The Wikipedia page on Sun gives these three velocities,
- ~220 km/s (orbit around the center of the Galaxy)
- ~20 km/s (relative to average velocity of other stars in stellar neighbourhood)
- ~370 km/s(relative to the cosmic microwave background)
So my inference is that 220km/s is the estimated orbital velocity. It is not constant velocity because the orbital motion around galactic center is not circular.
The velocity of Sun around the Milkyway is in fact same as the spin motion of Milkyway around itself.
All stars in the galaxy rotate around
a galactic center but not with the
same period. Stars at the center have
a shorter period than those farther
out
Sun's orbital motion is calculated with galactic north pole as the frame of reference. It is called the galactic coordinate system. See this
It's a complicated calculation, because stars have arbitrary motion in local regions, which need to be subtracted out.
That's a really good question. You're right that measuring the tranverse velocity is a very difficult measurement, mostly due to Andromeda's distance from the Sun. The problem can be tackled in two ways: directly, and indirectly.
Direct measurements mean actually tracking a positional change between Andromeda and even more distant objects assumed to be essentially at rest, like quasars. The recent discovery of water masers mentioned above should make this possible; a transverse velocity of ~100 km/s is an angular shift on the order of 10 microarcseconds per year. This is much smaller than is possible with optical telescopes; the extreme baselines of radio telescopes like the Very Long Baseline Array, however, do make direct measurements feasible. These observations are currently taking place, and we should have a published measurement within a couple of years.
Indirect measurements of Andromeda's transverse velocity use a few different techniques. The Loeb et al. (2005) paper made their estimate based on the fact that M33, a neighboring galaxy to Andromeda, shows no sign that its stellar population has been disturbed by passing nearby Andromeda. This constrains the possible range of directions and speeds of Andromeda's velocity. They combine this with data on M33's orbit, plus simulations of how close the galaxies would have to be to show an effect, and estimate both a direction (mostly eastward) and speed ($100 \pm 20$ km/s) of Andromeda's proper motion.
A second indirect method was published by van der Marel & Guhathakurta in 2008; they used information on the orbits of satellite galaxies orbiting M31 to estimate the center of mass (or barycentre) of our Local Group. Since the position and velocity of the Local Group barycentre depend partially on M31's orbit, they also estimated a transverse velocity. Their result is -78 km/s W, -38 km/s N.
The upcoming direct measurement of M31's proper motion should answer which (if either) of these other estimates are correct. In addition, we're looking forward to answering several interesting questions regarding both the past and future of our Local Group of galaxies. Stay tuned!
Best Answer
There is no guarantee or likelihood that the Sun was in its present orbit in the past. In fact it is more likely that it has migrated to its present position ($r \simeq 8$ kpc) from a smaller galactocentric radius ($4<r<7$ kpc). This is inferred from the fact that the Sun has a larger metallicity than most of the stars in its current neighbourhood together with the fact that there is a negative metallicity gradient with galactocentric radius (e.g. Minchev et al. 2013; although others disagree - see Martinez-Barbosa et al. 2015).
That being so (and it is by no means certain), and with the Galactic rotation curve being approximately flat, this means that the orbital velocity at smaller galactocentric radius was the same, so the orbital period would have been shorter.
In other words, it is likely that the Sun has executed more circuits of the Galaxy than 4.57 billion/230 million $\simeq 20$ and perhaps as many as $\simeq 30$.
You are right that the Milky Way has evolved over time, but I think its gravitational potential has probably been reasonably settled for the last 5 billion years.