Question

When was one year in our calendar worked out and by who? Did they base it on the tilting of the Earth or the orbit?

Answer 1

Calendar year is sidereal year that is defined as the orbit period for the Earth, with reference to stars. It has bearing on the Earth's day-night spin, for the unit day..

Explanation:

The calendar year has no direct bearing on the tilt of the Earth's axis.

All orbital characteristics involve the transcendental number `pi` in the formulas. So, they are all transcendental. Calendar year is one such transcendental number.

Like `180^o` for `pi` radian, transcendental day is conveniently divided into 34 X 60 X 60 = 86400 seconds. The calendar year is expressed in days as 365 for normal year and 366 for leap years, .

The earlier Julian calendar year = 365.25 days and this is IAU year. The error is higher in this approximation. I do not know when this will be done away with in astronomical computations, giving room for, a better than Julian approximation.

The currently followed in calendars, Gregorian year = `365 + (97/400)` = 365.2425 days, with leap year additions of 1 day in February, for 97 times in a period of 400 years. Of course, the error is less in Julian calendar, by comparing with 9-sd approximation sidereal year = 365.256363 days.

Duration of the small interval of time called second is also subject to correction for cumulative error, over a long period.

If anyone of the orbital characteristics (like eccentricity) of the orbit is
corrected, it will reflect on the values of the others, in the existing Tables. So, it is going to be a long wait, for making the next cycle of corrections. . , , .