Add a day to the calendar every four years, and the problem is solved. Our year is not based on the time it takes Earth to orbit the sun. In fact, the time it takes for Earth to travel from one point on its orbit back to that same point is 365.2596 days, which creates a horror-story for calendar makers. Besides, our calendar dates to a time when humans didn't know that Earth traveled around the sun. We're pretty much stuck with the older notion that the sun moves around Earth.
Astronomers choose a fixed point on that circle and measure the motion of the sun from there.
Good points to choose are the equinoxes, the points on the ecliptic where the sun crosses the celestial equator, the extension of earth's equator on the sky. On those days, day and night are equal. Also, those days define the beginnings of spring and autumn. That makes sense on a deep, emotional level. We still intuitively measure the year by the passing of the seasons, and the position and angle of the sun determine just what season we are in.