Index of Functions: A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X
kepleq

 Procedure Abstract Required_Reading Keywords Declarations Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version

#### Procedure

```     KEPLEQ ( Solve Kepler's Equation --- Equinoctial Form )

DOUBLE PRECISION FUNCTION KEPLEQ (ML,H,K)
```

#### Abstract

```     Solve the equinoctial version of Kepler's equation.
```

```     None.
```

#### Keywords

```     SPK
```

#### Declarations

```     IMPLICIT NONE

DOUBLE PRECISION  ML
DOUBLE PRECISION  H
DOUBLE PRECISION  K
```

#### Brief_I/O

```     VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
ML         I   Mean longitude.
H          I   h component of equinoctial elements.
K          I   k component of equinoctial elements.

The function returns the solution to the equinoctial version of
Kepler's equation, given the mean longitude and the h and k
components of the equinoctial elements.
```

#### Detailed_Input

```     ML       is the mean longitude of some body following two body
motion. (Mean longitude = Mean anomaly + argument of
periapse + longitude of ascending node.)

H        is the h component of the equinoctial element set
( h = ECC*SIN( arg of periapse + long ascending node) )

K        is the k component of the equinoctial element set
( k = ECC*COS( arg of periapse + long ascending node) )
```

#### Detailed_Output

```     The function returns the solution to the equinoctial version of
Kepler's equation, given the mean longitude and the h and k
components of the equinoctial elements.

The solution is the value of F such that

ML = F + H * COS(F) - K * SIN(F)

Note that ECC = DSQRT ( K*K + H*H )
```

#### Parameters

```     None.
```

#### Exceptions

```     1)  If the sum of the squares of H and K is not less than .9,
the error SPICE(ECCOUTOFBOUNDS) is signaled.

2)  If the iteration for a solution to the equinoctial Kepler's
equation does not converge in 10 or fewer steps, the error
SPICE(NOCONVERGENCE) is signaled.
```

#### Files

```     None.
```

#### Particulars

```     This routine solves the equinoctial element version of
Kepler's equation.

ML = F + H * COS(F) - K * SIN(F)

Here F is an offset from the eccentric anomaly E.

F = E - argument of periapse - longitude of ascending node.

where E is eccentric anomaly.
```

#### Examples

```     None.
```

#### Restrictions

```     None.
```

#### Literature_References

```     [1]  W. Owen and R. Vaughan, "Optical Navigation Program
Mathematical Models," JPL Engineering Memorandum 314-513,
August 9, 1991.
```

#### Author_and_Institution

```     J. Diaz del Rio    (ODC Space)
W.L. Taber         (JPL)
```

#### Version

```    SPICELIB Version 1.0.1, 26-AUG-2021 (JDR)

Edited the header to comply with NAIF standard. Updated
\$Procedure section for consistency with KPSOLV routine.

SPICELIB Version 1.0.0, 11-DEC-1996 (WLT)```
`Fri Dec 31 18:36:29 2021`