Application of Accelerometer Data to Mars Global Surveyor
Aerobraking Operations
R. H. Tolson, G. M. Keating, G. J. Cancro, J. S. Parker, S. N. Noll, and B. L.
Wilkerson
George Washington University and NASA Langley Research Center, Hampton,
Virginia 23681-2199
Aerobraking was selected for the Mars Global Surveyor mission as a primary and
enabling operation. The application of accelerometer data for determining
atmospheric density during operations for the first phase of aerobraking is
reported. Acceleration was measured along the body z axis, which is the axis
nominally into the flow. For a 1-s count time, the data have a resolution of
0.332 mm/s, permitting the recovery of density to 3% at nominal aerobraking
altitudes near 115 km and on many orbits, permitting the recovery of density
to altitudes as high as 180 km. Accelerometer data were analyzed in near real
time to provide estimates of density at periapsis, maximum density, density
scale height, latitudinal gradient information, and longitudinal wave
variations. Summaries are given of the aerobraking phase of the mission, the
accelerometer data analysis methods and operational procedures, some
applications to determining thermospheric properties, and some remaining
issues on interpretation of the data. Preflight estimates of 70% 2 sigma
natural variability are shown to be realistic, and predictions that dust
storms could produce rapid and large increases in thermospheric density have
been verified.
Received Jan. 20, 1998; revision received Aug. 15, 1998; accepted for
publication Feb. 22, 1999. This paper is declared a work of the U.S.
Government and is not subject to copyright protection in the United States.
Nomenclature
A = reference area for aerodynamics
a = acceleration
C_z = aerodynamic force coefficient along body z axis
h_s = density scale height
m = Mars Global Surveyor (MGS) mass
q = dynamic pressure
r = position of accelerometer in body system
<u> = relative wind unit vector
V = MGS speed relative to atmosphere
delta = SAM deflection
rho = density
omega = body angular rate
Introduction
AEROBRAKING is the utilization of atmospheric drag for beneficial orbit
changes. The first application of aerobraking in a planetary mission was
during the Magellan mission at Venus.(1) The primary Magellan mission took
three Venus days in an orbit with an eccentricity of 0.39, inclination of 85
deg and periapsis at 280-km altitude and 10 deg N latitude. Gravity field and
radar image resolution in the polar regions was reduced due to the high
eccentricity and the lack of apsidal precession. To increase polar
resolution, aerobraking was performed in 1993 over about 750 orbital passes to
reduce the eccentricity to 0.03 in about 70 days. The primary drag surfaces
were the solar arrays, and the limiting criterion for the pace of aerobraking
was solar array heating. Nearly real-time adjustments were made to the Venus
atmospheric model, which were developed based on mass spectrometer data and
over 500 orbits of Pioneer Venus Orbiter drag data.(2) The success of this
operation demonstrated the significant benefits of aerobraking over propulsive
maneuvers.(1)
Aerobraking was an enabling technology for the Mars Global Surveyor (MGS)
mission. Prelaunch plans called for chemical propulsion to establish an
initial orbit with a period of 45 h (Ref. 3). After initial system checkout
during the first few orbits, a walkin phase was planned. During this phase
the periapsis altitude would be decreased by apoapsis propulsive maneuvers to
drop deeper and deeper into the Mars thermosphere until the target dynamic
pressure of 0.6 N/m^2 was reached. Aerobraking would then take place from
about Sept. 12, 1997, through Jan. 15, 1998. This planned orbital period
decay is shown by the dashed line in Fig. 1.
Unlike Venus, the only relevant data on the Mars thermosphere were a few
measurements from the two Viking entries in 1976 and the Pathfinder entry in
1997. All three entries occurred at different latitudes, local solar times
(LST), phases of the solar cycle, and/or seasons from those during the MGS
mission. Because of this dearth of data, the project allocated 70% 2 sigma
for orbit-to-orbit natural variability of atmospheric density. Further, data
from the inertial measurement unit (IMU) axial accelerometer were to be used
to complement radio tracking data by determining local atmospheric density
scale height, to provide latitudinal look-ahead capability, and to infer
atmospheric density, temperature and pressure in near real time for planning
subsequent passes.
MGS Aerobraking Mission History
An overview of the mission is given elsewhere (4) and only a summary is given
here for continuity. The prelaunch aerobraking configuration consisted of
both solar arrays swept 30 deg to assure longitudinal aerodynamic stability.
The photovoltaic cells were oriented away from the flow to minimize cell
heating. During postlaunch deployment, damage to one of the solar arrays
prevented the array from locking into the fully deployed position by about 20
deg. As a result, the configuration utilized during the initial aerobraking
orbits had an offset between the yoke and inner panel, as seen in Fig. 2. The
broken or minus y solar array (SAM) had to be deployed so that the solar cells
faced into the flow to limit deflection of the array under aerodynamic loads.
