Best Gyroscope Usage To Maximize the HST Mission Lifetime

Transcription

1 Instrument Science Report ACS Best Gyroscope Usage To Maximize the HST Mission Lifetime Roeland P. van der Marel January 21, 2004 Abstract Without SM4, gyroscope survival is a critical factor for the HST Mission lifetime. I present a simple Monte-Carlo model to calculate the survival probabilities for various scenarios. I calibrate the model to reproduce and update more accurate, but somewhat outdated, calculations by Aerospace Corporation. Continued three-gyroscope guiding will become impossible by late January Subsequent two-gyroscope guiding will further extend the mission to late May 2007 (if no other hardware fails). I discuss the importance of alternative strategies. We can extend the HST Mission if we switch to two-gyroscope guiding sooner; this extends the lifetime of the gyroscope that is powered off. Starting two-gyroscope guiding by January 2005 could extend the HST Mission by another 10 months, to April Any 6-month implementation delay beyond January 2005 decreases the mission by 3 months. The 1-σ uncertainty in all the aforementioned 50% probability (median) dates ranges between months. To achieve maximum lifetime it is important to guide with the gyroscopes that have the lowest failure probabilities. This strategy is important during three-gyroscope guiding as well. I recommend that: (a) More detailed gyroscope survival models should be calculated to validate these results; (b) With knowledge of the individual gyroscope failure probabilities, an effort should be made guide with the gyroscopes for which these probabilities are lowest; (c) Implementation and testing of the two-gyroscope guiding capability should be expedited as much as possible; (d) A study should be undertaken of the (net) trade-off between 13 months of three-gyroscope observations and 23 months of two-gyroscope observations; (e) any remote possibility of one-gyroscope guiding should be actively investigated, since it is expected that one functional gyroscope will be available into 2009 or beyond. 1 Copyright c 2003 The Association of Universities for Research in Astronomy, Inc. All Rights Reserved.

2 2 1. Introduction The Hubble Space Telescope (HST) has six gyroscopes on board, three of which are required for scientific operations. Each gyroscope contains a spinning wheel inside a sealed cylinder. The gyroscopes provide a frame of reference for Hubble to determine where it is pointing and how that pointing changes as the telescope moves across the sky. After many years of extended use, gyroscopes ultimately fail. The possibility of being left with fewer than 3 functional gyroscopes has been one of the primary risks jeopardizing the continued operation of the observatory. For example, on November 13, 1999 the telescope entered a situation in which only two functional gyroscopes were left. The telescope was then unable to observe for the remaining 6 weeks until Servicing Mission SM3a in December All 6 gyroscopes were replaced during SM3a. Subsequently, Gyroscopes 3, 4, 5 and 6 were used for telescope control, either in a four-gyroscope configuration, or in a three-gyroscope configuration with one of the gyroscopes in shadow mode. The latter prevents the telescope from going into safe mode during a gyroscope failure. In March 2001 it was decided that it was more desirable to have the telescope go into safe mode rather than to accrue wear on one of the gyroscopes, and since that time only three gyroscopes have normally been in use. Gyroscope 5 failed in April 2001, after which Gyroscope 2 was brought into the control loop. No gyroscopes were replaced during Servicing Mission SM3b in March This choice was made to allow sufficient time during the mission to revive the Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) through the installation of a cryocooler. Gyroscope 3 failed in April 2003, after which Gyroscope 1 was brought into the control loop. No gyroscope failures have occurred since. So HST currently has four functional gyroscopes, of which three are actually being used (Gyroscopes 1, 2, and 4) and one is a backup (Gyroscope 6). Gyroscope 6 suffers from anomalous bias performance, but a software workaround has been developed to allow its use even if this bias performance further degrades with time. After the tragic loss of the Space Shuttle Columbia on February 1, 2003, it was realized that the next HST Servicing Mission SM4 might be delayed considerably. As a result, it became a possibility that the observatory would be left with less than three functional gyroscopes before it could be serviced again. An effort was therefore started to rework telescope commanding to allow scientific operations with only two functional gyroscopes. This mode will use the HST magnetometers for added control information. The possibility of pursuing this two-gyroscope guiding capability had become possible due to increases in on-board computing power. In SM3A the original DF224 spacecraft computer was replaced by a 486 upgrade. On-orbit tests of the two-gyroscope guiding capability are currently planned for April, June and October 2004, with an operational readiness review scheduled for January 2005 (Myers 2004). Full operation is not currently planned any earlier than the

