Projecting SAA-Free Times

Below is a periodically updated (every week or so) list of the projected start and end times of the SAA-free periods of the HST
orbit as determined from the SOGS scheduling software for each SAA model.

Projected SAA-Free Start/End Time Models from Current Extrapolated Orbit File:
SAA Model 02 (FGS guiding)	SAA Model 05 (FGS exposures)	SAA Model 23 (NICMOS)
SAA Model 24 (STIS/CCD)	SAA Model 25 (STIS/MAMA)
SAA Model 27 (ACS/SBC)	SAA Model 28 (ACS/CCD)
SAA Model 29 (WFC3/UVIS)	SAA Model 30 (WFC3/IR)
SAA Model 31 (COS NUV/MAMA)	SAA Model 32 (COS FUV/XDL)

This data should be understood in the proper context.
Changes to the ephemeris occur, and estimates of the SAA crossings become
increasingly uncertain the further into the future the projection
is made. Typically, the uncertainty is a function of the
error in the nodal regression rate, with added uncertainty due
to HST's in-track position. These two uncertainties can be
considered in their effect independently (although, in fact, they are not
and they are both manifestations of precession error):

• In-Track Error can shift the start-end times by up to +/-48 minutes.
  
• In-Track Error can shift the duration of the crossing times.
  
• In-Track Error can add or take away SAA-crossings which occur at +/-1 orbit separations from the start/ends.
  
• Nodal-Regression Rate Error can shift the start-end times by integer numbers of orbits.
  (when in-track error accumulates to greater than a single orbit)
  

The in-track uncertainty can directly be thought of as influenced by the variable rate of atmospheric drag on the telescope.
The graph below shows the relationship between constant amounts of error in the drag-rate, in-track error, and the duration
between when the ephemeris was generated and when the projection is to be made for.

Note the log-log plot above expresses something fundamental about the in-track uncertainty: in-track error grows quadratically in time. If the
uncertainty is 'x' at some time 'T', then at time '2*T', the uncertainty will be 4 times larger.

The HST extrapolated orbit file contains (currently) no altitude decay rate, so the in-track error for the times corresponds
directly with the contours in the plot. For the 10-week orbit file, the events do have a decay rate applied, so the contours
in the plot would correspond to the error in the decay rate used to fit and produce the orbit file.

The decay rate is variable and not predictable beyond approximate levels. The decay rate is a function of the ballistic
profile of HST (which changes each orbit) and the level of solar activity and its history. Generally, decay rates are highest
during solar-maximum, and least during solar minimum. The decay rate uncertainty is a function of the projection time
interval. In the plot below, the altitude decay rate history of HST is plotted from launch to the current time-frame with
49-day and 1-year rolling averages. To get an estimate of the solar activity level in some future year, subtract the
approximate duration of the solar cycle (11.4 years) and compare with the plot. However, each solar cycle is different in
intensity and duration (and even period), so such projections are only approximate.

Question: How is this useful for program coordinators?







Answer: You can use the above two charts to estimate uncertainty in the SPSS orbital events.












Procedure:













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Problem statement:









Suppose the date is January 2007, and you wish to estimate by how much the SPSS event projections
may be in error in July 2007 for a visit that must be timed accurately on day 190.








Resolution:









Go to the 2nd graph and note that Jan-July 2007 corresponds to approximately Sept-March 1995-6. Note that the decay rate is
~0.5 km/s, but fluctuates by 0.5 km/yr on the 49-day timescale. Therefore, the decay rate could be as high as 1.0 km/yr.





Go to the 1st graph and note that a decay rate of 1.0 km/yr (0.5 nominal + 0.5 uncertainty) over a ~180 day time interval
corresponds to ~ 13-14 minute in-track error. The nominal decay rate of 0.5 km/yr would yield a shift of just over 6 minutes
(so the events would be about 6 minutes earlier than those listed in the events tables), with the additonal 0.5 km/yr
yielding an additional 7 minutes added error if the decay rate were higher than expected.










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Problem statement:









Suppose the date is April 2011, and you wish to estimate by how much the SPSS event projections
may be in error in August 2011 for a visit that must be timed accurately on day 220.













Resolution:









Going to the 2nd graph, April 2011 corresponds to ~ December 1999 where the nominal decay rate is 8 km/yr, but the variation
could lie anywhere in the range of 3-18 km/yr.





The first graph shows that event times at T-120 days are expected to be earlier than shown in the tables (for the nominal
decay rate) by about 25 minutes.





Which orbit and where in the orbit HST is are too uncertain at a range of 120 days. For the maximum decay rate variation, only at T-60
days would one be able to guess within 30 minutes, and at the nominal decay rate, T-90 days would be the horizon to get within
about 30 minutes.













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ijej 07-02-20