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6.2 The Shad ow Observations
The Shadow of Phobos on Mars 118
The similarity of the spacecraft to Phobos' orbit combined with Termoskan's anti- solar orientation (zero solar phase angle) conspired to put Termoskan's instantaneous field of view near the location of the shadow as it traveled across Mars' surface. However, because the spacecraft and moon were not actually in the same place, this orientation alone would have missed observing the shadow. "Fortunately," the spacecraft, and hence Termoskan, rocked slightly back and forth. Thus, Termoskan's instantaneous field of view rocked into and out of observing the shadow. This fortuitous combination of factors has allowed a unique analysis of the cooling from the shadow. This analysis gives never before available insight into the nature of the upper millimeter of Mars' surface in selected locations.
Tomas Svitek, working with Bruce Murray, did initial modelling and analysis of the shadow. I then independently produced a thermal model that reproduced Svitek's preliminary results. This model evolved just slightly into the form that is described as Model 1 here.
Since the time that the initial results were published in Murray et al. [1991], I have created two more detailed and realistic models. Here I present those models and their results for the first time. Model 2, my non-isothermal model, does not assume that the pre-eclipse temperatures are constant with depth as Model 1 did. Haberle and Jakosky [1991] compared theoretical considerations to Betts et al., [1990a]. They concluded that atmospheric effects are less important for eclipse derived thermal inertias than for diurnally derived thermal inertias. To test atmospheric effects, I created Model 3 by adding a downward atmospheric flux term to Model 2.
119
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The Shadow of Phobos on Mars 120
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6.2 The Shadow Observations
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Figure 6.4: East-West profile- VIS channel. Reflectance from Martian surface as measured by visible channel on Terrnoskan. The curves in the figure are again an average of ten scan lines.
Profile A is retrieved from just outside (south) of shadow region (15°S). Profile B is the same but
just north of shadow (13°S). Profile C goes straight through the middle of the shadow area
The Shadow of Phobos on Mars 122
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123 62 The Shadow Observations
South dimension of the shadow in both the visible and infrared. 1bis is an important independent demonstration of the absence of significant visible or infrared light scattering in the Termoskan instrument
There are seven factors that influence the shadow's shape and intensity. First is the geometric shape of Phobos. Phobos is in synchronous rotation about Mars, was illuminated nearly end on (except near the limbs), and exhibited a nearly circular cross section of about 21 km in diameter. A second effect is distortion due to projection onto the spherical surface of Mars. Phobos' orbit is equatorial and its shadow was being projected to only l4°S latitude at the time of Termoskan's observations. Thus, this effect was minor except near the limbs. Third is the distance from Phobos to where the shadow intersected Mars' surface. This distance changed only an insignificant amount over the time scale of the observation. Similarly, local topography could cause a significant distortional effect only if the shadow crossed through very major topographic relief, e.g., Valles Marineris. Fifth is the penumbral effect. The shadow of Phobos is always completely penumbral, deepest at its center, and diminishing toward the edges. Sixth, atmospheric scattering further diffuses the shadow, smoothing the profile and reducing its maximum depth while increasing its size over the purely penumbral effect. All of the above mentioned effects will influence any observations of Phobos' shadow.
In our observations, there is a further effect on the apparent shape of the shadow:
the relative motion of the spacecraft's field of view with respect to Phobos' shadow.
Termoskan is a scanning instrument and the geometry of the observation was unusual.
Phobos and the spacecraft were nearly coorbiting at the time of observation. Termoskan looked in the anti-solar direction - the same direction Phobos' shadow was projected.
Therefore, Termoskan's line scanning system tended to follow the shadow on the surface, causing an apparent elongation of the shadow in the panorama. Furthermore, there was modulation of the apparent shadow because of a slight E-W rocking motion of the spacecraft. Figure 6.6 shows telemetry data taken before and after the observing session.
The Shadow of Phobos on Mars 124
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Figure 6.6: Deviations of the spacecraft's field of view from looking anti-solar. The horizontal axis is given in Moscow TI.me (hour, minute). The vertical axis measures the deviation from the anti- solar direction (180°) in degrees and minutes. These telemetry data were taken before and after the
Termoskan panoramas. The upper graph corresponds to the time just before and just after the first
March 26 panorama. Similarly, the lower graph is for the second March 26 panorama.
125 6.3 Thermal Models of the Eclipse Cooling
It depicts the magnitude of the rocking motion as function of time. In Figure 6.1, the field of view rocked first past the beginning of the shadow, then progressively through the shadow, and finally past the end of the shadow. Thus, an apparently elliptical shadow appears first in the visible. Subsequently, there is a band of cooling in the infrared channel resulting from the shadow's passage.
I assumed the E-W rocking motion to be uniform over the brief shadow observation shown in Figure 6.1. I also assumed that the N-S shadow length was unaffected by the rocking. Then, I calculated angular rocking motion by comparing the additional E-W shadow length (in seconds) to the N-S length. The angular rate found is 3 x lQ-5 radians/second, in good agreement with the spacecraft data of Figure 6.6.