3 3 spring of 2005 (Reinhart, priv. comm). On January 16, 2004, NASA announced the cancelation of SM4. This implies that HST will not be serviced again, and that HST will have to do with its current complement of gyroscopes for the remainder of its lifetime. Predictions for the expected lifetime are detailed in the document Expected HST Science Lifetime after SM4, which was presented by the HST Program Office to the HST-JWST Transition Review Panel ( The Bahcall Committee ) in July These predictions are based on calculations for the situation as it existed on July 1, The likelihood for HST to have less than three functional gyroscopes drops monotonically with time, and in these calculations it fell below 50% at the predicted date of December 1, After this, the telescope would have to switch to two-gyroscope guiding. This provides for another expected 15 months of operations before only 1 functional gyroscope would be left (Beckwith 2003). So as of July 1, 2003, the prediction was that on average one would not expect HST to have enough functional gyroscopes for operation beyond approximately March 1, In the development and planning of a two-gyroscope guiding mode the assumption has been that this mode would only be used after three-gyroscope guiding had become impossible. However, in light of recent developments it now seems worthwhile to reassess this assumption. An alternative approach is to start two-gyroscope guiding as soon as possible. The advantage would be that instead of using three gyroscopes until approximately December 1, 2005, we would be using two. This would have two advantages. First, it would decrease the overall probability of a gyroscope failure in this period by a factor 2/3. So the average predicted number of functional gyroscopes late in the mission would increase. Second, any gyroscope that is still functional late in the mission would on average have been used for a smaller period of time. Since the failure probability increases with past usage (due to wear) this implies that the probability of loosing a gyroscope at a fixed time late in the mission is smaller. As a result, the time at which HST would be expected to have only one functional gyroscope left out of the total complement of six would be pushed further into the future. Thus: the overall expected lifetime of HST can be increased by switching to two-gyroscope guiding as soon as possible. Given the drastic impact of the cancelled SM4, this might be very important for the HST mission as a whole. There are several down-sides to two-gyroscope guiding, apart from the fact that its functionality remains to be demonstrated. The main impact on data quality is that it degrades the quality of the HST Point Spread Function (PSF). The lack of a third gyroscope will generate increased jitter in one direction, yielding an elongated PSF. The jitter magnitude and direction will depend on which gyroscopes are alive, and the direction of elongation will change across the sky. The expected worst case jitter is mas

