Draft Internal Technical Memorandum ITM-2002-XX
Forecasting HST SAA impacts for the Deep
Impact-9P/Temple 1Encounter
I. Jordan
November 13, 2001
Concurrence: Anybody want to concur?
ABSTRACT
HST will be an important scientific tool for studying the consequences of the encounter of the
Deep Impact kinetic probe with comet 9P/Temple 1. The two missions require some coordination,
but Deep Impact’s planned encounter on July 4, 2005 is too far in the future to reliably plan with
HST because HST’s orbit and position within the orbit are subject to numerous uncertainties.
Here, we quantify the uncertainties and lay out a timetable of their evolution which can be used as
a guide for coordinated planning of the Deep Impact/HST observations.
1. Introduction
On July 4, 2005 at 05:52 UT +/- 45 minutes, the Deep Impact probe is planned to strike the
nucleus of Comet 9P/Temple 1, producing a large impact visible from instruments aboard the flyby
portion of the Deep Impact spacecraft as well as from Earth. The Hubble Space Telescope (HST)
has the potential for observing this unique event and providing unique coverage. HST’s Space
Telescope Imaging Spectrograph ultraviolet (UV) Multi-Anode Microchannel Array (STIS/
MAMA) detectors are prime candidates for use at the time of impact to help identify the
composition of the material liberated from the nucleus by the impactor. The use of other HST
science instruments will also be important in the orbits that follow for characterizing composition,
material properties and coma evolution. Ensuring that HST will be in view of the comet at the time
of impact--and not in target occultation--has been identified as an important element of the Deep
Impact mission design.
Many mission constraints make it difficult to change the impact time beyond about +/- 45 minutes.
A trajectory correction burn at impact minus 60 days will allow the impact time to be adjusted by
an amount sufficient to ensure that HST will be primely situated in its own orbit if the in-track
position can be predicted with sufficient accuracy. HST’s orbit is approximately 96.4 minutes long,
with approximately xx.x minutes viewing on target, yy.y of which will be available for science
observations.
1
Draft Internal Technical Memorandum ITM-2002-XX
2. Impact & Observation Geometry from Earth and HST
Because the position of HST is not predictable over such long time spans, it is important to
understand the factors involved in determining when the HST position will become well
determined enough to finalize aspects of the mission design which involve cooperative
observations.
There are 3 important aspects of the configuration of HST’s position for the purpose of considering
the July 4, 2005 impact:
• the orientation of the orbital plane of HST,
• HST’s location (in-track) within that orbital plane, and
• whether HST will be passing through the South Atlantic Anomaly (SAA) during the orbits
of interest surrounding impact time.
We will show that there are evolving uncertainties with predicting each of these and characterize
what can be known, when it can be known, and how the uncertainties evolve in time.
The Earth-Sun-comet geometry at the time of impact is very well determined from the vantage of
determining where the SAA will be for any given encounter time. Unfortunately, as we will see,
this geometry has consequences for observing with HST.
Whenever the longitude range between about 20E to 80W points in the general direction of a
target, the orbital plane of HST passes through the SAA. Because of the degrading effects on HST
science instruments and spacecraft subsystems sensitive to energetic particles trapped in the
Earth’s radiation belts, observations cannot occur when HST physically passes through the area
bounded by the SAA. The net effect is that of the 14.5 orbital revolutions each day, approximately
half (contiguously clumped) intersect the SAA.
It is useful to describe the geometry of the Sun, Earth and 9P/Temple 1 at the time and date of
impact in order to understand HST observing constraints. On the date of impact, 9P/Temple 1 is
approximately 0.78 a.u. from Earth, trailing the Earth, about 1.5 a.u. from the sun and near the
ecliptic with a Sun-Earth-Comet angle of approximately 111 degrees and approximately 1 degree
below the ecliptic. Since the date is approximately two weeks past northern summer solstice, the
north pole is oriented about 126 degrees away from the comet, with a sub-earth point near 16
degrees latitude south.
