Mars Prime Meridian

Copyright © 2001 by Michael Allison
Goddard Institute for Space Studies
pcmda@giss.nasa.gov

03:14 PM ../2001 -0500:

Tom, the Mars Cartographic Working Group (MCWG) has established a new determination of the Mars prime meridian, to be published sometime next year in the journal Celestial Mechanics and Dynamical Astronomy as a part of a report by the IAU working group on planetary cartography.

The new value for W, defined according to the IAU convention as the angle along the Mars equator from its ascending node on the J2000 equator of the Earth to the planet's prime meridian is

W = 176.630deg + 350.89198226(deg/d)*d2000,

where d2000 is the elapsed time in days from J2000=J.D.2451545.0 (Barycentric Dynamical Time or TDB). For comparison, the last IAU working group report, published in 1996, gave W(J2000) = 176.901deg!

The new value has been determined in reference to both imaging and MOLA (Mars Orbiter Laser Altimetry) data. If you're interested you can read about the new analysis in an extended conference abstract by Duxbury et al. which you can download at

http://wwwflag.wr.usgs.gov/USGSFlag/Space/Isprs/meetings.html

In terms of the angle Vm, measuring the Mars prime meridian from the Mars vernal equinox, I make this out to be about

Vm = 313.384deg + 350.891985(deg/d)*d2000.

The calculation of Vm-W, what I call the "delta-IAU", is a slightly complicated matter. Owing to what appear to me to be certain ambiguities regarding what orbital/equatorial frames have actually been held fixed or allowed to move when in the new calibration, I'm left with an uncertainty of about 0.001deg in my own calculation of this. Furthermore, Duxbury admits to an uncertainy in the new anlge W of about 0.004deg. But even with a total uncertainy in Vm as large as say 0.008deg, that would imply a Mars clock-time error of no more than 2 seconds now for the Mean Solar Time.

The new angle is about 0.09deg smaller than the one ("guessed") in the Allison and McEwen (2000) paper. So my touted alignment of 2000Jan06 00:00:00 UTC with a Mars Mean Solar Midnight would now be modified to 2000Jan06 00:00:21 UTC (NOT TDB). Or, with our "Fictitious Mean Sun" angle

FMS = 270.386deg + 0.5240384(deg/d)*d2000,

the Mars Mean Solar Time becomes

MST = Mod[(Vm-FMS)*(24hour/360deg) + 12 hour, 24hour]

= Mod[14.8665h + 23.3578631h*d2000,24h],

where again d2000 represents the difference in days given in dynamical time from JD2451545.0.

(As you probably know, the "modulo" function just provides a reset within 0 to 24 hours. Equivalently, you can of course just write a loop to subtract off appropriate multiples of 24hours.) And in terms of a Julian Date in Universal Coordinated Time, the Julian Date in Barycentric Dynamical Time can be calculated to fair accuracy as

JD(TDB) = JD(UTC) + 0.000743 + 3*10**-8(d2000)[1 + 10**-5(d2000)].

e.g. the difference between dynamical time and UTC is currently about 0.000743day or about 64.2sec.

The implied lander longtitudes are now

VL1: 47.95 deg West

VL2: 225.72 deg West

MPF: 33.25 deg West.

I have alerted my colleague Rob Schmunk as to this new calibration, but as of today (Friday December14) I don't think he as implemented this for our on-line Mars clock.

As I have noted to the MCWG, the new W definition is actually quite close to the equivalent Vm adopted by Mayo et al. (1977) in their analysis of the Viking Lander radio tracking. Sometime between then and about 1991, there was a huge 0.2-0.3 deg forward jump in the IAU definition of W. This was about the time that people switched from the B1950 to the J2000 epoch conventions. I suspect (but cannot yet prove) that the jump might have reflected an erroneous propagation of the difference in W as referred to the 1950 and 2000 equinox and ecliptic coordinates.

So this is my news on Mars solar timing. Hope you have a good weekend, Tom.

Regards,

Michael