4 4 (Beckwith 2003). This will degrade the quality of science at the highest resolution, e.g., with the High Resolution Channel (HRC) of the Advanced Camera for Surveys (ACS), including coronagraphic work. However, such work makes up only 5% of the HST science program. Spectroscopy with the Space Telescope Imaging Spectrograph (STIS) and its smallest slits would also be affected. By contrast, science with the ACS Wide Field Channel (WFC) or with NICMOS would not be much affected. These modes comprise 70% of the HST science program. Observations of point sources would need to integrate slightly longer to achieve the same signal-to-noise ratio (S/N). For the WFC this would be a factor 1.3 for 25 mas jitter. On the other hand, not all observations observe point sources, and not all programs have limiting S/N as their primary constraint. Other disadvantages of two-gyroscope guiding are that operational aspects are less desirable than with three-gyroscope guiding. Two-gyroscope guiding will be more restrictive as to what targets are visible at any given time; orbit-to-orbit pointing registration will likely not be as good; moving targets will not be supported (at least in the initial implementation); scheduling efficiency in terms of orbits per week will be lower; adjacent visits may not schedule as close together in time; and orbits in which the South-Atlantic Anomaly leads to loss of normal visibility time are likely to be less usable. Advantages of extending the lifetime of HST by switching to two-gyroscope guiding as soon as possible would be: (i) to allow more HST orbits to be used; (ii) to provide a general purpose UV/optical/near-IR space facility to the worldwide astronomical community for a longer period of time; (iii) to provide more opportunity for target-of-opportunity observations late in the decade (the next supernova in the Milky Way...?); and (iv) to provide extended opportunity for follow-up studies based on new results from SIRTF or other observatories. And also, even if one chooses to do two-gyroscope guiding at an early stage, it might still be possible to perform selected high resolution studies with three gyroscopes in a campaign mode. The advantages of an extended mission will need to be weighed carefully against the disadvantages of using two-gyroscope guiding during a period in which three-gyroscope guiding had been possible. Also, there is a little point in extending the gyroscope lifetime if there is an expectation that other critical hardware components on HST will fail first. The batteries on the telescope are a prime candidate for this, although their actual lifetime is not entirely clear at the present time. Either way, the primary number of relevance for any trade-off study is the amount of time by which the HST lifetime can actually be extended by switching to two-gyroscope guiding before this is operationally imperative. The present ISR discusses simple models that provide an answer to this question. It also addresses the question which individual gyroscopes should be used at any given time so as to maximize the overall lifetime of the mission.

5 5 Fig. 1. Probability calculated by Aerospace Corporation of having three or more functional gyroscopes as function of time, based on the assumption that there are four functional gyroscopes on July 1, These predictions are now outdated. 2. A Simple Model for Predicting Gyroscope Survival Gyroscope failure probabilities can be calculated with fair accuracy. Performance histories are known, both from ground-testing and in-flight operation, across many programs, for over 90 gyroscopes similar to those in HST. Aerospace Corporation made a detailed calculation of the probability for having three or more functional gyroscopes on board HST, assuming that there are 4 functional gyroscopes on July 1, The results, taken from the HST Program Office Expected Lifetime Document (2003), are shown in Figure 1. For a detailed assessment of the questions posed in this ISR it will be necessary to redo the calculations in Figure 1, using up to date information and complete knowledge of the nature and failure modes of the individual gyroscopes. However, in the absence of such a calculation it is useful to construct a simple model that reproduces the main characteristics of the more detailed calculations that have been performed in the past. This simple model

6 6 then provides an efficient means to quickly explore the full parameter space of the problem, and to serve as a basis for more detailed investigation. The probability that a gyroscope fails at any given time is not a deterministic process. For example, there is no consumable (e.g., fuel or cryogen) in a gyroscope that gets used up at a known rate. In such a case one would be able to calculate with fair accuracy when exactly the consumable will be used up. However, a gyroscope can fail at any given time due to any number of potential random or wear-related failures. In this sense, gyroscope failure is a statistical Poisson process. A useful analogy is to think of lifetime predictions for humans, as used by the life insurance industry. To calculate probabilities for the future availability of functional gyroscopes I adopt a Monte-Carlo approach to simulate the Poisson process. With a simple FORTRAN program I calculate a simulated future M times. Each simulation i (for i = 1,..., M) starts with a known (or hypothetical) situation at a starting month m = m 0. Throughout this ISR I adopt a time-system in which month l in year 200X is represented by the number 12X + l. So January 1, 2004 corresponds to m = 49. The gyroscopes were installed on the telescope at m 0. It is assumed that in each month of the simulation, a gyroscope that is used for operations has a probability p of loosing its functionality. Whether or not a given gyroscope actually looses its functionality depends on whether a randomly chosen number between 0 and 1 has value p. Once a gyroscope looses its functionality, it is ignored for the remainder of the simulation. If there is a remaining functional gyroscope that isn t already in the control loop, it can be added at that time (depending on what approach one wants to simulate). This procedure is repeated month after month, until some month far in the future. For each simulation i, and for each month m, it is recorded what the total number n i (m) of functional gyroscopes on the telescope was at the end of the month. It is also recorded for each number N = 0, 1, 2,... what the first month m = µ i (N) is in which n i (m) < N. After the M futures have been simulated, several statistics are calculated. The quantity M µ (N) = (1/M) µ i (N) (1) i=1 is the average (expectation value) of the month in which the number of functional gyroscopes will for the first time fall below N. The dispersion in this number is given by [ 1/2 M σ µ (N) = {(1/M) µ 2 i (N)} µ (N)] 2. (2) i=1 The function Prob(N; m) = (1/M) M i=1 { 1 ni (m) = N, 0 n i (m) N, (3)

