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Proper motion

Not to be confused with proper velocity or stellar parallax.
Relation between proper motion and velocity components of an object.
A year ago the object was d units of distance from the Sun, and its light moved in a year by angle μ radian/s. If there has been no distortion by gravitational lensing or otherwise then μ = where is the distance (usually expressed as annual velocity) transverse (tangential or perpendicular) to line of sight from the Sun. The angle is shaded light blue from the Sun to the object's start point and its year later position as if it had no radial velocity.
In this diagram the radial velocity happens to be one of the Sun and object parting, so is positive.

Proper motion is the astrometric measure of changes in the apparent places of stars or other celestial objects as they move relative to the center of mass of the Solar System. It is measured relative to the distant stars or a stable reference such as the International Celestial Reference Frame (ICRF).[1] Patterns in proper motion reveal larger structures like stellar streams, the general rotation of the Milky Way disk, and the random motions of stars in the Galactic halo.[2]

The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μα) and of declination (μδ). Their combined value is computed as the total proper motion (μ).[3][4] It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year.

Knowledge of the proper motion, distance, and radial velocity allows calculations of an object's motion from the Solar System's frame of reference and its motion from the galactic frame of reference – that is motion in respect to the Sun, and by coordinate transformation, that in respect to the Milky Way.[5]

  1. ^ Theo Koupelis; Karl F. Kuhn (2007). In Quest of the Universe. Jones & Bartlett Publishers. p. 369. ISBN 978-0-7637-4387-1.
  2. ^ Leeuwen, F. van (2007-11-01). "Validation of the new Hipparcos reduction". Astronomy & Astrophysics. 474 (2): 653–664. arXiv:0708.1752. doi:10.1051/0004-6361:20078357. ISSN 0004-6361.
  3. ^ D. Scott Birney; Guillermo Gonzalez; David Oesper (2007). Observational Astronomy. Cambridge University Press. p. 75. ISBN 978-0-521-85370-5.
  4. ^ Simon F. Green; Mark H. Jones (2004). An Introduction to the Sun and Stars. Cambridge University Press. p. 87. ISBN 978-0-521-54622-5.
  5. ^ D. Scott Birney; Guillermo Gonzalez; David Oesper (2007). Observational Astronomy. Cambridge University Press. p. 73. ISBN 978-0-521-85370-5.

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