How fast does the sun move around the celestial sphere?
As the planet moves in its orbit, a line from the sun to the planet sweeps out equal areas in equal times. When the earth is nearest to the sun, the angle from where the sun is one one day on the celestial sphere and where it is the next day is a little greater than average. This means that the sun moves on the celestial sphere a little farther than usual: Call the time of day when the sun crosses the meridian (he great circle in the sky that contains the north celestial pole and the zenith) “local noon.” On average, the time from one local noon to the next is 24 hours. But with the sun having moved farther than normal, it will take a little longer for it to get to the meridian. Thus the time from one local noon to the next will be a little longer than 24 hours.
