Exactly correct from a frame of reference that by December 22nd stops moving north and rests for three days, until December 25th when it moves approximately one degree downwards with respect to the sun.

d(phi_{zenith})/dt ~ 23 ( 2pi/365.25 ) sin ( t 2pi/365.25 ) , where t = days since solstice, or t_{0} = solstice dates. Highest daily rate of change of zenith angle (elevation) is 1/3 degree per day, and occurs at the vernal and autumnal equinoxes.

As Bystander is trying to say. The Suns motion is sinusoidal, at the solstice it reaches its extreme position for the season. The rate of change is very small at these times (Summer and Winter) So the sun appears to hover briefly as it changes direction. It is not really stationary it is just moving very slowly. It then begins to accelerate, slowly initially, then as it speeds up, reaches the maximum rate of change at the Equinox. At this time the sun races past the equator but even then the rate of change begins to drop as the sun moves toward the other extreme.

Thanks for all three of the replies, I figured it would be sinusoidal motion, and it just slowerly and slowerly moved, until it reversed it's path of acceleration. Thanks for the math, Bystander.

Maybe it's just because I was born a non-Terracentric, but I prefer to think that the sun just pretty much stays the same and the motion of the Earth makes it appear to move.

Hello to all!
I don't know if anyone will check this but....here is my question:

what is the sun time equation that describes sun's movement ?
I have found plots of sun's height (in degrees) (vertical axes height-horizontal sun azimuth in degrees) but I can't find it's mathematical expression...