7 7 measures the probability at month m that there are still N functional gyros. The function Prob( N; m) = Prob(j; m) (4) measures the probability at month m that there are still N or more functional gyros. So the curve plotted in Figure 1 corresponds to Prob( 3; m m 0 ). The value m = µ med (N) is the month for which Prob( N; m) = 50%; so µ med (N) is the median expected month in which the number of functional gyroscopes will for the first time fall below k. In the calculations performed in the context of this ISR it was always found that µ (N) and µ med (N) differed by no more than 1 2 months, which is of order 10% of the statistical dispersion σ µ (N). In the remainder I therefore present only µ med (N) for the various models that are discussed. The expectation value of the number of functional gyroscopes at month m is given by j N n (m) = j 0 j Prob(j; m), (5) where the sum runs from zero to the maximum possible number of functional gyroscopes. The dispersion in the number of functional gyroscopes at month m is given by σ n (m) { j 2 Prob(j; m)} n 2 (m) j 0 1/2. (6) To fit the model to reality one needs to choose the probability p. The simplest assumption is to assume that p is a constant. This corresponds to unpredictable random failure with a given probability. While certainly part of the story, it doesn t reflect the fact that gyroscopes are more likely to fail after they have been used longer. Therefore, one should choose a probability p that increase with time. A simple functional form is p(u) = max{ p 0, [p 4 (u/48) b ] }. (7) Here u is the number of months during which a gyroscope has been used. The per-month probability of failure for a brand-new gyroscope (u = 0) is p 0. The power b determines how fast the failure probability increases with time due to wear. After four years of usage, the probability has increased to p 4. Several important simplifying assumptions are made here. First, it is assumed that the failure probability and its relation to usage is the same for all gyroscopes. This is not expected to be true in practice, due to known differences in the properties of the individual gyroscopes. Second, it is assumed that other factors than usage do not affect the probability. This is an oversimplification, because in reality other issues will almost certainly contribute as well, e.g., aging while not in use, and the number of times that a gyroscope was cycled on or off. This should be kept in mind when assessing

8 8 the predictions of the model. In particular, statements about the ensemble of gyroscopes are more accurate than those about any individual one, and the general trends predicted by the models are more accurate than the specific details. With some experimentation it was found that the Aerospace Corporation results in Figure 1 can be well approximated using parameters p 0 = 0.5%, p 4 = 3.13% and b = 2.5. The calculations in Figure 1 apply to the situation on July 1, 2003 (m 0 = 43). For this same value of m 0, the simple model presented here yields the probabilities Prob( N; m m 0 ) that are shown in the bottom panel of Figure 2 for N = 4, 3, 2, 1 (left to right). The top panel shows the probabilities Prob(N; m m 0 ) of having exactly N functional gyroscopes at any given time. The calculations assume that the usage for the gyroscopes at the start of the simulations is u 1 = 3, u 2 = 26, u 4 = 42, and u 6 = 14. These numbers are based on the HST Gyroscope Configuration Log (maintained by the HST project at OTA Hardware/RGA/RGA main.htm); see also the gyroscope usage history outlined in Section 1. Operation in shadow mode is counted as usage, because the gyroscope is turned on, even though its information is not used to control the telescope. Any usage in testing while still on the ground was ignored. The calculations in Figure 2 assume that three-gyroscope guiding is used as long as there are at least three functional gyroscopes, and that Gyroscope 6 is not used until one of the other ones breaks. The predicted function Prob( 3; m m 0 ) can be compared directly to the probabilities shown in Figure 1, and matches well. The median value µ med (3) m 0 in the calculations is 29.0 months, in agreement with the results quoted in the HST Program Office Expected Lifetime Document (2003). This is no surprise, because the adopted parameters in equation (7) were chosen to fit the curve in Figure 1. However, the predicted lifetime that can be achieved with two-gyroscope guiding was not considered. This quantity can therefore be used as an independent test of the predictions of the simple model. Indeed, the model does well. It gives µ med (2) µ med (3) = 16.1 months, which can be compared to the value of 15 months that has been quoted on the basis of Aerospace Corporation calculations (Beckwith 2003). 3. Comparison of Scenarios Now that there is a simple model that predicts the fate of the gyroscopes on HST in a statistical sense, it can be used to calculate and compare a variety of scenarios. The first order of business is to update the Aerospace Corporation predictions in Figure 1. Those predicted that HST would have a 50% probability of having less than 3 functional gyroscopes by December 1, However, this did not take into account the knowledge