Because the panel was not latched in place, it was expected to deflect and
vibrate about the yoke-panel hinge line during aerobraking. The project
developed a nonlinear spring model during interplanetary cruise to predict
panel deflection during aerobraking. A deflection of 10 deg was expected
during nominal aerobraking and could be verified by analyzing spacecraft (S/C)
orientation about the x axis because a 10-deg deflection would result in
about a 5-deg change in heading. (5)
The walkin phase began with orbit 4 with a barely measurable atmospheric
effect at 149-km altitude. Orbit 5 was the first aerobraking pass with a
periapsis altitude of 128 km and a maximum density of about 5 kg/km^3. On
orbit 11 at a dynamic pressure of 0.49 N/m^2, the SAM took a permanent set of
4 deg toward the latched position. The next orbit at q = 0.53 resulted in
another 15-deg shift, so that the panel should have been near the latch
position. On orbit 15 at an altitude of 110 km, the dynamic pressure
unexpectedly increased by 50% to 0.93 N/m^2. At maximum q, the panel deflected
more than 16 deg beyond the latched position and was left with a permanent set
of about 3 deg. This was the first of many large orbit-to-orbit variations in
density. The anomalistic SAM behavior resulted in an immediate raising of the
periapsis altitude and the performance of various experiments on orbits 16-18.
Results of these tests, numerous laboratory tests, and extensive analyses were
performed during orbits 19-36 and resulted in a re-evaluation of the original
solar array problem and a replanning of the entire aerobraking sequence.' The
new sequence was planned with two aerobraking phases. The first would end in
March/April of 1998 with an orbital period of 11.6 h. This phase would be
followed by six months of science experiments in a high-altitude phasing
orbit. The second phase of aerobraking would begin in September 1998 and end
in March 1999 with periapsis near the south pole and the 2 a.m./p.m. orbit
plane that is optimal for science observations. The replanned orbital period
decay for phase 1 is shown by the solid line in Fig. 1, and the actual decay
through the end of phase 1 is shown by the rightmost dots in Fig. 1. Except
for a dust storm near the end of 1997, the actual followed the plan rather
closely.
Aerobraking Environment
Originally, the limiting factor for aerobraking was the heating of the solar
arrays. Drag flaps, shown in Fig. 2, were added to the solar array assembly
to increase the ratio of drag to heating to ameliorate the effects of the
assumed 70% atmospheric density variability. For the replanned aerobraking
operations, dynamic pressure or SAM deflection is the limiting factor.
Extensive analyses were performed during the design phase (6) and pre-Mars
orbit insertion (5) (pre-MOI) phase to characterize the
aerothermodynamic environment. The original MGS aerobraking was to take place
at a dynamic pressure of about 0.6 N/m^2, which corresponded to an atmospheric
density of about 60 kg/km^3 and a Knudsen number of about 0.2, which is well
into the transition region. Aerodynamic properties were calculated with
direct simulation Monte Carlo (DSMC) and free-molecular flow codes. The DSMC
method was required to accurately quantify aerothermodynamics in the regions
of highest dynamic pressure. Extensive description of these and other MGS
aerothermodynamic simulation are described elsewhere. (7)
The utilization of the z-axis accelerometer to infer atmospheric density is
based on
a_z = [ rho * V^2 * C_Z * A ] / [ 2 * m ] (1)
Thus, it was required to develop an aerodynamic data base of C_z over a range
of S/C orientations to the relative wind, delta from 0 to 20 deg, and rho up
to twice the target density or 120 kg/km^3. Figure 3 shows the axial force
coefficient over the range of expected densities for flow along the z axis and
with delta = 0 and 10 deg. DSMC calculations were performed at 0.1, 12, 72,
and 120 kg/km^3. Below densities of 0.1 kg/km^3 the free-molecular flow values
are utilized. All calculations are based on assumed momentum accommodation
coefficients of unity. (7) On orbit 15, the inferred density reached the peak
mission value of 81 kg/km^3 and the calculated SAM deflection was 15.7 deg.
From orbits 38-201, the end of phase 1, inferred densities ranged from about 4
to 41 kg/km^3. Preflight attitude control simulations indicated that the
relative wind could deviate as much as 15 deg from the z axis. DSMC and
free-molecular simulations (7) were performed at the four densities and three
panel deflections mentioned earlier and over heading angles of +/- 15 deg.
Contours of a typical C_z variation are shown in Fig. 4. The variables u_x and
u_y are the components of the relative wind unit vector in the S/C body
coordinates shown in Fig. 2. The maximum C_z occurs at (u_x, u_y) = (0.04, 0)
because the high-gain antenna introduces an asymmetry in pitch or rotation
about the y axis. To determine SAM deflection, aerodynamic forces on the SAM
were also calculated over the same range of variables.
In recovering density from accelerometer data, the aerodynamic database is
used in an iterative manner. For each accelerometer measurement, the relative
wind vector, including rigid rotation of the atmosphere with the planet, is
determined from the attitude quaternions and the orbital ephemeris.
