Internal Technical Memorandum ITM-1998-01
Forecasting HST SAA impacts for the Deep
Impact-9P/Temple 1Encounter
I. Jordan
November 5, 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 accurately 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, 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 spacecraft as well as Earth-based instruments. The Hubble Space Telescope (HST) has the potential for
observing this unique event. HST’s Space Telescope Imaging Spectrograph ultraviolet (UV)
Multi-Anode Microchannel Array (STIS/MAMA) detectors are prime candidates for observing at
the time of impact to help diagnose the composition of the material thrown off by the Deep
Impact’s cometary impactor has ben identified as an important scientific priority. The use of other
HST science instruments is also important in the orbits that follow, so ensuring that HST will be in
view of the comet, and not in target occultation, is important for mission design.
Currently, the Deep Impact impactor has been targeted to strike the nucleus of Comet 9P/Temple 1
at 05:52 UT on July 4, 2005. Many mission constraints make it difficult to change this impact time
beyond about +/-45 minutes. A trajectory correction burn at impact minus 60 days will allow
adjusting the impact time by this amount. Fortunately, this allows sufficient offset to center the
impact time when HST can maximize the amount of observing time during an orbital period.
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.
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2. Impact & Observation Geometry from Earth and HST
Because the orbit of HST is not predictable over such long time spans, it is important to understand
the factors involved in determining when the HST orbit 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 orbit for the purpose of considering
the July 4, 2005 impact: i) the orientation of the orbital plane of HST, ii) HST’s location (in-track)
within that orbital plane, and iii) 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 of xx to yy 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 sensitive spacecraft subsystems by energetic particles trapped in the Earth’s radiation
belts, observations cannot occur when HST passes thorugh the area bounded by SAA. The net
effect is that of the 14.5 orbital revolutions each day, approximatley half intersect the SAA and are
clumped contiguously.
It is useful to describe the geometry of the Sun, Earth and 9P/Temple 1at the time and date of
impact in order to understand HST observing constraints. On the date of impact, 9P/Temple 1is
approximately 0.78 a.u. from Earth, trailing the Earth, 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 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 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 aquisition
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.
2.2 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
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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?’ (address this when data is in hand)
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 left to its own accord. 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 actiivity.
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 mini-
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Internal Technical Memorandum ITM-1998-01
mum 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 be specified, since
there are maximum altitudes to which the shuttle can reboost HST and still return to earth.
3. Modelling the Uncertainties
To attempt to model the uncertainty in the orientation of the HST orbit plane, a python programwas written (q.v. Appendix A) and run with varied parameters. Likely values for each variable
were specified, and by looping the algorithm successively with each source variable changed by
some amount representative of a likely dispersion, changes in the HST ascending node can be
noted. Table 1 shows the nominal values used for the various parameters.
Table 1: 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
7.9 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
In Table 2 below, with author’s guesses at 95%-confidence dispersions, shows computed uncertainties on the RA of the ascending node. The entries at the table bottom give the combined
uncertainty with the individual sources added independently in quadrature. Five significant start
times were used: Dec 2001, Post SM3B (mid-Feb 2002), post Solar Maximum (December 2002),
post SM4 (presumed April 2004), and on May 4, 2005.
One uncertainty is modelled twice in the table: the date of 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 is simple and assumes
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Internal Technical Memorandum ITM-1998-01
piece-wise linear rates in the respective regions, which is only a crude representation, adding the
uncertainties separately is probably not over-conservative.
The precession constant’s uncertainty is small (Boden 1992) with the major contributions coming
from the moon and sun.
Table 2: Modelled Uncertainty Evolution in HST Orbit Plane Orientation
Source
2-Sigma
Estimate of
Variance
Post SM4
Encounter
minus 60
days
Initial Orbital Altitude
-3.3 deg
-1.6 deg
-0.2 deg
0
0
0
0
2.8 deg
2.8 deg
2.8 deg
0
0
200 days
6.5 deg
6.5 deg
0
0
0
Solar Max Orbit Decay Rate
2 km/yr
7.8 deg
5.4 deg
0
0
0
Solar Min Orbit Decay Rate
0.5 km/yr
2.1 deg
2.1 deg
2.1 deg
0.5 deg
-0.01 deg
SM3B Reboost
3 km
-12.5 deg
0
0
0
0
SM4 Reboost
2 km
-3.2 deg
-3.2 deg
-3.1 deg
0
0
Eccentricity
0.0002
0.02 deg
0.02 deg
0.01 deg
0.01 deg
0
Inclination
0.01 deg
-0.8 deg
-0.8 deg
-0.6 deg
-0.3 deg
-0.04 deg
Nodal Regression Rate
0.0002 deg/day
0.25 deg
0.25 deg
0.2 deg
0.1 deg
0.01 deg
17.6 deg
10.6 deg
5.8 deg
1.7 deg
0.2 deg
Dec
2001
Post
SM3B
Solar
Min
1 km
-4.5 deg
-4.1 deg
SM3B Launch Date
20 days
2.6 deg
SM4 Launch Date
100 days
Solar Min -> Solar Max Date
Net Uncertainty
In part, the evolution of the uncertainty in the orientation of the orbit plane 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 the simultation presented here, we take SM3B
before end of Solar Max.
References
Boden, Daryl G, “Introduction to Astrodynamics”, in Space Mission Analysis and Design,
Larson, W. and Wertz J., eds,.Kluwer 1992.
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Internal Technical Memorandum ITM-1998-01
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
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Internal Technical Memorandum ITM-1998-01
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
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alpha, ",
parameter