9 9 Fig. 2. Predictions of the simple model described in this ISR, as function of the number of months after July 1, Top panel: probability of having N functional gyroscopes. Bottom panel: probability of having N or more functional gyroscopes. Curves are shown for N = 4 (solid), N = 3 (heavy), N = 2 (heavy dashed), N = 1 (long dashed), and N = 0 (dotted). The predictions are based on the assumption of having four functional gyroscopes on July 1, 2003, similar to the assumption underlying Figure 1. These predictions are therefore outdated. The model parameters were chosen so that the heavy curve in the bottom panel reproduces the more detailed calculations shown in Figure 1. that there are still four functional gyroscopes in January 2004; it only assumed there were four in July The fact that we have had no failure in the past 6 months pushes forward

10 10 the time at which HST is expected to have less than 3 functional gyroscopes. The reason for this is that the predictions in July 2003 included the possibility of failure in the subsequent six months, which has not happened. This possibility had a negative effect on the predicted lifetimes as of last July. Lifetime predictions for humans again form a useful analogy. The life expectancy (age at which 50% probability of having died is reached) for someone age 50, is to live to age 80. However, someone who is currently at age 75 will statistically be expected to live to an age of 86. So the expected lifetime increases by merely managing to continue living, even though the probability of expiring at any time continues to rise. To address this quantitatively for the HST gyroscopes, I repeated the calculations of Figure 2, but now starting with four functional gyroscopes at m 0 = 49 (January 1, 2004). The usage for the gyroscopes at the start of the simulations is u 1 = 9, u 2 = 32, u 4 = 48, and u 6 = 14. This yields the results in Figure 3. As function of m m 0, the curves have shifted to the left as compared to Figure 2. This is because the probabilities for gyroscope failure have increased due to aging. However, the shift is less than the 6 months that have elapsed between July 2003 and January So in a net sense, dates have shifted into the future, as expected. The predictions give µ med (3) m 0 = So the month in which the probability is 50% for having less than 3 functional gyroscopes is now late January The 1-σ uncertainty in this date is σ µ (3) = 11.0 months. Also, µ med (2) m 0 = 40.9, with a difference µ med (2) µ med (3) = 16.2 months. So in late May 2007 the probability of being able to do two-gyroscope guiding drops below 50%. The 1-σ uncertainty in this date is σ µ (2) = 12.9 months. These are the up-to-date predictions if we stick with our plans to do three-gyroscope guiding as long as we can, use Gyroscope 6 only when we have to, and switch to two-gyroscope guiding only when we have to. I will henceforth refer to this as the standard approach. Instead of using Gyroscopes 1, 2 and 4 for the time being, we could switch to another combination. In the model presented here, the probability for gyroscope failure increases with use. So if we want to optimize the time µ med (3) m 0 for which we can continue to do three-gyroscope guiding, then the best approach is to stop using Gyroscope 4, which has the most current usage (u 4 = 48), and to start using Gyroscope 6 instead. With this approach, it is predicted that µ med (3) m 0 can be pushed forward to 29.8, which is 5.1 months more than in the standard approach. We would then expect to be able to continue three-gyroscope guiding until late June However, the time µ med (2) m 0 at which we would expect two-gyroscope guiding to become impossible would only increase by 0.1 month as compared to the standard approach. The method that would maximize µ med (2) m 0 is actually to stop using Gyroscope 2. This predicts µ med (3) m 0 = 28.3 (early May 2006) and µ med (2) m 0 = 41.4 (mid June 2007). These results are illustrated in Figure 4. It shows the expectation value n of the number of functional gyroscopes as function of time. The

