Local standard of rest (LSR)

Every velocity you measure from your backyard includes your own motion. To get rid of it, you project three motions onto the direction you’re pointing and add them to your measured (topocentric) velocity:

1. Earth’s rotation. At most about 0.47 km/s at the equator, less at higher latitude. Small, but it changes through the night.
2. Earth’s orbit around the Sun. Up to about 30 km/s. This one is the big term and it changes over the year, so the same patch of sky gives a different raw frequency in March than in September.
3. The Sun’s motion relative to nearby stars. The kinematic LSR is defined by a standard solar motion of 20 km/s toward RA 18h, Dec +30° (1900 coordinates). Projected onto your pointing that is anywhere from −20 to +20 km/s.

The sum is the correction. Add it to the topocentric velocity and you have v_LSR, the number HI surveys publish and the one you want on your plot.

Worked example

Site at 40° N, 75° W, pointing at Galactic longitude 30° on the plane (RA 281.52°, Dec −2.61°), at 03:00 UTC on 15 October 2026. Our Doppler calculator gives:

• rotation: −0.34 km/s
• orbital: −27.54 km/s
• solar: +16.55 km/s
• total: −11.33 km/s

So a peak that reads +60.00 km/s topocentric is +48.67 km/s relative to the LSR. Skip the correction and your spiral-arm features are 11 km/s out, which is several channels and enough to wreck a rotation curve.

Kinematic vs dynamical

There are two LSR definitions. The kinematic one above is a convention from the early twentieth century and it’s what radio HI surveys still use. The dynamical LSR is the velocity of a hypothetical circular orbit at the Sun’s position, and modern measurements put the Sun’s peculiar motion relative to it at somewhat different numbers. For comparing your spectra against published HI data, use the kinematic definition, which is what our calculator implements. It lands within about 0.1 km/s of a full barycentric reduction, which is far below a 1 to 2 km/s channel.

The calculator takes Galactic coordinates directly; see Galactic coordinates if you only know RA and Dec. LAB-012 uses the correction on a full spectrum.