SLA_PERTEL

Perturbed Orbital Elements

ACTION:
Update the osculating elements of an asteroid or comet by applying planetary perturbations.
CALL:
CALL sla_PERTEL (JFORM, DATE0, DATE1, EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0, EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1, JSTAT) 
GIVEN (format and dates):
 JFORM I choice of element set (2 or 3; Note 1) DATE0 D date of osculation (TT MJD) for the given elements DATE1 D date of osculation (TT MJD) for the updated elements

GIVEN (the unperturbed elements):
 EPOCH0 D epoch of the given element set (${t}_{0}$ or $T$, TT MJD; Note 2) ORBI0 D inclination ($i$, radians) ANODE0 D longitude of the ascending node ($\Omega$, radians) PERIH0 D argument of perihelion ($\omega$, radians) AORQ0 D mean distance or perihelion distance ($a$ or $q$, AU) E0 D eccentricity ($e$) AM0 D mean anomaly ($M$, radians, JFORM=2 only)

RETURNED (the updated elements):
 EPOCH1 D epoch of the updated element set (${t}_{0}$ or $T$, TT MJD; Note 2) ORBI1 D inclination ($i$, radians) ANODE1 D longitude of the ascending node ($\Omega$, radians) PERIH1 D argument of perihelion ($\omega$, radians) AORQ1 D mean distance or perihelion distance ($a$ or $q$, AU) E1 D eccentricity ($e$) AM1 D mean anomaly ($M$, radians, JFORM=2 only)

RETURNED (status flag):
 JSTAT I status: +102 = warning, distant epoch +101 = warning, large timespan ($>100$ years) +1 to +10 = coincident with major planet (Note 6) 0 = OK $-$1 = illegal JFORM $-$2 = illegal E0 $-$3 = illegal AORQ0 $-$4 = internal error $-$5 = numerical error

NOTES:
(1)
Two different element-format options are supported, as follows.

JFORM=2, suitable for minor planets:

 EPOCH = epoch of elements ${t}_{0}$ (TT MJD) ORBINC = inclination $i$ (radians) ANODE = longitude of the ascending node $\Omega$ (radians) PERIH = argument of perihelion $\omega$ (radians) AORQ = mean distance $a$ (AU) E = eccentricity $e$$\left(0\le e<1\right)$ AORL = mean anomaly $M$ (radians)

JFORM=3, suitable for comets:

 EPOCH = epoch of perihelion $T$ (TT MJD) ORBINC = inclination $i$ (radians) ANODE = longitude of the ascending node $\Omega$ (radians) PERIH = argument of perihelion $\omega$ (radians) AORQ = perihelion distance $q$ (AU) E = eccentricity $e$$\left(0\le e\le 10\right)$
(2)
DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in the TT time scale (formerly Ephemeris Time, ET), expressed as Modified Julian Dates (JD$-$2400000.5).
• DATE0 is the instant at which the given (i.e. unperturbed) osculating elements are correct.
• DATE1 is the specified instant at which the updated osculating elements are correct.
• EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1 (respectively) for the JFORM=2 case, normally used for minor planets. For the JFORM=3 case, the two epochs will refer to perihelion passage and so will not, in general, be the same as DATE0 and/or DATE1 though they may be similar to one another.
(3)
The elements are with respect to the J2000 ecliptic and mean equinox.
(4)
Unused elements (AM0 and AM1 for JFORM=3) are not accessed.
(5)
See the sla_PERTUE routine for details of the algorithm used.
(6)
This routine is not intended to be used for major planets, which is why JFORM=1 is not available and why there is no opportunity to specify either the longitude of perihelion or the daily motion. However, if JFORM=2 elements are somehow obtained for a major planet and supplied to the routine, sensible results will, in fact, be produced. This happens because the sla_PERTUE routine that is called to perform the calculations checks the separation between the body and each of the planets and interprets a suspiciously small value (0.001 AU) as an attempt to apply it to the planet concerned. If this condition is detected, the contribution from that planet is ignored, and the status is set to the planet number (1–10 = Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus, Neptune, Earth, Moon) as a warning.
REFERENCE:
Sterne, Theodore E., An Introduction to Celestial Mechanics, Interscience Publishers, 1960. Section 6.7, p199.