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 and its components.

The space velocity may be resolved into a component perpendicular to the line of sight that is called the tangential velocity, vt and a component along the line of sight called the radial velocity, vr.

Measuring the Components of the Space Velocity

It is the tangential 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 tangential 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 Pythagoras' Theorem if both the tangential and radial velocities are known. Notice that this generally requires that we know the distance to the star. Typical values for the space velocities of stars are 20-100 km/s.

Calculations of Star Velocities

Here is a Star Velocity Calculator that allows you to make simple calculations for space velocities in terms of radial velocities, proper motion, and distance to the star. (Caution: this applet is written under Java 1.1, which is only supported by the most recent browsers. It should work on Windows systems under Netscape 4.06 or the most recent version of Internet Explorer 4.0, but may not yet work on Mac or Unix systems or earlier Windows browsers.)

Gleise 710 is Coming to See You

Presently there is a faint red dwarf star 63 light years away in the constellation Ophiucus that is called Gleise 710. Recently it has been realized that this star is moving toward the Sun at relatively high velocity and will pass within a light year in about a million years. It is now too faint to be seen except with a telescope, but in a million years it will be one of the brighter stars in Earth's sky, with apparent visual magnitude 0.6. Although not a direct threat to the Solar System at that passing distance, it is likely that its gravitational influence will disturb the Oort Cloud of comets and send many more comets than usual into the inner Solar System (Ref).

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