Q: In astronomy terms, why are January 3rd and July 4th important?

A: It is summer in the northern hemisphere when the Earth is closest to the sun (perihelion, January 3rd, 147 million km), and winter when it is farthest away (aphelion, July 4th, 152 million km). Thus, the tilting of the northern hemisphere towards the sun in summer (longer days, more solar energy input) and the tilting away from the sun in the winter (shorter days, less solar energy input) are more important than the actual distance to the sun.