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. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. 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. Due to the constant, and unvarying speed of light (that is also constant; without regard to whatever is the velocity of the eminating or reflecting source), the true (i.e., instantaneous) velocities of distant stars cannot be observed; the observed proper motion reflects the motion (velocity) of a star at the time the light was emitted from that source.
Read more about Proper Motion: Introduction, Usefulness in Astronomy, History, Stars With High Proper Motion, Software
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