direction of the proper motion on the celestial sphere (with 0 degrees meaning the motion is due north, 90 degrees meaning the motion is due east, and so on), and the second quantity gives the motion's magnitude, in seconds of arc per year.

Proper motion may also be given by the angular changes per year in the right ascension (μα) and declination (μδ). On the celestial sphere, positions are located by latitude and longitude. The coordinate δ corresponds to latitude. The coordinate α corresponds to longitude measured from the vernal equinox V, the point on the sky where the Sun crosses the celestial equator on near March 21.[3]