11 11 Fig. 3. Predictions as in Figure 2, but now taking into account the fact that we still have four functional gyroscopes as of January 1, 2004 (and not just as of July 1, 2003). These curves are the up-to-date predictions if we stick with our plans to do three-gyroscope guiding as long as we can, use Gyroscope 6 only when we have to, and switch to two-gyroscope guiding only when we have to (the standard approach ). The abscissa is the number of years that have passed since January 1, historically available number of gyroscopes, from their installation to the current epoch, is shown as well. In this representation, the expected time at which three-gyroscope guiding becomes impossible is when the curves drop below n = 2.5. The expected time at which two-gyroscope guiding becomes impossible, and when the HST Mission will presumably end,

12 12 Fig. 4. Number of functional gyroscopes as a function of time. The heavy solid histogram shows the known past behavior. The curves show the predicted expectation value n for cases in which we keep using three-gyroscope guiding as long as possible. The curves differ in which gyroscope is not used as long as there are four functional ones. The standard approach doesn t use Gyroscope 6 (heavy solid curve). The cases of not using Gyroscope 4 (short-dashed curve) and not using Gyroscope 2 (long-dashed curve) are shown as well. The error bars show the statistical uncertainty σ n on the predictions. is when the curves drop below n = 1.5. The heavy solid curve shows the expectation value for the standard approach. The short-dashed curve corresponds to the situation in which we stop using Gyroscope 4, and the long-dashed curve corresponds to situation in which we stop using Gyroscope 2. The dispersion (uncertainty) in the predicted number of functional gyroscopes is considerable, and ranges from σ n = in the period Now let s consider the situation in which we voluntarily switch to two-gyroscope guiding before we actually have to. Although two-gyroscope guiding is currently not planned any earlier than spring 2005, let s assume that with some effort we could make this step already on January 1, To make a specific prediction one needs to specify which gyroscopes will be used in each stage of the future of HST. To restrict the number of models to study, I assume that we can switch gyroscopes at the start of the simulation, that one gyroscope gets turned of on January 1, 2005, and that any other changes are made only when a gyroscope fails. I then performed calculations for all possible permutations of allowed choices, and selected the one that maximizes the HST lifetime µ med (2). The best strategy is the one in which: (a) we use Gyroscopes 1, 2 and 6 until January 1, 2005; (b) we turn off Gyroscope

13 13 Fig. 5. Predictions as in Figure 3, but now assuming that we use three-gyroscope guiding until January 2005, and then switch to two-gyroscope guiding. The break in the curves is due to this change in strategy. Whenever a change is made in the gyroscope complement used for telescope control, the best strategy is to give control to the gyroscopes with the smallest probability for failure (i.e., in the model these are the gyroscopes with the lowest past usage). This approach is expected to extend the lifetime of the HST mission by 10 months, as compared to the standard approach in which we continue to use three-gyroscope guiding for as long as we can (Figure 3). 2 on January 1, 2005; (c) we turn on Gyroscope 2 before Gyroscope 4 whenever there is a gyroscopes failure. In other words, this strategy uses at each stage those gyroscopes that

