1. Radial Velocity and Proper Motion
Barbieri Chapter 9
Kathy Geise

2. Stellar or Annual Parallax
The apparent motion of a nearby star is a small ellipse in the sky relative to background stars over the period of a year.
The parsec is the distance for which the annual parallax is one arcsecond.
The reciprocal of the parallax is the distance in parsec.

3. Two Components of Velocity
Over time, star X moves to position X’ as seen from the heliocenter S along velocity vector, V. The velocity vector has components vr in the radial direction and vt in the transverse direction.

4. Proper Motion, μ
A slow, angular change to equitorial coordinates due to a star’s transverse velocity relative to the viewer (Carroll and Ostlie) or heliocenter (Barbieri)
Units of arcseconds per year.
Tangential velocity vt is related to proper motion, μ, as follows:
μ = π/4.740 *vt (arcsec/yr) where π is annual parallax in arcsec and vt in km/s.
The linear drift in this graph is from proper motion. The elliptical motion is from the annual parallax.

5. Barnard’s star Second closest to Sol after Alpha Centauri
6.0 light years away
Constellation Ophiuchus
Dim red dwarf (m. 9.55)
Old star, possibly by
Approaching Sol
Largest known proper motion of all stars (10.3”)
The Sky 6

6. Radial Velocity
Radial velocity is the component of the velocity toward or away from the observer.
Radial velocity is measured through the Doppler effect.
When the velocities measure less than 0.01c, we can use prerelativistic formulae:
Vr = c*(λobserver – λs)/ λsource
z=Δλ/λ=Vr/c
Z>0 red-shifted; radial velocity positive
Z<0 blue-shifted; radial velocity negative

7. Astrometric Velocities
“Precise astrometry permits accurate determination of stellar radial velocity from purely geometric measurements without using spectroscopy nor employing the Doppler principal.”
Changes in parallax and proper motion over time reveal radial velocity.
Possible only with precise measurements.
Hipparcos satellite data in combination with older stellar data.
Changing angular separation of stars sharing the same space velocity as in a moving cluster measured by Hipparcos.
View a Java animation of Bernard’s Star proper motion on the Hipparcos website:
The Hipparcos and Tycho Catalogues: Nearby Stars

8. Hipparcos animations Motion of the Pleiades over 120,000 years.
This is an 8x6 degree field.
Animation of intermediate astrometry data of Hipparcos star.

9. Relativistic Considerations
The whole velocity vector is affected by relativity, not just the radial component. Relativity predicts a transverse Doppler effect.
General relativity is important for high accuracy, for example, spacecraft moving within the solar system.
High velocity stars, like Barnard’s
Expanding gaseous envelopes of exploding supernovas
High red-shifted, very distant galaxies
Light emitted from atoms in a gravitational field, for example the surface of a star, may be red-shifted.

10. The Sky 6
Snake Nebula
Cover photo APOD Snake Nebula