Interpolation into the free-molecular versions of Fig. 4 with no SAM
deflection is used to estimate C_z and, thence, density. This density is used
to calculate dynamic pressure and the resulting torque on the SAM. SAM
deflection is determined from a slightly nonlinear spring model with a spring
constant of about 2.6 N-m/deg. Linear interpolation in both log density (Fig.
3) and SAM deflection continue until the density converges to within 1%.
Accelerometer and Other Data Types
Four accelerometers (x, y, z, and skew) along with four gyros are contained in
the IMU located on the nadir deck, as shown in Fig. 2. The principal
accelerometer used in the aerobraking analysis is the z-axis accelerometer.
This accelerometer is located at <r> = (-0.44, -0.38, 0.72) m relative to the
center of mass. The accelerometers are Sundstrand QA1200-AA08 model Q-Flex
and continuously integrate acceleration to obtain velocity data. The
instrument is sampled 10 times per second. The data are recorded in
instrument counts or quantized velocity increments equivalent to 0.332 mm/s
per count, providing 38 times more sensitivity than the Viking entry probes.
(8) The accelerometer bias has a specified temperature sensitivity of 10 mg/K
or approximately 0.3 counts/K. The IMU temperature is actively controlled.
IMU telemetered temperatures are quantized at 0.12 K, and typical changes
during an entire aerobraking pass are between two quantized values.
The z-accelerometer sampling rate during the aerobraking phase was originally
set at 10 contiguous 0.1-s measurements every 8 s. This sample rate was based
on simulations that indicated density could be recovered with at least 3%
accuracy below altitudes of 140 km, assuming no aerodynamic coefficient
errors. (9) After orbit 40, the data rate was increased to transmit every
0.1-s sample to improve atmospheric recovery and also to monitor the dynamics
of the SAM. The primary accelerometer data used in operations are 1-s counts
of change in velocity. These data are interpreted as an acceleration and time
tagged at the center of the count interval. The measured acceleration is
composed of a number of terms given by
a_meas = a_bias + a_aero + a_grav + a_ACS + omega x (omega x r)
+ omega-dot x r + a_SAM (2)
where the terms are acceleration due to the instrument bias, aerodynamic
forces, gravity gradient, attitude control system (ACS) thruster activity,
angular motion of the accelerometer about the center of mass (two terms), and
relative translational motion of the SAM with respect to the rest of the S/C.
The bias was measured during periods of S/C inactivity. During the cruise to
Mars, the bias was monitored before and after two of the midcourse maneuvers
and the main engine firing for MOI. The results from these maneuvers showed a
variation of less than 0.05 counts/s. As part of the operational procedure,
the bias is checked every orbit pass. Data before and after entry into the
atmosphere are used to estimate the bias. No statistically significant
difference has been detected between the inbound and outbound legs or from
orbit to orbit.
Angular motion contributions to the acceleration were generally removed using
the filtered rate gyro data, which are received at 1 sample per second. In
some of the early orbits, the angular rate exceeded the telemetry cutoff, and
quaternions were differentiated to determine rates. In either case, the
angular acceleration required in Eq. (2) are determined by fitting a
polynomial to the rates and then differentiating the polynomial to determine
the acceleration at the central point. Digitization is not an issue in these
calculations. For typical aerobraking passes, the contribution due to these
terms is less than 0.6 mm/s^2. Some extreme orbits have reached as high as 2
mm/s^2.
Acceleration caused by thruster firing is the most difficult to remove. The
factors that determine thruster effectiveness include specific impulse,
propellant blowdown, temperature of the catalyst bed, and interference with
the flow. (5) Past experience has shown that calibration within +/- 50% is
difficult for the short thrusting times and variable duty cycle associated
with attitude control. (10) For operations, the accelerometer data during a
thruster firing that produced torque about either MGS x or y were simply
removed from the data set. Times during which roll (about z) thrusters fired
were not removed because they produce no acceleration at the z accelerometer.
The sections of data to be removed were determined by monitoring the
accumulated thruster firing times. The cumulative thruster duration is
updated every computer cycle and transmitted to the ground every 8 s for all
12 attitude control jets (see Fig. 2). Deleting the described data has
essentially no effect on operational predictions because most x-y thruster
firings occur only on the outbound leg and at least 150 s after periapsis.
Methods for refining firing times and estimating impulse have been developed
and will be utilized for data archiving.
The last term in Eq. (2) is due to the vibration of the SAM. The SAM
structural failure is believed to have been a compressive failure in the
composite facesheet of the yoke. This type of failure is expected to produce
a ragged interface between the two edges of the facesheet. It is thought that
as dynamic pressure increases various sections of the interface build up
compressive loads and then slip relative to each other. Similar, but perhaps
smaller effects, would be expected as dynamic pressure decreases and the
interface locks up. This slipping or locking excites a vibration of the SAM
outboard of the fracture. This oscillation of the SAM induces oscillations in
the bus and consequently in the z-accelerometer. The resulting acceleration
at the IMU is due to 1) direct translational acceleration of the bus center of
mass as the SAM center of mass vibrates and 2) additional induced rotational
contributions in Eq. (2). The period of this oscillation is about 6.5 s but
depends on both the dynamic pressure and the amplitude of the vibration.
