update: I think I've found what I'm looking for. The file JGDWN_CER18C_SHA.TAB
has what looks like spherical harmonics up to order 18, except I don't know the definitions. I still need the expression for the gravitational potential that uses this particular set of indices.
Each harmonic has four floats. Two could be the sine and cosine terms, but would the third and four float be their uncertainty? The low-order values show the last pair of floats to be much lower than the first pair, so this might be a reasonable interpretation.
For the first line of each group ((2, 0), (3, 0), (4, 0)...), the 2nd coefficient is always exactly zero. This suggests that the first line of each group represents the $\tilde{J}_n$ and the rest the $\tilde{C}_n^m$ terms in Eq. 10 in Wikipedia's Geopotential model for example, but I don't know.
For the top line, 0.470E+03 could be the normalizing radius $R_0$ since is close to the radius of Ceres of about 473 km, and 0.626E+02 is very close to the standard gravitational parameter $GM_{Ceres}$ of about 62.63 km^3/s^2. The next number I don't recognize (an uncertainty?) the next is 18 the maximum order, the rest is 1, 0, 0.
0.4700000000000E+03, 0.6262735874220E+02, 0.3985003000000E-03, 18, 18, 1, 0.0000000000000000E+00, 0.0000000000000000E+00
1, 0, 0.0000000000000E+00, 0.0000000000000E+00, 0.0000000000000E+00, 0.0000000000000E+00
1, 1, 0.0000000000000E+00, 0.0000000000000E+00, 0.0000000000000E+00, 0.0000000000000E+00
2, 0, -0.1185081209724E-01, 0.0000000000000E+00, 0.4423323117973E-07, 0.0000000000000E+00
2, 1, 0.4584485474872E-08, 0.3639162051337E-08, 0.2155525472595E-07, 0.2153934044801E-07
2, 2, 0.2469729305807E-03,-0.2743726604078E-03, 0.5213051258454E-07, 0.5076931635838E-07
3, 0, 0.4152413352854E-04, 0.0000000000000E+00, 0.1520927120725E-07, 0.0000000000000E+00
3, 1, 0.2337951903625E-04, 0.6215005087427E-04, 0.1947755967293E-07, 0.1954951268792E-07
3, 2, -0.1917104114695E-04, 0.7075307362085E-04, 0.1863860600869E-07, 0.1818690157217E-07
3, 3, -0.4883368345013E-04,-0.9002646059395E-04, 0.2876655517205E-07, 0.2665508252055E-07
4, 0, 0.5729460133105E-03, 0.0000000000000E+00, 0.2259871225770E-07, 0.0000000000000E+00
4, 1, -0.2273796738721E-04,-0.2351160823946E-05, 0.2631912096005E-07, 0.2625579001914E-07
4, 2, 0.1237405960611E-04,-0.1722009659098E-04, 0.2902786583947E-07, 0.2915156210308E-07
4, 3, -0.2344736481214E-04,-0.3324468519353E-05, 0.2300918515991E-07, 0.2324047471504E-07
4, 4, 0.2661506582348E-04, 0.2753957135508E-04, 0.2313102127907E-07, 0.2316537801342E-07
5, 0, -0.3969538990586E-06, 0.0000000000000E+00, 0.3732369694857E-07, 0.0000000000000E+00
[...]
18, 16, -0.3285042287832E-05,-0.2204432934687E-05, 0.4782896096099E-05, 0.4777775535815E-05
18, 17, -0.3053493116667E-05,-0.2491134971988E-05, 0.4437864110763E-05, 0.4434679553983E-05
18, 18, -0.7169766777004E-06,-0.9266714099251E-05, 0.4488625034504E-05, 0.4493431031223E-05
above: GIF of Ceres image and surface gravity maps from here, originally from https://photojournal.jpl.nasa.gov/catalog/PIA22083 Credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA
I've found and downloaded the contents from the Planetary Data Systems (PDS) page Dawn Ceres Gravity Models. The file AAREADME.TXT includes the following diagram and guide.
Reading that, ideally what I'd like to find is something like a SHA
or Spherical Harmonics ASCII Data Record. The .DAT
files are binaries (which I don't know how to read) and not small ~0.5 MB and so are probably more data than I need or know how to process, however they might contain what I'm looking for but I don't know how to open them.
The answer might be a guide how to find the data here, or an independently published list of spherical harmonics coefficients in an easy to read format. Either is fine.
|===================================================================|
| |
| Dawn Gravity/Radio Science |
| Derived Data Directory Structure for Ceres |
| |
|===================================================================|
| |
| root |
| | |
| |- AAREADME.TXT |
| |- VOLDESC.CAT |
| | |
| |- [CATALOG] |
| | |- CATINFO.TXT |
| | |- DAWNMISSION.CAT |
| | |- DAWNINSTHOST.CAT |
| | |- INST.CAT |
| | |- REF.CAT |
| | |- PERSON.CAT |
| | `- DATASET.CAT |
| | |
| |- [DOCUMENT] |
| | |- DOCINFO.TXT |
| | |- ... |
| | |
| |- [INDEX] |
| | |- INDXINFO.TXT |
| | |- INDEX.LBL |
| | `- INDEX.TAB |
| | |
| `- [DATA] |
| |- [SHADR] |
| |- [SHBDR] |
| `- [RSDMAP] |
| |
|===================================================================|
and further down:
==============================================================================
ACRONYMS AND ABBREVIATIONS
==============================================================================
ASCII American Standard Code for Information Interchange
DOY Day of year
DSN Deep Space Network
JPL Jet Propulsion Laboratory
NAIF Navigation Ancillary Information Facility
NASA National Aeronautics and Space Administration
PDS Planetary Data System
RS Radio Science
RSDMAP Radio Science Digital Map
RSS Radio Science Subsystem
SHA Spherical Harmonics ASCII Data Record
SIS Software Interface Specification