English: Path of sun around the Milky Way from 250 million years ago till 250 million years in the future, 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). We take the present distance to the centre of the galaxy to be 8 kiloparsecs. The galaxy centre is at (0, 0), and the units of the axes are kiloparsecs. We are presently at (0, 8) and moving to the right. The square symbols on the curve are at intervals of 25 million years. The view is from "north" of the Milky Way. The Andromeda Galaxy is 765 kiloparsecs to the upper right.

In order to convert the functions X(t) and Y(t) of the model into the x and y coordinates of this figure, 8−X(t) is interpreted as the distance to the centre of the galaxy, called R, and Y(t) is taken to be Rθ where θ is the angle in radians (clockwise in this picture) of the sun's position relative to where its present stellar environment was or will be. This is moving in a circle with radius R₀ and frequency Ω, so the angle in our picture is the sum of that rotation and a rotation by θ.

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), 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.

The actual path of a star may be perturbed by the gravitational attraction of gas clouds or inhomogene of the density of stars.