Modal analyses of the vibration were performed during numerous orbits using
the x rate gyro data and during 30-s time spans that appeared to be free
response. Natural frequencies varied from 0.13 to 0.19 Hz, and damping varied
from 5 to 20%. These variations are thought to be related to the extent to
which the interface is locked up because higher frequencies, i.e., higher
stiffness, are generally associated with lower dynamic pressures. The mean
value of these oscillations is nearly zero because the bus and the SAM return
to the preaerobraking relative orientations after aerobraking. Prior to
aerobraking, the large amplitudes of oscillation were not anticipated, and the
operational approach has been to simply remove the effect by averaging 6 s of
data.
Eight solar cell temperatures are also received from the S/C every 4 s. During
the early high-dynamic-pressure orbits, the increases in temperature on the
solar array were correlated with the dynamic pressures inferred from the
atmospheric densities. After orbit 15, the temperature of the solar arrays
was not an issue.
Operational Procedures
The operational use of accelerometer data involved an iteration between the
navigation (NAV) and the accelerometer (ACCEL) teams. The NAV model for drag
utilized a constant drag coefficient and an exponential density variation with
altitude. Both density at periapsis, rho_p, and scale height h_s, can be
formally estimated from the tracking data. However, radio tracking is not
possible while the S/C is in the aerobraking attitude. Utilizing radio
tracking data before and after aerobraking essentially provides a single
atmospheric observable equivalent to the total change in orbital period over
the drag pass. For high-eccentricity orbits, the change in orbital period is
proportional to rho_p * sqrt(h_s) (Ref. 11). Knowledge of the scale height
is, therefore, essential for accurate measurement and prediction of periapsis
density from radio tracking data that excludes direct measurements at
periapsis.
The operations plan called for NAV to process radio tracking data prior to the
beginning of the drag pass and to provide predictions of the osculating
elements at the next periapsis. These predictions were called the preliminary
orbit. The ACCEL team, after receiving data about 2 h after periapsis, used
the preliminary orbit to process the accelerometer data to determine periapsis
density, maximum density, and scale height in the vicinity of periapsis. In
addition, an effective scale height for NAV was calculated to account for the
differences between the ACCEL and NAV models of aerodynamic forces. These
results were transmitted via E-mail and file servers to flight operations in a
report called the "Accelerometer Preliminary Quick-Look" and was due 2 h after
accelerometer data receipt. By the time this report was published, sufficient
postaerobraking radio tracking data had accumulated so that an intermediate
orbit could be determined by NAV using the updated estimate of scale height
and tracking data before and after the pass. Accelerometer data were then
reprocessed using the intermediate orbit ephemeris to produce the
"Accelerometer Intermediate Quick-Look" report. In addition to updates of the
data included in the preliminary quick-look report, this report also included
1) inbound and outbound conditions at a reference altitude (typically 130 km)
for assessment of north-south gradients of temperature and density, 2)
estimates of atmospheric disturbance levels based on density variations over
the previous five orbits, 3) predictions of densities and dynamic pressure for
the next seven orbits, and 4) narrative interpretation of results. Although a
final iteration was included in the pre-MOI plans, it was rarely required
because the intermediate orbit estimates from NAV were always sufficiently
accurate for prediction of the time and altitude of periapsis. In most cases
the preliminary orbit estimate would have been adequate.
To derive the results for the reports, numerous empirical representations were
developed pre-MOI. It should be recalled that this is a polar orbit and that
over a typical aerobraking pass the S/C is in the detectable atmosphere less
than 400 s. During this time, the latitude varies by about 30 deg. The S/C
travels about 12 deg (750 km) in latitude while within one density scale
height (7 km) of periapsis. Thus, the latitudinal variations cannot be
ignored in the MGS profiles, and hydrostatic equilibrium may not be applicable
across an entire pass. The models most utilized during operations included 1)
the constant density scale height model usually applied to a limited altitude
range in the vicinity of periapsis or to a reference altitude on the inbound
and outbound legs and 2) the model with density and/or temperature at a
reference altitude varying linearly with latitude. The latter model included
diffusive separation so that mean molecular weight varied with altitude.
Special models were also developed and used to directly extract exospheric
temperature but were not essential for operations. On a nearly daily basis,
the ACCEL team presented reduced data products and interpretation to the
Atmospheric Advisory Group (AAG). The AAG, composed of atmospheric scientists
and MGS investigators, formed consensus opinions on operational issues related
to the atmosphere and reported these formally to the project.
