determination and control
3.4 Attitude actuators
3.4.2 Cold gas thrusters
Figure 3.22:The principle of attitude control using cold gas thrusters
The thrusters are designed to be secondary attitude actuators for GRACE. They are activated only when the control torques generated by the magnetic torquers do not suffice to maintain the desired attitude. The thrusters operate based on adaptive strategy. This means the length of the pulse depends upon the strength and the results of the preceding ones. In other words, if the first correction was too small, the second will be slightly larger, the third even larger or smaller again etc. (Herman and Steinhoff, 2012).
The geographical location of the thruster activations is shown in Figure 3.23. The roll thrusters are activated mainly along the geomagnetic equator, because the efficiency of the attitude control about the roll axis using MTQ is very low in this region. In contrast, in this particular region, the attitude about the yaw axis can be controlled well using MTQ, but at high latitudes, thrusters need to be activated in order to generate the required control torque.
The pitch thrusters are activated very rarely, because the magnetic torquers suffice to control well the rotation about the pitch axis at any position along the orbit. The statistics with the number of thruster activations per day and the propellant consumption can be found in Section 6.2.
(a) roll (b) pitch
Figure 3.23: Geographical location of thruster activations in roll, pitch and yaw for a time span of 18 days (Jan 1st-18th 2008) for GRACE-A ascending orbit
The attitude control using thrusters has two critical limitations for the mission operation.
The first limitation arises from the fact that the propellant is non-renewable. The second
Table 3.2:Number of activation cycles of the roll, pitch and yaw thrusters during 2002-2007, i.e. at the planned mission lifetime, and during 2002-2014. The 106 cycles were exceeded already by the roll and yaw thrusters,
pitch thrusters are well below this limit
2007 2014 2007 2014
roll 0.45 106 1.00 106 0.39 106 1.00 106 pitch 0.19 106 0.35 106 0.10 106 0.38 106 yaw 0.55 106 1.31 106 0.38 106 1.27 106
limitation is thruster operation which is guaranteed only up to certain number of activation cycles.
OnceGN2 propellant is completely depleted, the attitude control using thrusters is no longer possible. Because the magnetic torquers alone do not suffice to control the satellite’s attitude along the whole orbit, the thruster outage will be fatal for the maintenance inter-satellite pointing. Consequently, the inter-satellite ranging which is one of the primary observations needed for gravity field recovery, will not be performed anymore.
This fact was properly taken into account in the mission design. For the planned 5 years of GRACE operation, enough fuel was stored onboard for the mission operation. Figure 3.24 shows the amount of fuel onboard since the beginning of the mission until today. Clearly, in 2007, i.e. at the predicted mission end, only 10 kg onboard GRACE-A and 8 kg onboard GRACE-B out of 32 kgGN2 was exhausted. Luckily, GRACE operated most of the time during the solar cycle minimum (Figure 3.25), hence the disturbing torques due to the atmosphere and the solar radiation were minimal. At the end of 2014, there was still∼9 kg and∼10 kg fuel left onboard GRACE-A and GRACE-B, respectively.
Today the mission keeps operating already 8 years after its planned termination. As the current goal is to operate the mission as long as possible, the fuel amount left onboard is one of the major concerns for the mission extension. The fuel consumption depends not only the efficiency of the attitude control strategy, on the magnitude of the disturbing torques acting upon the spacecraft and the efficiency of magnetic torquers, but also on the accuracy of the attitude data delivered by the primary star camera. The latter is further discussed in Chapter 6.
The functionality of the thrusters is guaranteed by the manufacturer up to 106 activation cycles. This apparent limitation became a concern first in the last years, when the nominal limit of 106 activation cycles was exceeded for the yaw and roll thrusters. Fortunately, all thrusters continue to operate well, hence this limitation seems to be not so critical so far.
20020 2004 2006 2008 2010 2012 2014 5
10 15 20 25 30
planned mission termination
Figure 3.24: Propellant consumption onboard GRACE-A and GRACE-B during the whole mission operation
19900 1995 2000 2005 2010 2015
20 40 60 80 100 120 140 160 180
Figure 3.25: The solar activity (number of sunspots) during the GRACE mission operation period. Data source: http://solarscience.msfc.nasa.gov/SunspotCycle.shtml
having no wings is just a little detail.
Jane Lee Logan
-Inter-satellite pointing 4
The inter-satellite pointing is the very fundamental requirement for the inter-satellite ranging technique, which is one of the GRACE primary observation techniques (cf. Section 2.3.2).
The measured range is related to the phase center (PhC) of each antenna horn and hence the goal is to keep the antenna phase centers aligned with the line-of-sight (LOS), which is the imaginary straight connection line between the satellites’ center of mass.
One of the challenges related to the inter-satellite pointing is its maintenance in orbit. The precise pointing is maintained in the science mode and back-up science operational mode in which all scientific measurements needed for the gravity field recovery are collected. In the ideal case, the PhCs should be perfectly aligned with the LOS (Figure 4.1(a)). However, due to continuous attitude perturbations caused by both external and internal torques, such as the aerodynamic torque, magnetic torque, Earth’s gravitational torque, solar radiation torque or due to propellant motion inside the tanks, the attitude variations are inevitable (Figure 4.1(b)).
The characteristics of the inter-satellite pointing variations are discussed in Section 4.4.
The requirements on the inter-satellite pointing are defined by the so called deadband which is the maximum allowed angular deviation of the CoM-to-PhC vector relative to LOS. The deadband is set to 3 mrad for roll and 4 mrad for pitch. The value of the yaw deadband was changed several times during the mission operation, it was set to 4.0 mrad since 2002, 4.4 mrad since October 2007, 4.8 mrad since June 2008 and 5.2 mrad since January 2012 (Herman and Steinhoff, 2012).
There are two major reasons for keeping the inter-satellite pointing variations as small as possible. The first one is that the pointing jitter strongly affects the inter-satellite ranging observations. Consequently, the ranging observations need to be corrected for the imperfect pointing in the post-processing, cf. Section 4.5. The other reason is the multipath effect caused by the reflections of the microwave signal on the satellite’s surface elements.
Another challenging aspect is the in-flight and on-ground determination of the inter-satellite pointing. This requires precise attitude information, precise orbit information, and various calibration parameters related to the star cameras and to the KBR horns. The in-flight and on-ground processing significantly differ (see Section 4.2 and 4.3), hence any inconsistency in these input data will affect the accuracy of the inter-satellite pointing and consequently also the ranging observations (see Section 4.6).
52 4 Inter-satellite pointing
PhC measured ρ PhC
PhC measured ρ PhC
Figure 4.1: The ideal and the real inter-satellite pointing. In the ideal case, the PhC of the KBR antenna would be perfectly aligned with the LOS (a). In the real case, however, attitude variations due to continuous
perturbations are inevitable (b)