Nonconservative force modelling

The nonconservative force model must take into account the complex geometry and material properties of the spacecraft. The spacecraft is treated as a combination of flat plates arranged in the shape of a box, with attached solar arrays and drag flaps (ie. 'Box-Wing' or 'Macromodel'). The solar radiation pressure, atmospheric drag, and Mars radiation pressure forces acting on each plate are computed and vectorially summed to compute the total nonconservative force acceleration acting on the spacecraft. The Mars radiation pressure includes the reflected solar radiation, and the natural thermal emission of the planet. The same approach has been used to model the nonconservative forces acting on other spacecraft, for instance TOPEX/Poseidon[19], TDRSS[20], and GEOSAT-Follow-On[21]. Self-shadowing of spacecraft elements is not considered. A ten plate box-wing model for MGS was derived from engineering drawings of the spacecraft[22,23]. The box-wing model included six plates for the spacecraft bus, and a total of four panels to represent the front and back sides of the +Y and -Y solar arrays. Each +Y or -Y panel is represented as a weighted sum of the area and material properties of the solar array yoke, the inboard solar array (which has gallium arsenide solar cells), the outboard solar array (which has silicon solar cells), and the drag flaps. The areas and reflectivities are summarized in Table 2. The reflectivity was assumed to be 80 percent diffuse and 20 percent specular. Multi-layer insulation (MLI) was assumed to cover the yoke and the spacecraft body. The spacecraft configuration in Feburary and March 1999 is depicted in Figure 1. In the spacecraft body-fixed frame, the +Z direction points at nadir, when MOLA is collecting data (MOLA, the Mars Orbiter Camera, and the Thermal Emission Spectrometer are located on the +Z face of the spacecraft bus). The +X direction is the axis through the stowed position of the High Gain Antenna.

Table 2: MGS Macromodel Characteristics
Panel	Area	Reflectivity	Comment
	(m2)
Solar Arrays
Yoke	0.499	0.65	MLI.
Inner Panel (front)	3.077	0.11	GaAs cells.
Inner Panel (back)	3.077	0.43	44 % white paint;
			56 % black substrate.
Outer Panel (front)	3.152	0.25	Si cells.
Outer Panel (back)	3.152	0.23	10 % white paint;
			90 % black substrate.
Drag Flaps	1.418	0.15	black kapton.
Composite (front)	8.146	0.20
Composite (back)	8.146	0.32
Spacecraft Bus
+X, -X	3.04	0.65	MLI.
+Y, -Y	3.37	0.65	MLI.
+Z, -Z	1.82	0.65	MLI.

 

Figure 1: Nominal MGS spacecraft configuration during Array Normal Spin.

The solar radiation pressure, Mars radiation pressure, and drag accelerations on Mars Global Surveyor are shown in Figure 2 for a 13 hour period starting at 11:00 on March 6, 1999. The dominant nonconservative force is the solar radiation pressure. The average total acceleration is 3.2 x 10^-8 m/s² for the solar radiation pressure, 5.4 x 10^-9 m/s² for the Mars radiation pressure, and 4.8 x 10^-10 m/s² for the atmospheric drag. The Mars radiation pressure peaks in the vicinity of the subsolar point due to the concentration of the planet's thermal emission and reflected solar radiation on the sunlight hemisphere[13]. It is merely fortuitous that the atmospheric drag is relatively unimportant compared to the solar radiation pressure. The Mars areocentric longitude on March 6, 1999 was 107, corresponding to summer in the northern hemisphere of Mars. Since Mars had past aphelion at this time, a substantial portion of the atmosphere had condensed onto the southern polar cap of Mars, reducing the mean density at the MGS altitude (370 to 430 km). By early 2000, Mars will have past perihelion. This, in combination with the onset of summer in the southern hemisphere, means that the the southern polar cap will have largely sublimated, and the expected atmospheric density at the MGS altitude (and hence drag acceleration) will increase by a factor of 10 to 100[24].

 

Figure 2: Nonconservative force model accelerations on Mars Global Surveyor computed from the MGS macromodel on March 11, 1999. The solar radiation pressure acceleration dominates at this time. The spacecraft operating mode affects the orientation of the solar arrays and the calculation of the solar radiation pressure. Through approximately 19:00 on March 11, the spacecraft was nadir pointing, and the solar arrays articulated, tracking the Sun. From about 19:00 through 22:00, the spacecraft was in Earth point and the solar arrays were held in a fixed orientation.