14 14 have the least usage, and hence the smallest probability for failure. With this strategy one obtains the predictions in Figure 5. They give µ med (3) m 0 = 41.6 and µ med (2) m 0 = The 1-σ uncertainties are σ µ (3) = 16.4 months and σ µ (3) = 16.0 months. So we would expect to have at least three functional gyroscopes until mid-june 2007, and at least two functional gyroscopes until approximately early-april These dates are, respectively, 16.9 and 10.2 months further into the future compared to the standard approach. So with prudent use of the gyroscopes we could potentially add some 10 months to the lifetime of HST. Figure 6 compares the predictions of this model (short-dashed curve) to the standard approach (heavy solid curve), by showing the expectation value for the number of functional gyroscopes (similar to Figure 4). The dispersion (uncertainty) in the predicted number of functional gyroscopes ranges from σ n = in the period The long-dashed curve shows another model that switches to two-gyroscope guiding on January 1, 2005, but which doesn t optimize the order in which the gyroscopes are used. This approach is based on the current and past priority setting used for telescope control: Gyroscope 6 is not used until we have to, and when a gyroscope is removed from the control loop we choose the one that was added most recently. This strategy still extends the HST mission by 5 months. So in the optimum model (which extends the mission by 10 months), half the gain comes from switching to two-gyroscope guiding on January 1, 2005, and the other half comes from adopting the best order for using the gyroscopes. The calculations were repeated for other dates of switching to two-gyroscope guiding. The results show that for every six-month delay beyond January 1, 2005 in starting the use of two-gyroscope guiding, the mission lifetime decreases by 3 months. It is therefore important that the development of the capability for doing two-gyroscope guiding be expedited as much as possible. 4. Discussion and Conclusions In the absence of a servicing mission SM4 it is of vital importance to extend the HST Mission for as long as possible with the presently available hardware and software. The longevity of the gyroscopes on HST provides probably the most critical factor, although certainly not the only one, that determines the amount of time for which we can realistically expect to operate HST. In this ISR I have presented a simple Monte-Carlo model that yields predictions for the future survival of the gyroscopes. The model is used to generate predictions for a variety of possible approaches of operating the observatory in the years to come. The results provide important insight that will aid decisions on what the best course of action will be.

15 15 Fig. 6. Number of functional gyroscopes as a function of time, as in Figure 4. The heavy solid curve is the standard approach, and keeps using three-gyroscope guiding as long as possible. By contrast, the dashed curves assume that we switch to two-gyroscope guiding on January 1, The short-dashed curve is for the model shown in Figure 5. Whenever a change is made in the gyroscope complement used for telescope control, this model gives control to the gyroscopes with the smallest probability for failure. The long-dashed curve uses a strategy based on current priorities: Gyroscope 6 is not used until we have to, and when a gyroscope is removed from the control loop we choose the one that was added most recently. These strategies extend the HST mission by 10 and 5 months, respectively. The error bars show the statistical uncertainty σ n on the predictions. The model is calibrated to reproduce the results of more detailed calculations by Aerospace Corporation performed 6 months ago. The calibrated model is then applied to the present day situation to yield the following updated predictions. If we continue to use three-gyroscope guiding for as long as we can, and do not start using Gyroscope 6 until we have to, then in late January 2006 the probability is 50% that this will become infeasible because of an insufficient number of functional gyroscopes. Assuming that the capability to guide using two gyroscopes is successfully implemented, the probability is 50% that this will extend the HST Mission to late May I have argued, and demonstrated quantitatively, that the HST Mission can be extended beyond these predicted dates if we switch to two-gyroscope guiding as soon as possible, rather than to wait until we only have two functional gyroscopes left. If we do this on January 1, 2005, about 1 year from now, then we could potentially extend the HST Mission

