Orbital Elements from Position/Velocity
CALL sla_PV2EL (PV, DATE, PMASS, JFORMR, JFORM, EPOCH, ORBINC,
ANODE, PERIH, AORQ, E, AORL, DM, JSTAT)
PV | D(6) | heliocentric [x,y,z,ẋ,ẏ,ż], equatorial, J2000 |
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| (AU, AU/s; Note 1) |
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DATE | D | date (TT Modified Julian Date = JD−2400000.5) |
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PMASS | D | mass of the planet (Sun = 1; Note 2) |
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JFORMR | I | requested element set (1-3; Note 3) |
JFORM | I | element set actually returned (1-3; Note 4) |
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EPOCH | D | epoch of elements (t0 or T, TT MJD) |
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ORBINC | D | inclination (i, radians) |
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ANODE | D | longitude of the ascending node (Ω, radians) |
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PERIH | D | longitude or argument of perihelion (ϖ or ω, |
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| radians) |
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AORQ | D | mean distance or perihelion distance (a or q, AU) |
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E | D | eccentricity (e) |
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AORL | D | mean anomaly or longitude (M or L, radians, |
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| JFORM=1,2 only) |
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DM | D | daily motion (n, radians, JFORM=1 only) |
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JSTAT | I | status: |
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| 0 = OK |
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| −1 = illegal PMASS |
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| −2 = illegal JFORMR |
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| −3 = position/velocity out of allowed range |
JFORM=1, suitable for the major planets:
EPOCH | = | epoch of elements t0 (TT MJD) | |
ORBINC | = | inclination i (radians) | |
ANODE | = | longitude of the ascending node Ω (radians) | |
PERIH | = | longitude of perihelion ϖ (radians) | |
AORQ | = | mean distance a (AU) | |
E | = | eccentricity e(0≤e<1) | |
AORL | = | mean longitude L (radians) | |
DM | = | daily motion n (radians) |
JFORM=2, suitable for minor planets:
EPOCH | = | epoch of elements t0 (TT MJD) | |
ORBINC | = | inclination i (radians) | |
ANODE | = | longitude of the ascending node Ω (radians) | |
PERIH | = | argument of perihelion ω (radians) | |
AORQ | = | mean distance a (AU) | |
E | = | eccentricity e(0≤e<1) | |
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 Ω (radians) | |
PERIH | = | argument of perihelion ω (radians) | |
AORQ | = | perihelion distance q (AU) | |
E | = | eccentricity e(0≤e≤10) |
JFORMR | JFORM | meaning | |
1 | 1 | OK: elements are in the requested format | |
1 | 2 | never happens | |
1 | 3 | orbit not elliptical | |
2 | 1 | never happens | |
2 | 2 | OK: elements are in the requested format | |
2 | 3 | orbit not elliptical | |
3 | 1 | never happens | |
3 | 2 | never happens | |
3 | 3 | OK: elements are in the requested format |
JFORM | 1 | 2 | 3 | |
EPOCH | t0 | t0 | T | |
ORBINC | i | i | i | |
ANODE | Ω | Ω | Ω | |
PERIH | ϖ | ω | ω | |
AORQ | a | a | q | |
E | e | e | e | |
AORL | L | M | - | |
DM | n | - | - |
where:
t0 | is the epoch of the elements (MJD, TT) | |
T | is the epoch of perihelion (MJD, TT) | |
i | is the inclination (radians) | |
Ω | is the longitude of the ascending node (radians) | |
ϖ | is the longitude of perihelion (radians) | |
ω | is the argument of perihelion (radians) | |
a | is the mean distance (AU) | |
q | is the perihelion distance (AU) | |
e | is the eccentricity | |
L | is the longitude (radians, 0−2π) | |
M | is the mean anomaly (radians, 0−2π) | |
n | is the daily motion (radians) | |
- | means no value is set |