Method of Solution

Least squares normal equations were created for the tracking data in February 1999 and March 1999, and these normal equations were merged with the normal equations of the earlier MGS data from Hiatus and SPO, and the historical data from the Viking Orbiters and Mariner 9. The SOLVE program, a companion program to GEODYN which combines and manipulates normal equations, was used to obtain the least squares solutions [25]. No changes were made to the processing of the historical Mariner 9 and Viking Orbiter data described in Lemoine et al.[6]. The Mars gravity solutions were computed using least squares collocation[26,27]. An a priori Kaula-type power law constraint was applied in the derivation of the gravity solutions. The power law 13.0 x 10^-5/l²was applied in the MGM0890 and MGM0890I solutions, whereas the power law x 13.0 x 10^-5/l² was used in MGM0964C5A, MGM0964C18, and MGM0964C20.

A sequence of solutions were developed that gradually included more data, and refined the models. This paper summarizes the performance of five landmark models developed at NASA GSFC that included the new tracking data from the MGS, low-altitude, mapping orbit:

1. MGM0890, the a priori model[6] to 70x70 that included MGS data from Hiatus and SPO, as well as the historical tracking.
2. MGM0890I, a solution to 70x70 that included 19 days of GCO data from February 4, 1999 through February 23, 1999, in the form of one-day arcs.
3. MGM0964C5A, a 70x70 solution that included all the available data in February and March 1999. The February data were processed in three day arcs, whereas the March data were processed in one-day arcs. the MGS Doppler tracking data from February were upweighted from an effective weight of 7 mm/s to 0.357 mm/s.
4. MGM0964C20, a 70x70 solution derived from the normals were recreated based on data reductions using the MGM0964C18 solution and improved quaternion files for the spacecraft and the solar arrays. In this solution the February 1999 data were processed in three day arcs, whereas the March 1999 data were processed in four to five day arcs. Both the February and March 1999 data were weighted at 0.357 mm/s (0.01 Hz).

Whereas MGM0890, MGM0890I, and MGM0964C5A continued to incorporate the historical Mariner 9 and Viking Orbiter tracking. The MGM0964C18 and MGM0964C20 solutions only included the MGS data from Hiatus, SPO, and the low-altitude mapping orbit. The new MGS tracking data from the low-altitude, near-circular orbit completely supercede the historical data in both quality and coverage. Indeed, as will be shown it is possible to fit the historical data almost as well with MGS only gravity solutions (MGM0964C18, and MGM0964C20), as with solutions that incorporate the historical data (MGM0890I, MGM0964C5A).

Table 3: Summary of Mars Gravity Solutions
Model	Include	No. of observations		Effective Data Wt.		Kaula Power
	historical	Hiatus		(mm/s)		Law
	data	& SPO	Mapping	Feb. 99	March 99	Applied
MGM0890	yes.	257,165	0	7.14	7.14	13.0 x 10-5/l2
MGM0890I	yes.	257,165	66,605	7.14	7.14	13.0 x 10-5/l2
MGM0964C5A	yes.	257,165	96,486	7.14	7.14	13.0 x 10-5/l2
MGM0964C18	no.	257,165	96,483	0.36	7.14	13.0 x 10-5/l2
MGM0964C20	no.	257,165	93,030	0.36	0.36	13.0 x 10-5/l2