Stories and science behind calendars

Why are there only 28 days in February? The story goes. February is the month criminals are executed. It is a bad month. So, people shorten February as much as possible.

Why do both July and August have 31 days? Usually, two neighboring months have 30 and 31 days alternating. The story goes. Caesar and Augustus both wanted their months to have more days. 

Despite these arbitrary irregularities from earthly matters, important celestial positions, such as spring equinox, autumn equinox, winter solstice, summer solstice, stay at remarkably regular dates. How can these be possible? 

The orbit of the earth is an ellipse. The sun is at one focus of the ellipse. The velocity of the earth's speed is changing at different positions of the trajectory. As a result, it takes shorter time to move from autumn equinox to spring equinox than from spring equinox to autumn equinox. For details, please check the link to the graph of the earth's orbit.

https://i.stack.imgur.com/TcFKl.jpg

Therefore, one month (February) has to be shortened to accommodate the faster movement of the earth at one part. Another long month (August) has to be added to accommodate the slower movement of the earth at other part. 

The design of calendar is based on celestial movements. Earthly matters may be considered for details. But it is the earthly matters that we are usually told.