# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Celestial data for the planet Mercury**

**From:**Paul Hirose

**Date:**2016 Feb 24, 23:36 -0800

On 2016-02-23 23:18, Herbert Prinz wrote: > Paul, > I agree that any significant discrepancy indicates an error. Now I am curious: How do you arrive at 95 mas difference? I get a little over 101 mas. What is it that one of the two of us is doing wrong (or differently from the other) in a simple subtraction and multiplication? The coordinates posted by Dave Walden are: ************************ http://aa.usno.navy.mil/cgi-bin/aa_geocentric.pl?ID=AA&task=6&body=1&year=2016&month=2&day=1&hr=11&min=0&sec=0.0&intv_mag=1.0&intv_unit=1&reps=5 2016 Feb 01 11:00:00.0 19 14 15.421 - 20 38 03.89 ************************ http://ssd.jpl.nasa.gov/horizons.cgi#results 2016-Feb-01 11:00 19 14 15.4172 -20 38 03.896 *************** http://vo.imcce.fr/webservices/miriade/?formsMercury2016-02-01T11:00:00.0019 14 15.42394 -20 38 3.8918 The last two differ by 95 mas. To get that figure, the first step is to convert from spherical format (assume radius = 1) to rectangular. +.297 943 774 -.887 153 335 -.352 403 843 HORIZONS +.297 944 211 -.897 153 195 -.352 403 824 IMCCE The dot product of those vectors is 1.000 000 000. That's the cosine of the separation angle. The magnitude of the cross product of the vectors is 4.59e-7. That's the sine of the separation angle. In this case we simply take the arc sine and obtain 2.63e-5 degrees, or .0947 seconds. A more general solution is to treat the cosine and sine as x and y respectively, and do a rectangular to polar conversion. That yields a precise result whether the angle is tiny or large. In addition, the result is correct even if the vectors have different magnitudes. In practice, the computation was simpler than what I showed above. My HP 49G calculator allows vector input in rectangular, spherical, or cylindrical format. Also, it has functions to compute dot and cross products without any explicit conversion to rectangular format. The hardest part is entering the digits without a mistake. Regarding the reason for the 95 mas discrepancy, in a private communication someone suggested the IMCCE may still be using the IAU 1976 precession and 1980 nutation models. Let's test that with the DE430 ephemeris, IAU 1976/80 precession and nutation, with and without frame bias. Geocentric apparent place at 2016 Feb 1 11:00:00 UTC: 19 14 15.42394 -20 38 03.8918 IMCCE 19 14 15.4244 -20 38 03.892 IAU 76/80 (with bias) 19 14 15.4239 -20°38'03.893 IAU 76/80 (no bias) The first and second lines agree within 6 mas. The first and third are only 1 mas different. So my guess is that IMCCE does not apply the frame bias correction. That's wrong. Frame bias is the difference between the mean equator and equinox coordinate system at J2000.0 (= 2000 Jan 1 0 hours Terrestrial time) and the ICRS (International Celestial Reference System). When the latter was created, it was intended to be as close as practical to the former. We now know there's a small offset. It's negligible if you're only working to a tenth of an arc second. But at higher accuracy there's a disconnect. Modern star catalogs and solar system ephemerides are based on the ICRS. On the other hand, the IAU precession models transform coordinates from the J2000.0 system to the mean equator and equinox system of date. Thus in precise work you're supposed to get the ICRS coordinates of the body (including effects such as aberration and light time), apply frame bias to obtain its J2000.0 coordinates, then apply precession, then nutation. It's ironic that the IMCCE coordinates have the most decimal places, but throw away much of their precision due to an oversight. When precise computations of a body's position differ by nearly a tenth of an arc second, it usually indicates a mistake somewhere. With reasonably modern tools and data you shouldn't be that far off.