2.1 The SAA, HST, and Comet/Deep Impact Observations
At impact time, the comet is just above the horizon from Bolivia, Bogota, Tampa, and Chicago
along one limb of the Earth, and the day-night terminator is near Hawaii (with Mauna Kea in
darkness). The SAA stretches from near local midnight to near the dawn line. This implies that if
the orbital plane of HST intersects the SAA, it will do so from near the “end” of an orbit pass with
two-thirds to three-quarters of the HST orbit free from intersecting the SAA. This is good news
from the perspective of observing the comet with HST since it implies that most of the orbit’s
target viewing time will be unobstructed by the SAA. As the target comet rises above the horizon,
as viewed from HST, science observations will be able to commence as soon as guide star
acquisition is achieved and can proceed until encountering the SAA (if it impacts the orbit) some
30-40 minutes later. Also favorable is that subsequent orbits have diminishing chances of SAA
impacts.
2
Draft Internal Technical Memorandum ITM-2002-XX
2.2 HST’s In-Track Position
Although the question of where in the HST orbit an SAA impact is likely to occur is forecastable,
the question of where within that orbit HST will be cannot be predicted with much accuracy until
some months prior to the encounter. Even near solar-minimum, ephemeris slides of several
seconds per week are quite common. A major factor in producing uncertainty in HST’s orbital
position in the future is the inability to accurately forecast the amount of drag on HST because of
its changing orientation caused by looking at objects in different parts of the sky. HST’s pointing
orientation is determined only a few weeks in advance of actual observations, and even average
estimates of HST’s drag coefficient fail to produce accurate estimates very far into the future. The
relevant question for timing the Deep Impact HST-synch maneuver comes down essentially to one
of ‘how far in advance of encounter can HST’s in-track orbit position be known to within a few
minutes?’ <will address this when data is in hand>.
To address this question a comparison was made between definitive ephemerides (11 days in
length, generated to cover 1-week duration HST flight science calendars) and predictive
ephemerides (1 year long, predicting into the future).
Table 1: Solar Max Ω Crossing Times at T-70 Days (Year 2001)
Ascending
Node
Revolution #
Definitive/Predictive
Ephemeris File
names
Actual
Crossing
Time
Predicted
Crossing
Time
Delta-T
59316
OR01071WA
OR01001XA
071:01:17:28
071:01:15:35
1:53
60363
OR01141WA
OR01171XA
141:00:32:39
141:00:45:08
-12:29
61411
OR01211WA
OR01141XA
211:00:50:31
211:00:54:07
-3:36
62459
OR01281WA
OR01211XA
281:00:43:04
281:00:51:59
-8:55
62878
OR01309WA
OR01239XA
309:00:02:52
309:00:16:39
-13:13
HST ephemeris files prior to January 1, 2001 were not easily accessible, however, some predictive
ephemeris files from 1998-2000 containing SAA Model 05 event times were. They year 1998
would roughly correspond to 2009 in the solar activity cycle, and would probably represent upper
limits on uncertainties because 1998 saw the beginning of Solar Max and transition from
minimum HST orbital decay rates to maximal decay rates (the change in the decay rate actually
began in 1997).
<this section is incomplete and pending completion of the analysis>
3
Draft Internal Technical Memorandum ITM-2002-XX
2.3 HST’s Orbit Plane in Inertial Space
The orbital plane of HST ‘precesses’ or moves in a retrograde fashion at a rate of about 6.47
degrees per day, governed rather directly by the instantaneous altitude of the spacecraft. This
precession period describes a complete circuit with respect to the stars in about 56 days, and a
synodic period with respect to the sun in about 49 days. Between November 4, 2001 and July 4,
2005, HST’s orbit will precess approximately 24 complete revolutions.
HST’s altitude changes with time and decays. The decay rate during the period of maximum solar
activity is generally an order of magnitude higher than during solar minimum, and much more
variable. During solar maximum, the exospheric temperature of earth increases from 1000 K to as
much as 2000K and fluctuates depending upon the level of activity. These exospheric temperature
changes can dramatically increase the density at HST’s altitude by factors of 10-20 or more. The
increased atmospheric density creates higher levels of drag on the spacecraft, making its orbit
decay at quicker rates.
Between November 2001 and July 2005, there are a number of major events which contribute
significantly to knowledge of the altitude profile of HST:
• Transition from maximum levels of solar activity to minimum levels,
• Servicing Mission SM3B, and reboost in HST’s altitude,
• Servicing Mission SM4, and another reboost in HST’s altitude.
Although Solar Maximum should be nearing an end, the precise activity level over any given year
or two is not predictable with high levels of confidence. As we shall see later, these uncertainties
contribute heavily to projecting the orbit plane 3.5 years into the future.
