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
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
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
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