During our investigations of the twangs in the ACC1A data of the GRACE spacecraft we detected a significant influence onto the spatial distribution and shape of the twangs due to direct solar impacts, which shall now be referred to as group 2. As the GRACE satellite orbit is not sun-synchronous, the spacecraft go through a variety of phases with respect to eclipse and illuminated phases, where different planes of the spacecraft may be directly impacted by
12.2 Group 2 - βprime impact 107
Figure12.2:PositiveTwangs,GRACEB,2002-2010.
108 12.2 Group 2 - βprime impact
Figure12.3:NegativeTwangs,GRACEB,2002-2010.
12.2 Group 2 - βprime impact 109
Figure 12.4: Solar impact onto the zenith surface of the GRACE spacecraft by means of twangs of GRACE B.
the sunlight. The cycle of GRACE’s position and attitude with respect to the sun is known as theβprime-cycle and is with 322.3 days shorter than the annual period of approximately 365.25 days. As these two periods are nonetheless rather close to each other a long time-span of data needs to be considered in order to distinguish between the annual, i.e. seasonal, impact and the βprime-cycle influence. In figure 12.4 the twangs and the according solar impact onto the zenith surface of the GRACE B spacecraft are displayed. The βprime-cycle can be observed by the orange-red colored patterns that lean towards left or right with approximately 2007.5 as a center point. Here, the shift with respect to the season, and thus an annual period, can be observed.
There are several patterns of twangs that can be correlated to the βprime-cycle. For instance, the structures formed by twangs that are located near and around the poles (corresponding latitudes 90 and 270 degrees). When the spacecraft are approaching the polar area, this structure resembles a W-shaped pattern (as visible in figures 12.2 and 12.3), and is slightly less distinct when the satellite leaves this area. The orientation of this pattern is reversed for GRACE A and B. This pattern, however, is independent of a direct solar impact onto the GRACE spacecraft but does shift according to theβprime-angle. Beyond this, there are other cloud-like patterns at top and bottom of the rather oval shaped areas in the center latitudes of the figure that correspond to the solar impact cycle. These are only observable when the GRACE spacecraft are in direct sunlight.
In this chapter we want to address the question when which surfaces of the spacecraft are illuminated by the sun, and how this may affect the spatial distribution of the twangs and their behavior by means of shape and duration. In the previous chapter (cf. IV) we already stated that the oval pattern detected in the figures displaying the twangs for every day of the year with respect to the argument of latitude of the satellites orbits are caused by a direct solar impact onto the nadir surface of the satellite.
First we will show which outer surfaces of the satellites are illuminated at which parts of the orbit, and then we will emphasize in which of these cases the twangs are corresponding to the direct solar impact. A broader selection of figures concerning the illuminated satellite surfaces as
110 12.2 Group 2 - βprime impact
Figure 12.5: Schematic view of how Earth’s shadow is eclipsing the satellite (full shadow) and penumbra (semi-shadow).
contained within this chapter is provided in the Appendix D of this thesis. To aim at a better comprehension most images in this chapter will display twangs and scenarios of the year 2008, as most results in chapter IV have been a reference to this year as well.
Determination of solar impact on spacecraft surfaces
In order to determine which parts of the satellite are exposed to direct sunlight several facts need to be known. One parameter is the position of the satellite in orbit, which can be derived from the GNV1B data solution, provided by the major data distribution centers (cf. 6.3.1). This file contains the navigation solution for each satellite, derived by the on-board GPS assembly.
Another important parameter that needs to be known is the attitude of the spacecraft in orbit.
For this, the orientation provided by the star camera assembly of the GRACE spacecraft can be used, which is contained in the SCA1B data solution (cf. 6.3.3). With these two pieces of information the incidence solar angle upon the surfaces can be computed. This angle describes the orientation of the surfaces towards the sun, where 1 (if given as a cosine), 90° or 100% means that the normal of the surface is directly pointing towards the sun.
This approach, however, only applies for the center of the satellite’s reference system, for which those two data sets are given. As we already stated in the introduction to this chapter, twangs may behave differently if a special surface of the satellite is illuminated. Each surface of the satellite has a different incidence angle, depending on the direction in which the normal vector of the surface is pointing. In order to compute the incidence angle for each panel an exact model of the shape of the GRACE spacecraft needs to be taken into account. A description of the planes and the design of the GRACE spacecraft is given in chapter 3.
Further information that needs to be taken into account is the position of the Earth and Moon relative to the vector of the satellite to the sun. This is necessary as both objects may eclipse the satellite from sunlight or put it into a penumbra shadow, which is a part of the shadow where the light source is only partially blocked. A schematic view of how the Earth is blocking the light from the sun is given in figure 12.5. The computation of the solar impact onto the GRACE satellite planes has been carried out by Dr. ir. Eelco Doornbos of TU Delft in the Netherlands (Doornbos (2012)).
In figure 12.6 on the left side we display the direct solar impact onto the nadir surface of the GRACE spacecraft for each twang. The image displays each twang in the corresponding day it
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Figure 12.6: Solar impacts on GRACE B satellite (due to the small separation distance between the GRACE spacecraft also valid as a reference for GRACE A). Each dot represents a twang which is colored correspondingly. Left image: Solar impact onto the nadir surface of the satellite only - the scale displays the impact onto the plane, where at 100 per cent the sunrays are perpendicular to the plane. Right image:
Solar impact and eclipse onto satellite as a two color schematic.
occurred in the year 2008, and the argument of latitude. Black means that the nadir surface of the satellite was not exposed to any direct sunlight at the time and position of the twang, the other colors indicate the impact, where 100 per cent indicates a cosine incidence angle of 1, which means that the sun rays are impacting the surface perpendicularly. It is obvious that the pattern created in this image by the area in which the nadir surface of the satellite is exposed to direct sun rays is a strict correlation to the pattern previously introduced in most figures of the chapter 11, for example figure 11.5 on page 99. The areas within the oval shaped regions are a total eclipse phase, which can be deduced from the right image of figure 12.6. The left image of figure 12.6 is giving evidence for the fact that the nadir surface is influencing the asymmetry and shape of the twang significantly when it is exposed to direct sunlight (cf. chapter 11). This becomes more obvious when comparing this figure to figure 11.5, as the change of values for the asymmetry is more distinct towards the inner boundary, where the satellite is entering a complete eclipse phase, than towards the outer boundary. Corresponding to this, the eclipse phase is entered very suddenly in terms of solar impact onto the nadir plane, whilst towards the outer boundary the impact value is decaying. Also for other areas the boundary between total eclipse of the satellite and an illuminated nadir surface of the satellite is very obvious. For example the curve described by the solar impact onto the nadir surface in figure 12.6 (left) between DOY 220 and 365 between argument of latitude degrees 0° to approximately 150°. Especially the inner boundary is represented by a very distinct line of twangs with rather distinct values for most parameters.
Another indicator for a direct solar impact onto the GRACE spacecraft can be deduced from the behavior of the amplitude of the twangs in the radial component when a comparison is made between those twangs, which are detected in sunlight and those, which were detected in total eclipse phase (cf. figure 11.2, page 97). Here, it appears that the amplitude for the twangs is slightly greater when the twang is occurring while the spacecraft is in total eclipse phase than when it is being exposed to direct sunlight.
In the near polar regions the amount of twangs appears to decrease in general as can be seen in any image displayed so far concerning the geographical twang distributions, but is especially obvious in the left image of figure 12.6 and in the following figure 12.7. In the polar regions,