Proper Motion
The sky appears to turn once every 24 hours because of the daily rotation of the
Earth (the diurnal motion),
but the stars appear to be fixed in their relative
positions on the celestial sphere. This is an illusion, however, caused by the
very large distances to stars. In reality, the stars are in motion with respect to
each other and that causes them to slowly change their relative positions.
The apparent change in position of a star on the celestial sphere is called the
proper motion of the star. This
animation distinguishes between the diurnal and proper motion for stars, and
illustrates the long-term effect of proper motion on the shape of the Big Dipper.
Angular Motion on the Celestial Sphere
Proper motion is typically denoted by the Greek
symbol μ, and is a velocity that is usually quoted in units of seconds of arc
per year. The following image illustrates proper motion.
The total proper motion generally is composed of two components: a change in the right
ascension and a change in declination, as illustrated in the inset of the above figure.
Stars with the Largest Proper Motion
The stars with the largest proper motion, as determined by precision Hipparcos
astrometry, are listed in the following table.
|
Stars with Largest Proper Motion Using Hipparcos Data
|
| Star |
Change in R. A.
(arc sec / year) |
Change in Dec
(arc sec / year) |
Proper Motion
(arc sec / year)
|
| Barnard's Star |
- 0.79784 |
10.32693 |
10.3577
|
| Kapteyn's Star |
6.50605 |
- 5.73139 |
8.6705
|
| Groombridge 1830 |
4.00369 |
- 5.81300 |
7.0584
|
| Lacaille 9352 |
6.76726 |
1.32666 |
6.8961
|
| CD-37d 15492 |
5.63407 |
- 2.33794 |
6.0999 |
|
|
|
|
|
In this table the total proper motion (last column)
is broken down into the change in right ascension
(R. A.) and
the change in declination (Dec), and is measured in arc seconds per year. A negative number
means that the corresponding celestial coordinate decreases by the amount indicated, while a
positive number means that it increases.
|
Technically Speaking: Conversion from Angle to Time
The change in
right ascension is quoted in the table above in arc seconds, but recall that many
maps of
the celestial sphere instead give the right ascension in hours and minutes of time
relative
to the vernal equinox. The conversion between the two sets of units for right
ascension
is that one hour of
time is about 15 degrees (or 54,000 arc seconds) of sky rotation, but for our
basic
discussion it won't be necessary to make such conversions since we will always
quote proper
motion in units of arc seconds per year.
|
|
Example: Kapteyn's Star
For example, in a single year Kapteyn's Star moves
on the celestial sphere such that its right ascension increases by about 6.5 arc
seconds and
its declination decreases by about 5.7 arc seconds.
This corresponds to a total angular
motion of about 8.7 arc seconds per year for Kapteyn's Star.
Proper Motion and Parallax
Were it not for the motion of the Earth around the Sun, proper motion would lead to
a simple drift of the position for a star on the celestial sphere in a particular
direction. However, because of the motion of the Earth on its orbit, there is a
parallax effect for stars that are near enough to exhibit significant proper motion
that causes the star to execute motion in a small ellipse on the celestial sphere
over a period of a year (this ellipse is just a mirror of the actual motion of the
Earth on its elliptical orbit).
The superposition of these two motions (a straight
linear drift from the proper motion and elliptical motion from the parallax effect)
then leads to a wavy path of the star on the celestial sphere. The following
animation illustrates.