Results
During the 175 aerobraking passes of phase 1, there was no typical pass in the
sense of repeatability. This lack of repeatability was due to a number of
phenomena. After a sufficient amount of data were collected, it was found
that the natural variability of the atmosphere includes local and short
timescale density waves, standing waves fixed to the rotating planet with
time-dependent amplitudes, and strong time-dependent latitudinal gradients of
both temperature and density. (12) The running atmospheric variability index,
which was the deviation from the five-orbit mean density at a reference
altitude, varied from 11 to 239%. Further, the SAM behavior, which introduced
oscillatory and other rapid variations in the accelerometer data varied from
orbit to orbit. Finally, there are very rapid changes in accelerometer output
that have yet to be explained.
The results presented next are for periapsis 110 (P110). This orbit was
selected to provide variations somewhat similar to the classical bell curve
and to demonstrate some of the local variations just described. Some more
interesting passes will be presented later.
Aerobraking at P110
As already mentioned, the S/C z axis is expected to deviate substantially from
the freestream direction. Figure 5 shows the orientation of the calculated
relative wind in terms of u_x and u_y. At the beginning of the aerobraking
pass, but prior to entering the atmosphere, the S/C is placed in an attitude
that aligns the z axis with the predicted velocity vector at periapsis. The x
axis is aligned with the vertical at periapsis. This leads to the initial
relative wind being about 6 deg from aerodynamic equilibrium. The ACS is
switched from momentum wheel to thruster control, and the attitude error band
is opened to 20 deg to minimize fuel usage. The momentum wheels, held at
constant velocity, provide an onboard angular momentum source and couple
aerodynamic moments into all three axes. Because the S/C is essentially
neutrally stable about z, this coupling often leads to a few z-axis thruster
firings prior to periapsis but generally no x-y firings. The momentum wheels
are desaturated beginning at the predicted time of periapsis to take advantage
of aerodynamic torques. A few z-axis thruster firings and an occasional x-y
firing is associated with desaturation. By examining Fig. 5, it is seen that
in the vicinity of periapsis the S/C oscillates about a null point, which is
not at (0, 0). Contribution to this null offset include SAM deflection, which
would produce a positive u_y, the asymmetry caused by the high-gain antenna
(+u_x), atmospheric winds not adequately modeled by the rigidly rotating
atmosphere model, and perhaps differences in momentum accommodation
coefficient between the dissimilar solar arrays. (5,7)
Angular rates during the pass, which along with their derivatives are used to
correct the accelerometer data, are shown in Fig. 6. Thruster firing is
clearly evident in omega_z near -15, 10, 50, and 80 s and in omega_x and
omega_y near 180 s. As expected, the frequency of the S/C attitude
oscillations due to aerodynamic torques increase with dynamic pressure.
Oscillations about x have the shortest period (~40 s) because this is the
most aerodynamically stable axis. (5) Near times of -120, -50, and 0 s,
0.16-Hz oscillations are added to the overall motion due to SAM vibration.
Essentially none of this oscillation appears in the other two axes, confirming
that the SAM vibrates about an axis parallel to x. Because this oscillation is
at a much higher frequency than the aerodynamic oscillations, the induced
acceleration at the accelerometer is often greater than the aerodynamic
oscillation contribution and occasionally nearly as large as the direct
aerodynamic acceleration. Figure 7 shows the angular acceleration about the x
axis and the accelerometer contribution due to angular motion, i.e., the fifth
and sixth terms in Eq. (2). The 0.16-Hz signal is clearly evident in the
angular acceleration term and can be seen to contribute more than 1 count peak
to peak to the accelerometer data. Even after these terms are subtracted from
the measurement, considerable 0.16-Hz signal is left in the accelerometer data
due to the last term in Eq. (2), i.e., the acceleration due to SAM relative
translation. It should be mentioned that a linear dynamics model was
developed for the relative SAM-bus motion that removes this residual
oscillation and may be utilized in phase 2 of aerobraking. (9)
As already mentioned, during the calculation of density, the SAM deflection is
determined iteratively. In addition, the S/C team utilizes the sun sensors on
the SAM (Fig. 2) to measure SAM deflection. The sun-sensor data are sampled
every 8 s. Figure 8 gives a comparison to the measured values and those
calculated using the aerodynamic database. For this particular orbit, the
measured values have a bias of about 1 deg before and after the pass. This
offset has been interpreted as being due to thermal bending of the SAM from
solar heating. Even so, the comparison is within 1 deg, which is typical for
all orbits where sun-sensor data were available, and is adequate for
interpolation into the C_z database.
Raw accelerometer counts per second are shown in Fig. 9. The bias is 56.655
+/- 0.004 counts/s and the 6-s oscillations are evident at the times mentioned
earlier. After correcting these data using Eq. (2), the iteration scheme
converges on the axial force coefficient used to derive the density. This
variation is shown in the insert in Fig. 9. When the S/C is more than 150 s
from periapsis the flow is free molecular. The values here are less than the
free-molecular limit shown in Fig. 3 because, as seen in Fig. 5, the relative
wind is not along the z axis. Transitional effects can be seen in the
vicinity of periapsis. Here the flow is nearly along the z axis, and the
axial force coefficient has been reduced to 1.88 or 12% below the
free-molecular value of 2.13. Three realizations of density are shown in Fig.
