Solstice vs Equinox, daily and annual cycles

In less than a week the Solstice event occurs and the true definition is represented by the position of the North and South Poles to the circle of illumination and the greatest circumference of area in complete sunlight (South Pole) or complete darkness ( North Pole).

https://www.timeanddate.com/sun/uk/london

For convenience sake all values are very rough estimates to outline an idea

There are roughly 8 hours of rotation when London exits the circle of illumination (sunrise) and re-enters it (sunset) on the Solstice. As the latitude of London is 51 degrees, the rotational speed is about 635 mph so London covers a distance 635 miles*8 (hours of daylight) or 5,080 miles from one side of the circle of illumination to the other (sunrise to sunset) on the December Solstice.

On the June Solstice London covers a rotational distance of 635 miles*16 (hours of daylight) or 10,160 miles from the time its exits the circle of illumination until it enters the planetary division once more.

On the Equinoxes London covers 7,620 miles in rotational distance corresponding to 12 hours representing equal daylight/darkness and half the circumference for that 51 degree latitude.

As the Earth is 24901 miles circumference at the Equator and daylight/darkness symmetry is always the same, the distance the Equator covers each 12 hours corresponds to half the planet's circumference or 1037.5 miles per hour..

Even at a distance of 8 miles from the South pole, the distance traveled through rotation is 1 mile per hour. Of course Polar sunrise and sunset on the Equinoxes arises from a separate rotation where the Polar latitudes cover a distance of 5,487.5 miles from Equinox to Equinox as a function of the orbital surface rotation hence Polar day/night cycle of a single sunrise,noon,sunset and midnight each year.

All this needs to be tidied up but the components are fine as are the causes and effects.