English: Speed of sun relative to surrounding stars over 500 million years, according to a simple model (here), but using the more recent values of U, V, and W at the present time, namely (10.00, 5.25, 7.17) km/s. (See w:Stellar kinematics#The sun's motion in the galaxy.) These are the velocity components in the X, Y, and Z directions (see w:Galactic coordinates). The curve called "speed" is the square root of the sum of the squares. This is an example of w:quasiperiodic motion.

As said, the model is simple. A more accurate model would take into consideration the fact that the Oort "constants" A and B, as well as Ω, which is A−B, decrease with distance from the galaxy centre. If the gravitational attraction toward the centre is modeled as ${\displaystyle C_1/R^2-C_2/R^3}$ (say by matching its value and derivative at our location) where ${\displaystyle R}$ is the distance from the galaxy centre, then the angle around the galaxy centre and the elapsed time can be found as closed-form functions of R just as in the Keplerian case, and the equation for the angle can be inverted to find R and the time as functions of the angle around the centre. This allows the velocity to be calculated as a function of the angle, but not as a closed-form function of time.