10. The basic realization corresponds to correcting for all of the terms in
Eq. (2) except for direct SAM contribution. The second curve is obtained by a
6-s running mean of the basic realization. The purpose here is to remove any
remaining SAM contribution by just averaging over the vibration period. The
upper curve is a 40-s running mean of the second curve. This process removes
localized latitudinal and vertical variations in density and any remaining S/C
contributions. Some of these will be discussed later. The 40-s averaged data
are used to predict density at periapsis, latitudinal temperature and density
gradients, exospheric temperatures, and inbound and outbound differences. The
difference between the 6- and 40-s running means might be interpreted as
atmospheric waves or unmodeled S/C effects.
The altitudinal profile for P110 is shown in Fig. 11. At the top of the
atmosphere, on this particular pass, both inbound and outbound profiles have
about the same slope suggesting that exospheric temperature is nearly equal at
62 deg N and 32 deg N. In the vicinity of periapsis, there is little
difference between the density or temperature of the inbound and outbound
legs. Between 130- and 150-km altitude, the inbound leg, which is north of
periapsis, appears to have a much lower temperature than the outbound leg. At
140 km, the local density scale heights are 4.2 km inbound and 6.6 km
outbound. Interpreting the inbound scale height in terms of atmospheric
temperature in the traditional manner yields 75 K. This is much colder than
expected and suggests that a significant part of the density decrease in the
130-150 altitude range may be due to a strong latitudinal density gradient or
atmospheric wave.
Aerobraking at Some Other Orbits
There are a number of interesting phenomena that have occurred during this
first exploration of the thermosphere of Mars using aerobraking. Some of
these phenomena are still being investigated. Examples of these are shown in
Fig. 12 and are discussed next. Within 15%, 1 count/s is equivalent to an
atmospheric densitv of 0.7 kg/km^3.
Excessive SAM Oscillations
As mentioned earlier, the acceleration induced by SAM vibration was noticeable
on numerous orbits, and various methods were developed to remove the
oscillation so that the remaining signal represented atmospheric forces. The
upper left (Fig. 12) shows the raw accelerometer counts for P095, which is one
of the more extreme cases. For this orbit, the oscillatory contribution is
nearly as large as the aerodynamic acceleration. Most aerobraking passes
demonstrated some degree of SAM oscillation believed, as already mentioned, to
be excited by portions of the SAM crack slipping. Excessive oscillation like
those shown were infrequent and might be due to slippage of a large portion of
the crack after considerable stress buildup.
Other Oscillatory Variations
On numerous orbits there are oscillations in the data that nearly repeat
during the orbit and from orbit to orbit. An example is given in the upper
right (Fig. 12), which shows filtered accelerometer counts for P056. These
data were filtered to remove the 6-s oscillation. Note that for many of the
remaining oscillations on the inbound leg, there is an oscillation on the
outbound leg near the same count or dynamic pressure level. These data were
further filtered to leave only these oscillations. If harmonic motion is
assumed, the remaining signal can be converted into equivalent center-of-mass
displacement of about +/- 0.3 cm. This much motion of the bus center of mass
would take about 2 deg of rotation ofthe SAM. Though not a closed issue,
these variations may be explained by the fracture in the yoke slipping and
locking as discussed earlier. The count levels at which these oscillations
occur are somewhat repeatable from orbit to orbit, again suggesting that the
source could be S/C dynamics instead of atmospheric phenomena.
Nearly Instantaneous Changes in Acceleration
The two lower plots in Fig. 12 show two of a number of orbits where large
changes in accelerometer counts occurred in a very brief period. These plots
(Fig. 12) show the raw accelerometer data after the SAM oscillation has been
removed by performing a running average over 67 of the 0.1-s samples. Before
averaging, the 0.1-s data show that the sudden 40% increase on P041 and the
sudden 60% decrease on P114 take place in less than 3 s. During this time the
S/C has moved less than 15 km along the orbit and 1 km in altitude.
Sun-sensor measurements of SAM deflection support the suggestion that this is
due to a change in dynamic pressure and not changes in S/C projected area.
Yet, short of shock waves, gradients of this magnitude are difficult to
explain in terms of expected atmospheric wave activity.
There are numerous orbits with such dramatic changes and other orbits where
there are suggestions that the major change has taken place in a few smaller
steps. Sometimes such a change takes place in conjunction with the z-thruster
firing. Large transients are often associated with changes in angular
acceleration about the x axis that is not consistent with just a change in
dynamic pressure. Unless an acceptable atmospheric phenomenon is identified,
the explanation must lie with a major change in the gas-surface interaction
phenomena. One suggestion is that nearly spontaneous transition occurs
between specular interaction and the complete accommodation currently used in
the model. Mechanisms for changes in accommodation may include phase changes
at the surface due to low S/C surface temperatures.
