Space Velocities

The actual motion of stars involves a path in three space dimensions, so the proper motion is just the projection of this true motion on the celestial sphere.

The Space Velocity and Its Components
This true velocity of the star is called the space velocity. The space velocity is illustrated in the following figure as the vector vs.

The space velocity may be resolved into a component perpendicular to the line of sight that is called the transverse velocity and a component along the line of sight called the radial velocity. These are denoted by vt and vr, respectively.

When Gliese 710 Comes to Call

One fruit of the precise astrometry provided by the Hipparcos satellite was improved understanding of the space velocities for nearby stars. Presently the nearest star is 4.2 light years away. Hipparcos data indicate that at least eight nearby stars will pass closer than five light years from Earth in the next million years. One of these is Gliese 710, now 63 light years away in the constellation Ophiuchus. It will pass within a mere light year of the Sun in about a million years. Gliese 710 is a very small, intrinsically faint star called a red dwarf. It is now much too faint to be seen without a telescope, but in a million years it will appear to be one of the brightest stars in Earth's sky because it will be so close.

The Oort comet cloud may extend out to a light year from the Sun. Thus the gravitational influence of Gliese 710, and some of the other eight stars expected to come within five light years of Earth, could disturb the Oort cloud and trigger a rain of comets into the inner Solar System.

Measuring the Components of the Space Velocity
It is the transverse velocity that is responsible for the proper motion. If the distance to the star is known, the angular velocity associated with the proper motion can be converted to a transverse velocity using simple trigonometry. On the other hand, the radial component of the velocity is responsible for a Doppler shift of the spectral lines that can be used to determine it directly, even if the distance is unknown.
Typical Space Velocities
The full space velocity of a star follows from the Pythagorean Theorem if both the transverse and radial velocities are known (see the star velocity calculator in the right panel). Typical values for the space velocities of stars are 20-100 km/s. The star with the largest known space velocity is Arcturus, in the constellation Bootes. It has a transverse velocity of 119 km/s and a radial velocity of -5.2 km/s (the negative sign indicating motion toward us). Applying the Pythagorean Theorem to these two components (sum the squares and take the square root) gives a space velocity magnitude of slightly over 119 km/s. The motion of Arcturus is almost entirely at right angles to our line of sight, since the radial velocity is very small compared with the transverse velocity.