In March 2001, the planned launch date of SM3B was December 2001, however various changes
in schedules have produced a current planned launch in mid-February, 2002. HST servicing
mission launch slips of several weeks have occurred in the past with as little as several months
before the planned launch date. SM4 does not currently have a planned launch date, but is likely to
be at least 2 years following SM3B. Past servicing missions are not a good guideline for predicting
an SM4 launch date with much confidence. If SM3B does launch in mid-February 2002, the
average interval between servicing missions will be 35.5 months, with a minimum of 2 years 2
months. Two new instruments are planned for installation during SM4, so minimizing the amount
of time between SM3B and SM4 is a priority for those instrument teams for budgetary reasons.
SM3A was an “emergency” servicing mission to replace failing gyroscopes and might have
occurred many months later had the emergency not been declared. Servicing mission schedules are
not very reliable so far in advance.
In addition to the uncertainties in launch times, each of the upcoming servicing missions, HST is
scheduled for altitude reboosts to increase the longevity of science observations (below a
minimum altitude, HST cannot be indefinitely operated at high observing efficiencies). The
amount of altitude increase and the destination altitude depends upon many factors: intercept
altitude, shuttle payload weight, shuttle orbiter (not all are identical in mass), and on-orbit
propellant available. These cannot be anticipated accurately so far in advance, however a range can
4
Draft Internal Technical Memorandum ITM-2002-XX
be specified, since there are maximum altitudes to which the shuttle can reboost HST and still
return to earth.
3. Modelling the Orbit Plane Evolution and the Uncertainties
To attempt to model the evolution of the HST orbit plane orientation and likely uncertainties from
major sources, a python program was written (q.v. Appendix A) and run with varied parameters.
Likely values for each variable were specified and run to produce a nominal projection. By looping
the algorithm successively with each source variable changed from the nominal estimate by some
amount representative of a likely dispersion, changes in the HST ascending node were quantified.
Table 2shows the nominal values used for the various parameters.
Table 2: Model Input Parameters for Predicting HST’s Orbit Plane Orientation
Parameter
Value
Start Epoch (TJD) December 6, 2001
8250
RA of Ascending Node at Start Epoch
5.5 degrees
Semimajor axis at Start Epoch
6856.5 km
SM3B (TJD)
Start Epoch + 100 days
SM3B Altitude Boost
15 km
Solar Maximum Altitude Decay Rate
7.5 km/year
Solar Maximum end (TJD)
Start Epoch + 365 days
Solar Minimum Altitude Decay Rate
0.7 km/year
HST orbit eccentricity
0.0014
HST orbit inclination
28.454 degrees
SM4 (TJD)
Start Epoch + 850 days
SM4 Altitude Boost
8 km
Impact Date (TJD) July 4, 2005, 06 UT
9555.746
Table 3shows the computed uncertainties on the RA of the ascending node, with author’s guesses
at 95%-confidence dispersions. The entries at the table bottom give the combined uncertainty with
the individual sources added independently in quadrature. Five significant start times were used to
show how the uncertainties evolve after one of several major events occur: Dec 2001 (current
date), Post-SM3B (mid-Feb 2002), post-Solar Maximum (December 2002), post-SM4 (presumed
April 2004), and on May 4, 2005 (encounter - 60 days). The individual values in the table have
their “signs” retained to indicate the directional effect on the ascending node caused by an increase
in the relevant parameter’s value.
One uncertainty is modelled multiply in the table: transition from solar maximum to minimum and
the orbital altitude decay rates during both minimum and maximum are coupled quantities, and
therefore are not actually independent. Since the model simplifies solar activity levels by assuming
5
Draft Internal Technical Memorandum ITM-2002-XX
piece-wise linear rates in the respective regions, one needs to include uncertainties for all three
components of the model (transition date plus decay rates). However, the solar activity model
parameters are related and constrained by the encounter date which forces at least one of the
effects to have a sign opposite of the other two. Even more sophisticated models would not yield
effects on orbit plane which change in the same direction.
The precession constant’s uncertainty is small (Boden 1992) with the major contributions coming
from the moon and sun.