Atmospheric properties have also shown a great deal of variability. As
mentioned, care must be exercised in interpreting results in terms of either
altitudinal or latitudinal variations. To help resolve these issues, a
first-order model was developed that assumes the atmosphere is isothermal
vertically but with a linear temperature and density variation with latitude
at a base or reference altitude. Estimating the mean density and temperature
and the two gradients results in high correlation between the gradient
estimates. The solution was, thus, constrained to provide the minimum
gradients consistent with the data. Near phase 1 aerobraking altitudes,
density and temperature were expected to increase toward the equator due to
solar heating. A typical orbit showing this behavior is given in Fig. 13 for
P074. The lower part of the density vs altitude curve is inbound, and at 150
km altitude the latitude is 52 deg N. The outbound latitude at this altitude
is 31 deg N. The dots represent the data, and the line is the model with a
density gradient of -4.3% of the mean density per degree of latitude and a
temperature gradient of -1 K/deg. As expected both density and temperature
decrease toward the pole. Though a relatively strong density gradient, larger
gradients were found on numerous orbits. The lower part of Fig. 13 shows the
unexpected situation where the density decreased toward the equator at lower
altitudes. At 140 km, the lower density corresponds to the inbound leg at 45
deg N and the higher density to the outbound leg at 28 deg N. The density
scale height inbound is also lower than outbound over most of the pass,
suggesting that temperature also increases toward the equator. However, below
130 km, the density increases toward the pole. The model fit to these data
yields a density gradient of 4.6%/deg and a temperature gradient of -4.0
K/deg. An atmospheric interpretation might include waves that produce factor
of two changes in density over spatial scales of 5 km vertically and/or 4 deg
in latitude.
Using Accelerometer Data for Prediction During Operations
The ability to predict depends on having an underlying model. As seen from
the preceding section, the thermosphere of Mars at aerobraking altitudes is
highly variable and extensive postflight analysis will be required to
interpret the MGS data. For operations, a number of relatively simple models
were developed and utilized. The model selected for prediction was generally
the one that had been performing the best over the last few passes.
Persistence is the simplest of all models and was used in the initial
aerobraking orbits. For this prediction method, a constant density scale
height model was fit to the density in the vicinity of one periapsis and used
to predict density at the altitude of the next periapsis. The top of Fig. 14
shows the ratio of measured density to predicted density using this approach
for all orbits during phase 1. The few ratios greater than 2 are plotted as
asterisks at the upper edge. The standard deviation for persistence is 0.40
so that the 2 sigma variability is larger than the prelaunch estimate of 70%.
It became clear after just a few orbits that the thermosphere was highly
variable and that a more accurate predictor was desirable. After the first
five orbits, a running mean and deviation from the mean were used for
predictions and as an indication of prediction uncertainty. The deviation
from the mean eventually became called the atmospheric disturbance level and
was reported on the intermediate quick-look. The ability of the five-orbit
mean to predict one orbit ahead is shown in the middle of Fig. 14 and during
phase 1 resulted in a 25% reduction in the standard deviation below
persistence. Early in the mission there were not sufficient data to determine
how much of the variability was random and how much was systematic, although
as early as P7 a suggestion of a planetary wave with minimum density near zero
longitude was suggested as a possibility to explain the variations with
longitude for P5, P6, and P7.
The first major atmospheric anomaly occurred on P13, when the latitudinal
gradient of density as measured by the ratio of density at 130-km altitude on
the inbound leg to the density at 130-km altitude on the outbound leg dropped
from approximately unity on previous orbits to 0.65. Such a large density
gradient over 18 deg of latitude could indicate large pressure gradients and
corresponding high cross- or zonal winds to eventually equilibrate the
pressure. On orbit 14, the ratio continued to decrease to 0.46, but P14
periapsis density was consistent with P13 persistence. On P15, the density
was 50% higher than P14 persistence, and maximum dynamic pressure reached 0.93
N/m^2 or 55% above the nominal aerobraking value, although still well below
the maximum allowable. This orbit resulted in the termination of aerobraking
at high dynamic pressures as discussed earlier. Though these large
latitudinal density gradients appeared to be a harbinger of a variable
atmosphere, large gradients did not consistently correlate with variability
throughout the rest of phase 1.
Notice that the ratios for persistence oscillate about unity in the vicinity
of orbit 58. The orbital period here is slightly over 30 h, so that successive
periapses are shifted about 90 deg in longitude to the west. Because this
pattern suggested a standing, longitudinal wave in density, a prediction
capability was developed based on a model that included a mean density, and
the first (wave 1) and second (wave 2) harmonic variations in longitude at a
reference altitude. The five coefficients of this model were determined using
the most recent orbits that provided a reasonable coverage of all longitudes.
Generally this involved about 10-12 orbits. The lower part of Fig. 14 shows
the ratio of measured-to-predicted density using this wave model. The mean of
the ratio is less than one because the mean density is nearly monotone
decreasing after orbit 60. This drift was detected before orbit 100 and was
included in subsequent operational predictions. Over all of phase 1, the
standard deviation for the wave model is slightly greater than the five-orbit
mean primarily due to very poor prediction during the dust storm that occurred
around orbit 50. If this period is omitted the standard deviation becomes
0.26 and 15% below the five-orbit mean prediction.