16 16 by 10 months, until early April 2008 (50% probability). In this case the net trade-off is between doing 13 months of observations with three gyroscopes or 23 months of observations with two gyroscopes. Two-gyroscope guiding does have disadvantages, so the scientific pros and cons of this choice will need to be weighed carefully, as discussed in Section 1. Either way, it is important that the development of the capability for doing two-gyroscope guiding be expedited as much as possible. For every six-month delay beyond January 1, 2005 in starting the use of two-gyroscope guiding, the mission lifetime decreases by 3 months. Only half of the 10 month gain in the optimum approach is due to the switch to two-gyroscope guiding on January 1, The other half is due to adopting the best order for using the available gyroscopes. Even if we stick with the approach of doing three-gyroscope guiding for as long as we can, adopting the best order for using the available gyroscopes is still important. While with that approach it will not significantly extend the HST mission, it may be able to extend the period during which three-gyroscope guiding is possible by 5 months, i.e., until late June The best order is always characterized by the fact that the gyroscopes with the lowest probability for failure are used first. The reason for this is that it minimizes the probability of being left with one gyroscope at the end of the mission that still has a lot of life in it. The optimum situation is to be left with one gyroscope at the end of the mission that is almost ready to fail. In my models the gyroscopes with the lowest probability for failure are the ones with the lowest past usage, namely Gyroscopes 1 and 6. This is an oversimplification because other factors are important as well. In particular, Gyroscopes 1 was constructed with an older mechanism for filling the gyroscope cavity with fluid, using oxygen-pressurized air. The corrosive properties of oxygen increase the failure probability for the flex leads in the gyroscope, as compared to the newer gyroscopes that were filled using nitrogen. Gyroscope 6 suffers from anomalous bias performance, which has not been seen in any other previous gyroscope. It is therefore unknown whether this anomaly increases the probability for gyroscope failure. So even though Gyroscopes 2 and 4 currently have the higher past usage, it is not a priori clear whether they have the highest present-day failure probability. If they don t, then some of the potential gains reported in this ISR will not be achievable. The solid and long-dashed curves in Figure 6 would then be the best that we can do. Even so, switching to two-gyroscope guiding on January 1, 2005 would still extend the HST mission by 5 months. Either way, the important point is that the failure probabilities of all four gyroscopes should be calculated or estimated as well as possible. The ones with the lowest failure probabilities should then be used for telescope control. The gyroscope complement put in use for guiding directly after SM3a was chosen because it gave the lowest telescope jitter. There is no reason that this combination would also give the longest HST Mission lifetime. In the present circumstances, the latter is likely to be the more important

17 17 consideration to base gyroscope usage on. The assumption at present is that the observatory cannot be used when only one functional gyroscope remains. However, it seems worthwhile to investigate whether some form of (crude) pointing and guiding may not be possible anyway. As shown by Figures 5 and 6, this would be expected to extend the mission well into Of course, all this assumes that failure of other hardware components does not terminate the mission before lack of gyroscopes does. This is an optimistic assumption, especially as far into the future as 2009 (see the HST Program Office Expected HST Lifetime Document, 2003). Based on the calculations presented here I recommend the following actions: (a) The gyroscope survival rates should be recalculated with more detailed models (e.g., by Aerospace Corporation) for the same approaches discussed here, to validate the results obtained with my simpler model; (b) With knowledge of the individual gyroscope failure probabilities, an effort should be made to use only the gyroscopes with the lowest failure probabilities to control the telescope; (c) The implementation and testing of the two-gyroscope guiding capability should be expedited as much as possible; (d) A scientific trade-off study should be undertaken to weigh the value of an extended HST mission against the disadvantages of having a longer period of guiding with only two gyroscopes; and (e) Even a remote possibility of some form of one-gyroscope guiding should be actively investigated, since it has the potential to extend the mission into 2009 or beyond. I am grateful to Merle Reinhart and Ron Gilliland for proofreading early drafts of this ISR, and for providing information and thoughts on the workings of the HST gyroscopes and the potential scientific trade-offs to be considered for switching to two-gyroscope guiding. References Beckwith, S. 2003, Hubble Science Without Servicing (presentation to the NASA/OSS Origins Subcommittee; October 23, 2003) [spacescience.nasa.gov/admin/divisions/sz/seus0310/beckwith Extension.pdf] HST Program Office (NASA/GSFC) 2003, Expected HST Science Lifetime after SM4 (presentation to the HST-JWST Transition Review Panel; July 21, 2003) [hst-jwst-transition.hq.nasa.gov/hst-jwst/hstexpectedlifetime.pdf] Myers, C. 2004, Two-Gyro Science (TGS) Mode Status (internal STScI Mission Status Review presentation; Jan 13, 2004) [ MSRs/2004/January/5 Two Gyro.pdf]