Table 3: Modelled Uncertainty Evolution in HST Orbit Plane Orientation
Effect on HST Orbit Plane given Simulation Start Date
Source
2-Sigma
Estimate of
Variance
Dec
2001
Post
SM3B
Solar
Min
Post
SM4
Nodal Regression Rate
0.0002 deg/day
0.25 deg
0.25 deg
0.2 deg
0.1 deg
0.01 deg
Eccentricity
0.0002
0.02 deg
0.02 deg
0.01 deg
0.01 deg
-
Inclination
0.01 deg
-0.8 deg
-0.8 deg
-0.6 deg
-0.3 deg
-0.04 deg
Initial Orbital Altitude
1 km
-4.2 deg
-4.0 deg
-3.1 deg
-1.5 deg
-0.2 deg
SM3B Launch Date
50 days
2.4 deg
0
0
0
0
SM3B Reboost
3 km
-11.7 deg
0
0
0
0
Solar Max Orbit Decay Rate
3.5 km/yr
10.7 deg
8.8 deg
0
0
0
Solar Min -> Solar Max Date
200 days
10.8 deg
10.8 deg
0
0
0
SM4 Launch Date
100 days
2.6 deg
2.6 deg
2.6 deg
0
0
SM4 Reboost
2 km
-2.9 deg
-3.0 deg
-3.0 deg
0
0
Solar Min Orbit Decay Rate
0.5 km/yr
2.0 deg
2.0 deg
2.0 deg
0.5 deg
0.01 deg
20.3 deg
15.2 deg
5.5 deg
1.7 deg
0.2 deg
Net Uncertainty
Encounter
minus 60
days
In part, the evolution of the uncertainty in the orbit plane orientation is dependent upon the order in
which events become known. For example, it is unknown when Solar Maximum will end. It could
end before or after SM3B, however in November 2001 large sunspot groups were still visible on
the sun, and high activity storms were occurring.
Using the model (constructed to include servicing missions and changing solar activity levels) to
project the HST orbit plane at encounter time yields a very interesting result for the ascending
node: Right Ascension (RA) = 241.8 degrees, with an equivalent longitude at the time of impact of
230.9 degrees. HST orbit planes with ascending node RA between 160 and 320 degrees do not
intersect the STIS/MAMA SAA avoidance profile at 6h UT, while those outside that range do.
Orbit planes between the times of 00:30 UT and 10:30 UT in the nominal model do not intersect
the SAA.
6
Draft Internal Technical Memorandum ITM-2002-XX
When treated independently, the sources of uncertainty yield a net of about 20 degrees of
dispersion on the projected encounter orbit plane orientation (q.v. Table 3), indicating that the
encounter is likely to take place during SAA-free HST orbits when the STIS/MAMA detectors can
be operated under current instrument rules. The nominal orbit plane predicted by the model
indicates that the 3 orbits preceding encounter and the 2 orbits after encounter will not be impacted
by the SAA.
These equivalent interpretations about the model results must be taken with a note of caution
because the model relies on assumptions about future events which can be invalidated by changing
circumstances and plans. Although the net projected uncertainty in orbit plane orientation is only
20 degrees, this does not reflect the possibility of actual events resulting in changing parameters
which significantly exceed the specified confidence thresholds.
Figure 1: STK map showing HST orbit plane prediction and dispersions near the time of the
Deep Impact-9P/Temple 1 encounter. Solid green ground trace shows (nominal) model
prediction. The red dashed trace (minus 20 degrees) shows the orbit plane evolved with a
lower altitude profile, while the blue dotted trace (plus 20 degrees) shows the orbit plane
evolved with a higher altitude profile. The arc stretching from Chile to southern Africa is
HST’s STIS/MAMA SAA avoidance boundary.
To attempt to get a better handle on the characteristics of HST visits which will be used to observe
9P/Temple 1, the orbit planes of HST for 1999, 2000, 2001, and 2002 were examined to see which
most closely matched the orientation predicted for July 4, 2005. The ascending node RA on July 4,
2001 will be approximately 282 degrees--42 degrees away from the prediction for July 4.25, 2005.
The RA on July 11, 2001 closely matches that of July 4, 2005, and the Sun-Earth-target point
7
Draft Internal Technical Memorandum ITM-2002-XX
geometry is similar. Querying SPIKE’s report on orbital viewing time yields about 53.7 minutes of
target SI (including FGS acquisition time) viewing time.
