# [Spice_discussion] spkezr vs Geocentric Solar Ecliptic (GSE) Frame

William Thompson William.T.Thompson at nasa.gov
Fri Jan 29 11:44:32 PST 2016

```Donald:

We got side-tracked into a discussion of what's the correct definition of the
GSE frame, but it turns out that this isn't really relevant to your original
question.  When I do the same calculation that you did, using spkezr to
calculate the J2000 coordinates of Earth, and then using sxform to calculate a
transformation matrix from J2000 to GSE, I get very similar numbers as you

IDL> print,m ## sv
1.5208990e+08
4.6566129e-10
7.4505806e-09
0.021773487
-6.1201044e-15
4.4408921e-16

In particular, I get the same 21.77 m/s sunward velocity.  (I also get the same
values if I just use 'GSE' as the frame in the spkezr, without using sxform.)

Your expectation was that converting from the inertial J2000 frame to the
rotating GSE frame would zero out the Sun's velocity relative to Earth.
However, that's not quite correct.  It only removes the *rotating* component of
the velocity.  The magnitude of the J2000 velocity of the Sun relative to Earth
at the epoch ET is 29.293366 km/s.  Taking the cross product of the normalized
radius vector and the velocity velocity gives the velocity attributable to
rotation, which is slightly smaller at 29.293358 km/s.  The remaining component,
which is radial, works out to 0.021773487 km/s, i.e. just what the above
calculation shows.

Bill Thompson

P.S.  I highly recommend using the definition of GSE shared by the STEREO and
Van Allen missions.

On 01/27/16 19:33, Donald F. Linton wrote:
> I implemented the Geocentric Solar Ecliptic (GSE) Frame in the Frames
> <http://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/frames.html#Specifying
> a New Frame> reference:
>
> \begindata
>     FRAME_GSE                       =  314101
>     FRAME_314101_NAME           = 'GSE'
>     FRAME_314101_CLASS          =  5
>     FRAME_314101_CLASS_ID       =  314101
>     FRAME_314101_CENTER         =  399
>     FRAME_314101_RELATIVE       = 'J2000'
>     FRAME_314101_DEF_STYLE      = 'PARAMETERIZED'
>     FRAME_314101_FAMILY         = 'TWO-VECTOR'
>     FRAME_314101_PRI_AXIS       = 'X'
>     FRAME_314101_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION'
>     FRAME_314101_PRI_OBSERVER   = 'EARTH'
>     FRAME_314101_PRI_TARGET     = 'SUN'
>     FRAME_314101_PRI_ABCORR     = 'NONE'
>     FRAME_314101_SEC_AXIS       = 'Y'
>     FRAME_314101_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY'
>     FRAME_314101_SEC_OBSERVER   = 'EARTH'
>     FRAME_314101_SEC_TARGET     = 'SUN'
>     FRAME_314101_SEC_ABCORR     = 'NONE'
>     FRAME_314101_SEC_FRAME      = 'J2000'
> \begintext
>
> Using the epoch: 2017-07-01T00:00:00
> et = 5.521392681841135e8
>
> sv = spkezr( "SUN", et, "J2000", "NONE", "EARTH" )
>
>   -2.41323e7  1.37774e8  5.97261e7  -28.9257  -4.24521  -1.83927
>
> then
>
> M = sxform("J2000", "GSE", et )
>
>   -0.158671     0.905874      0.392703     0.0          0.0        0.0
>   -0.987331    -0.145594     -0.0630798    0.0          0.0        0.0
>    3.26993e-5  -0.397737      0.9175       0.0          0.0        0.0
>   -1.90166e-7  -2.80422e-8   -1.21495e-8  -0.158671     0.905874   0.392703
>    3.0561e-8   -1.7445e-7    -7.56986e-8  -0.987331    -0.145594  -0.0630798
>   -6.6631e-11  -9.82553e-12  -4.257e-12    3.26993e-5  -0.397737   0.9175
>
> M*SV yields
>
>   1.5209e8
>   2.79397e-9
>   7.45058e-9
>   0.0217735
>   6.64746e-15
>   2.22045e-16
>
> I don't understand why I see 21.77 m/s of sunward velocity
>
>
>
>
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>

--
William Thompson
NASA Goddard Space Flight Center
Code 671
Greenbelt, MD  20771
USA

301-286-2040
William.T.Thompson at nasa.gov
```