FUTURE GRAVITY MISSION SCENARIOS INVOLVING TWO PAIRS OF DRAG-FREE SATELLITES

Bender, P. L. (1), Wiese, D. N. (2), and Nerem, R. S. (2)
(1) JILA, Univ. of Colorado and Nat. Inst. of Standards & Technology, Boulder, CO 80309, USA
(2) Dept. of Aerospace Engineering Science and Colorado Center for Astrodynamics Research, Univ. of Colorado, Boulder, CO 80309, USA

In investigating possible scenarios for future Earth gravity missions, it seems useful to consider particularly what can be accomplished with two pairs of drag-free satellites. However, since the GRACE-2 mission is not expected to be drag-free, the performance that hopefully can be achieved with a single pair of drag-free satellites plus GRACE-2 also will be discussed briefly.

Putting two pairs of satellites with laser interferometry between them into polar or near polar orbits does not appear to be the optimum approach. Polar orbits will be considered here for simplicity, although having at least one pair in a sun-synchronous orbit certainly deserves to be looked at also. The well-known weakness of having both pairs polar is that the ground tracks for south-to-north (S-N) and N-S passes only make an angle of 0.13 radians, and thus the W-E gradients in the geopotential at satellite altitude are considerably less well determined than the S-N gradients, if measurement noise is the main limitation. The sensitivity to temporal aliasing also appears to be fairly high.

An alternate approach is to have one pair in a polar orbit and the second pair in an orbit with a moderate inclination I of perhaps 50 to 65 deg. This architecture will be assumed in the rest of this talk. As an example, we will assume 360 km altitude, a repeat ground track after 201 revolutions, and I = 55.8 deg. The repeat period is 12.8 days. This ground track repeat period is considerably less than the 22.7 day period assumed in an earlier study [1]. However, the maximum spacing between ground tracks near the equator is still only 199 km, and this coverage appears to be dense enough so that little information will be lost because of the gaps.

The main argument for putting one pair of satellites in a moderate inclination orbit has to do with short wavelength variations in the satellite altitude geopotential height in the east-west direction. For polar orbits, such variations have to be determined by combining data taken at quite different times, and thus fairly large variations in atmospheric and oceanic mass distribution models at low frequencies can affect the results. For orbits where the crossing angles are much larger over most of the globe, it is only the variations in the short wavelength model errors over the repeat period of perhaps 10 to 15 days that will be important, if the filtering of the data is done properly.

Probably the most important questions concerning this architecture are the effects of temporal aliasing on the results. Some of the effects based on spherical harmonic analysis for missions of this kind will be described in another talk by Bryant et al.. However, the limitations will be discussed in this talk from a local analysis point of view, based on the well-known constant orbital energy approximation. Uncertainties in ocean tide models will not be included, since attention will be focused on land areas not too close to coastlines.

The polar pair of satellites, in addition to filling in coverage of the polar regions, will provide strong ties between the highest latitude parts of the orbit for the moderate inclination pair. The coverage by the moderate inclination pair will be quite dense after only one day for the region within a couple of degrees of the maximum latitude. And the polar pair will give ties between parts of the moderate inclination pair orbit about 12 hours apart in time. Thus the combination will give quite dense coverage for at least a small part of the globe, and thus hopefully minimize temporal aliasing for this region. In view of the short arcs across the poles that are involved, it is possible that the polar pair not being drag-free would not be a serious limitation, although this has not yet been studied.

[1] Bender, P. L., Wiese, D. N., and Nerem, R. S., 2008, "A Possible Dual-GRACE Mission with 90 Degree and 63 Degree Inclination Orbits", in Proc. 3rd Int. Symp. on Formation Flying, Missions and Technologies, 23-25 April, 2008, Noordwijk, The Netherlands, European Space Agency Symposium Proceedings, ESA SP-654.