The calculation of the transit ephemerides is based on an algorithm developed by Greg Laughlin of UC Santa Cruz. The NASA Exoplanet Archive development staff has updated and extended the algorithm, utilizing various IPAC tools to provide the service.
The algorithm is linear and comprised of a small number of steps:
where i is the loop index.
The early and late transits, however, are not computed by simply subtracting or adding half the transit duration time t_{d} from the now-known time of central transit. Instead, the periastron passage times are first computed from the orbital elements,The following algorithm is used to convert a Julian Date to a calendar date. (See Murray, C.D., Dermott, S.F., Solar System Dynamics, Cambridge University Press, Cambridge, 1999, for the algorithm upon which this process is based.)
To convert a Julian date to a calendar date, you need to define the following quantities:
a | = int[JD+0.5] | |
b | = int [(a-1867216.25)/36524.25] | if a ≥ 2299161 |
c | = a+1524 | if a < 2299161 |
c | = a + b - int[b/4]+1525 | if a ≥ 2299161 |
d | = int[(c-122.1)/365.25] | |
e | = int[365.25/d] | |
f | = int[(c-e)/30.6001] |
where the function int[x] denotes the largest whole number less than or equal to (x). The calendar date is given by
D | = c - e - int[30.6001f] + frac[JD + 0.5] |
M | = f - 1 - 12[int(f/14)] |
Y | = d - 4715 - int[(7 + M)/10] |
The conversion from calendar to Julian date uses the same method as specified in Murray, C.D., Dermott, S.F., Solar System Dynamics, Cambridge University Press, Cambridge, 1999. Given a calendar year (Y), month (M), day (D), and Universal Time (UT), define the auxiliary quantities y and m by
y | = Y - 1 | and | m | = M + 12 | M ≤ 2 | |
y | = Y | and | m | = M | M > 2 |
and the quantity B by
B | = -2 | up to and including 4 Oct 1582 |
B | = int[y/400] - int[y/100] | from and including 15 Oct 1582 |
where int[x] is as above. Then, the Julian date is
Last Updated: 22 September 2016