References
Boden, Daryl G, “Introduction to Astrodynamics”, in Space Mission Analysis and Design,
Larson, W. and Wertz J., eds,.Kluwer 1992.
Deep Impact JPL mission website: http://deepimpact.jpl.nasa.gov
Deep Impact Project site: http://deepimpact.umd.edu
8
Draft Internal Technical Memorandum ITM-2002-XX
Appendix A
Python program used to evaluate uncertainties in HST orbit plane and predict orientation of that
plane in space.
# python program to project the ascending node of HST on impact date.
import math
import copy
#
#a = 6378.14 + 578.4
# initial semimajor axis of orbit (km)
#sm3b_date = 100
# delta TJD of SM3B launch
#sm4_date = 850
# delta TJD of SM4 launch
#solar_min_date = 365
# delta TJD onset date for solar minimum
#max_decay_rate = 7.9
# decay rate of HST altitude at solar maximum (km/year)
#min_decay_rate = 0.2
# decay rate of HST altitude at solar minimum (km/yr)
#sm3b_reboost = 15
# amount of altitude increase during SM3B (km)
#sm4_reboost = 8
# amount of altitude increase during SM4 (km)
#eccentricity = 0.0014
# HST mean orbit eccentricity 2000.
#inclination = 28.454
# HST orbit inclination in degrees.
#
impact_date = 9555.746
dt = 0.25
ref_date = 8250
# TJD of deep impact encounter
# timestep interval (days)
# reference TJD (December 6, 2001 = 8250)
# nominal settings of the orbit parameters (some values are tied to ref_date):
nominal = [0, 6856.5, 100, 850, 365, 7.9, 0.7, 15, 8, 0.0014, 28.454]
# Twang Matrix:
#
null
twang =
[0,
a
1,
3bd 4bd sold mx. mn. 3bb 4b
ecc
inc
50, 100, 100,
2, 0.5, 3, 2, 0.0003, 0.01]
for i in range(11):
print "---------------------------------------------------------------------------"
test_variance = copy.deepcopy(nominal)
test_variance[i] = test_variance[i] + twang[i]
print test_variance
delta_alpha = 0
alpha = 4.5
# accumulated orbit plane precession (degrees)
# ref RA of ascending node (degrees).
a = test_variance[1]
sm3b_date = test_variance[2]
sm4_date = test_variance[3]
solar_min_date = test_variance[4]
max_decay_rate = test_variance[5]
min_decay_rate = test_variance[6]
sm3b_reboost = test_variance[7]
sm4_reboost = test_variance[8]
eccentricity = test_variance[9]
inclination = test_variance[10]
angle_terms = math.cos(3.1415926538*inclination/180.) * (1-eccentricity**2.0)**-2.0
C= ( -2.06474*10**14.0) * angle_terms
# initial plane precession constant (deg*km^3.5/timestep).
decay_rate = max_decay_rate
# initial decay rate
# if you want to start on a different day, here is where to set it.
day = ref_date
# start day
# day = ref_date + 1 + sm4_date
# day = impact_date - 60
sm3b_date = ref_date + sm3b_date
sm4_date = ref_date + sm4_date
solar_min_date = ref_date + solar_min_date
# TJD of SM3B launch
# TJD of SM4 launch
# TJD onset date for solar minimum
while day < impact_date:
if (day > solar_min_date and decay_rate != min_decay_rate):
decay_rate = min_decay_rate
print "Solar Min transition on day ", day
if (day > sm3b_date) and (day <= (sm3b_date + dt)):
a = a + sm3b_reboost
print "SM3B reboost on day ", day
9
Draft Internal Technical Memorandum ITM-2002-XX
if (day > sm4_date) and (day <= (sm4_date + dt)):
a = a + sm4_reboost
print "SM4 reboost on day ", day
a = a - decay_rate / 365.25 * dt
omega_dot = C * a**(-7./2.)
delta_alpha = delta_alpha + omega_dot * dt
day = day + dt
delta_alpha = delta_alpha + omega_dot * (impact_date - day)
alpha = alpha + delta_alpha
alpha = (alpha / 360 - int(alpha/360)) * 360
if i==0:
benchmark = alpha
variance = benchmark - alpha
print "delta_alpha = ",delta_alpha, " Predicted RA of HST ascending node: ",
uncertainty = ", variance
# end program
10
alpha, ",
parameter