The high-low behavior in persistence is seen again near orbit 118. Here the
orbital period is about 18 h and successive periapses are shifted about 90 deg
to the east. In this region, as well as near orbit 50, the five-orbit mean
shows similar trends to persistence because an odd number of orbits was
selected, but the deviation is smaller. The two orbits with ratios greater
than 2 on the persistence plot also correspond to the occurrence of the dust
storm in the southern hemisphere. The density more than doubled in about 30 h,
which was consistent with preflight predictions. The scientific implications
of these and other phenomena are discussed in detail elsewhere.(12)
Conclusions
The first phase of aerobraking at Mars has at times demanded a relatively
intense activity. The preflight estimates of 70% 2 sigma natural variability
proved to be realistic, and preflight predictions that dust storms could
produce rapid and greater than factor of two increases in density were
verified. The accelerometer data provide the only means of measuring scale
height, which is essential for predictions of subsequent dynamic pressure
using any of the three models developed for operations. Accelerometer
measurements have demonstrated their utility for mission operations and
versatility in providing data for adaptively adjusting to changing
atmospheric conditions. Nevertheless, there are unexplained phenomena
remaining in the accelerometer data set. Future aerobraking missions may
occur at different seasons, levels of solar activity, LSTs, etc., and may
have to adjust to phenomena substantially different from the MGS experience.
References
1 Lyons, D. T., "Aerobraking Magellan: Plan Versus Reality," Advances in
the Astronautical Sciences, Vol. 87, Pt. 2, 1994, pp. 663-680.
2 Keating, G. M., Kliore, A., and Moroz, V., "Venus International Reference
Atmosphere," Advances in Space Research, Vol. 5, No. 11, 1985, pp. 117-171.
3 Dallas, S. S., "The Mars Global Surveyor Mission," Proceedings of the
1997 IEEE Aerospace Conference (Aspen, CO), Vol. 4, Inst. of Electrical
and Electronics Engineers, New York, 1997, pp. 173-189.
4 Lyons, D. T., Beerer, J. G., Esposito, P., Johnston, M. D., and Willcockson,
W. H., "Mars Global Surveyor: Aerobraking Mission Overview," Journal of
Spacecraft and Rockets, Vol. 36, No. 3, 1999, pp. 307-313.
5 Shane, R. S., Rault, D. F. G., and Tolson, R. H., "Mars Global Surveyor
Aerodynamics for Maneuvers in Martian Atmosphere," AIAA Paper
97-2509, June 1997.
6 Rault, D. F. G., Cestero, F. J., and Shane, R. W., "Spacecraft Aerodynamics
During Aerobraking Maneuvers in Planetary Atmospheres," AIAA
Paper 96-1890, June 1996.
7 Wilmoth, R. G., Rault, D. F., Cheatwood, F. M., Engelund, W. C., and Shane,
R. W., "Rarefied Aerothermodynamic Predictions for Mars Global Surveyor,"
Journal of Spacecraft and Rockets, Vol. 36, No. 3, 1999, pp. 314-322.
8 Blanchard, R. C., and Walberg, G. D., "Determination of the Hypersonic
Continuum/Rarefied Flow Drag Coefficient of the Viking Lander Capsule 1
Aeroshell from Flight Data," NASA TP-1793, Dec. 1980.
9 Cancro, G. J., Tolson, R. H., and Keating, G. M., "Operation Procedure for
Determining Atmospheric Density from Mars Global Surveyor Accelerometer
Measurements," NASA CR-1998-208721, Oct. 1998.
10 Cestero, F. J., and Tolson, R. H., "Magellan Aerodynamic Characteristics
During the Termination Experiment Including Thruster Plume-Free Stream
Interactions," NASA CR-1998-206940, March 1998.
11 King-Hele, D., "Satellite Orbits in an Atmosphere: Theory and
Applications," Blackie and Sons, Glasgow, Scotland, UK, 1987, Chap. 4.
12 Keating, G. M., Bougher, S. W., Zurek, R. W., Tolson, R. H., Cancro,
G. J., Noll, S. N., Parker, J. S., Schellenberg, T. J., Shane, R. W.,
Wilkerson, B. L., Murphy, J. R., Hollingsworth, J. L., Haberle, R. M.,
Joshi, M., Pearl, J. C., Conrath, B. J., Smith, M. D., Clancy, R. T.,
Blanchard, R. C., Wilmoth, R. G., Rault, D. F., Martin, T. Z., Lyons, D.
T., Esposito, P. B., Johnston, M. D., Whetzel, C. W., Justus, C. G., and
Babicke, J. M., "The Structure of the Upper Atmosphere of Mars: In Situ
Accelerometer Measurements from Mars Global Surveyor," Science, Vol. 279,
No. 5357, 1998, pp. 1672-1676.