palinsol (version 1.0)

day2l: Converts calendar day into true solar longitude and vice-versa

Description

Converts calendar day into true solar longitude for a given astronomical configuration and vice-versa

Usage

day2l(orbit, day)
l2day(orbit, l)
date_of_perihelion(orbit)

Value

day of year (360-d cal.) or true solar longitude (in radians).

Arguments

orbit

Output from a solution, such as ber78, ber90 or la04

day

calendar day, in a 360-d year

l

true solar longitude, in radians

Functions

• l2day(): Converts true solar longitude into calendar day

• date_of_perihelion(): Returns date of perihelion

Author

Michel Crucifix, U. catholique de Louvain, Belgium.

Details

The 360-d calendar is a conventional calendar, for which day 80 is the day of NH spring equinoxe. The tropic year, which in reality is 365.24219876 * 86400 seconds was the practical reference to define the Gregorian Calendar since this is the time needed to go through all the seasons. More discussion of calendars and conversions in Berger et al. (2010) appendix D.

The day2l and l2day is based on algoritms given in Berger (1978), but which can be traced back to expansions of the mean and true anomaly by Brouwer and Clemente (1961), pp. 65 and 77 (see code for further details).

References

Brouwer D. and G. M. Clemence, (1961), Methods of celestial mechanics, Academic Press, New York.

Berger, (1978) Long-term variations of daily insolation and Quaternary climatic changes, J. Atmos. Sci., 35, 2362-2367 1978, doi:10.1175/1520-0469(1978)035<2362:LTVODI>2.0.CO;2

Berger, A. Loutre, M.F. and Yin Q. (2010), Total irradiation during any time interval of the year using elliptic integrals, Quaternary Science Reviews, 29, 1968 - 1982, doi:10.1016/j.quascirev.2010.05.007

Examples

## date of perihelion throughout today
orbit=c(eps=0.409214, ecc=0.01672393, varpi=4.92251)
date_of_perihelion(orbit)
## date of winter solstice)
l2day(orbit, 270*pi/180.)