| DATA_SET_DESCRIPTION |
Data Set Overview
==================
This dataset consists of data products derived from data collected
by Inertial Measurement Units (IMUs) on the two Mars Exploration
Rovers (MERs) during their entries into the martian atmosphere. The
DATA/ directory contains one data file for each spacecraft (MER1.TAB
and MER2.TAB). Each time file contains time ordered records of
measured acceleration, derived velocity, derived position, derived
atmospheric properties and other derived quantities.
The MER-2 rover, which was launched on the MER-A mission to Gusev
Crater on 10 June 2003, was later renamed Spirit. The MER-1 rover,
which was launched on the MER-B mission to Meridiani Planum on 7
July 2003, was later renamed Opportunity.
Parameters
===========
Each data file contains the following items.
Time (Spacecraft Clock Time, seconds) SCLK_TIME
Axial acceleration (m s^(-2)) AXIAL_ACCELERATION
Normal acceleration (m s^(-2)) NORMAL_ACCELERATION
X-component of acceleration (m s^(-2)) X_ACCELERATION
Y-component of acceleration (m s^(-2)) Y_ACCELERATION
Z-component of acceleration (m s^(-2)) Z_ACCELERATION
X-component of velocity (m/s) X_VELOCITY
Y-component of velocity (m/s) Y_VELOCITY
Z-component of velocity (m/s) Z_VELOCITY
Speed of spacecraft relative to atmosphere (m/s) VREL
X-component of position (m) X_POSITION
Y-component of position (m) Y_POSITION
Z-component of position (m) Z_POSITION
Radial distance (m) RADIAL_DISTANCE
Areocentric latitude (degrees north) LATITUDE
Areocentric longitude (degrees east) LONGITUDE
Axial force coefficient, CA (dimensionless) CA
Normal force coefficient, CN (dimensionless) CN
Angle of attack (degrees) ALPHA
Mach number (dimensionless) MA
Knudsen number (dimensionless) KN
Density (kg m^(-3)) RHO
Pressure (Pa) PRESS
Temperature (K) TEMP
Each data file also contains 1-sigma uncertainties for those items.
Units for the uncertainties in item XXX are the same as for item XXX.
Those names, which are derived from the above names, are as follows:
SIGMA_SCLK_TIME
SIGMA_AXIAL_ACCELERATION
SIGMA_NORMAL_ACCELERATION
SIGMA_X_ACCELERATION
SIGMA_Y_ACCELERATION
SIGMA_Z_ACCELERATION
SIGMA_X_VELOCITY
SIGMA_Y_VELOCITY
SIGMA_Z_VELOCITY
SIGMA_VREL
SIGMA_X_POSITION
SIGMA_Y_POSITION
SIGMA_Z_POSITION
SIGMA_RADIAL_DISTANCE
SIGMA_LATITUDE
SIGMA_LONGITUDE
SIGMA_CA
SIGMA_CN
SIGMA_ALPHA
SIGMA_MA
SIGMA_KN
SIGMA_RHO
SIGMA_PRESS
SIGMA_TEMP
Timing
======
All data products in this dataset are derived from PDS volume
MERIMU_1001 [KASSETAL2004], which uses Spacecraft Clock Time
(SCLK time) as its time reference. For consistency, all times in
this dataset are also SCLK times.
Coordinate Systems
==================
All data products in this dataset are derived from 4 Hz backshell
IMU measurements in DATA/XTRANSFORMED.TAB in PDS volume MERIMU_1001
[KASSETAL2004], where X is either 1 or 2. These acceleration
measurements are given in an XYZ cartesian frame fixed relative to
the spacecraft. This spacecraft frame is neither inertial nor fixed
relative to Mars. The spacecraft is axisymmetric about the Z axis.
The axis to which axial and normal accelerations are referenced is
defined in the data processing section of this file.
Position, velocity and acceleration are given in an XYZ cartesian
frame whose origin is at the center of mass of Mars. The +Z axis
passes through the north pole and the +X axis passes through the
equator at zero degrees east areocentric longitude at a specified
time. The +Y axis completes a right-handed set. The specified time
is SCLK_TIME = 128270000.000 for MER1 and
SCLK_TIME = 126460000.000 for MER2. Position is also given as radial
distance, areocentric latitude, and areocentric longitude. This
is the standard spherical polar coordinate system found in
mathematical textbooks. Longitude increases to the east. Altitude
is defined as radial distance minus the radial distance from the
center of mass of Mars to the relevant landing site. Altitude is
not referenced to any equipotential surface.
Data Processing
===============
Data processing is also described in [WITHERS&SMITH2006A] and
[WITHERS&SMITH2006B].
Four data products from DATA/XTRANSFORMED.TAB in PDS volume
MERIMU_1001 [KASSETAL2004], where X is either 1 or 2, were used:
SPACECRAFT_CLOCK_START_COUNT, BACKSHELL_IMU_ACCEL_X,
BACKSHELL_IMU_ACCEL_Y and BACKSHELL_IMU_ACCEL_Z. Data after
backshell separation were discarded. Backshell separation occurred
when the terminal descent radar indicated that the spacecraft was
about 10 m above the ground. It is reasonable to assume that the
position and velocity at landing are the same as the reconstructed
position and velocity at backshell separation due to the magnitude
of the errors in reconstructed position and velocity. This is
relevant for the determination of the entry states.
Backshell separation was identified as the time of the last
non-zero value of BACKSHELL_IMU_ACCEL_X, BACKSHELL_IMU_ACCEL_Y,
or BACKSHELL_IMU_ACCEL_Z. Some lines of data are duplicates (for
example, SPACECRAFT_CLOCK_START_COUNT=128277624.125 for MER-1). The
extra lines of data were discarded. The nominal sampling rate is 4
Hz and times usually end on .125, .375, .625, or .875 seconds.
However, some sections of the data have a higher sampling rate of
8 Hz (for example, SPACECRAFT_CLOCK_START_COUNT=128278390.000 for
MER-1). In order to ensure a uniform timestep, such sections were
reduced to a 4 Hz sampling rate by discarding any lines of data
where the time did not end .125, .375, .625, or .875 seconds.
Two lines of data are missing from 1TRANSFORMED.TAB, corresponding
to SPACECRAFT_CLOCK_START_COUNT=128278462.875 and
SPACECRAFT_CLOCK_START_COUNT=128278463.125. Values of
BACKSHELL_IMU_ACCEL_X, BACKSHELL_IMU_ACCEL_Y and
BACKSHELL_IMU_ACCEL_Z at these times were replaced by linear
interpolation using neighbouring data points. Two missing lines of
data from 2TRANSFORMED.TAB, corresponding to
SPACECRAFT_CLOCK_START_COUNT=126462354.625 and
SPACECRAFT_CLOCK_START_COUNT=126462355.875, were replaced in the
same way.
Data prior to the time of atmospheric entry were discarded. At this
stage in the processing, each data series begins at the time of
atmospheric entry and ends at backshell separation, which occurs
after parachute deployment. Some of the analysis described in
[WITHERS&SMITH2006A, WITHERS&SMITH2006B] used these data series,
including the work on determining the entry states. The data
products archived in this PDS volume were generated from truncated
versions of these data series. Data after parachute deployment were
discarded to form these truncated data series. These low-altitude
data were discarded because the assumptions made about spacecraft
attitude for the trajectory reconstruction are significantly less
reliable after parachute deployment than before.
The MER-1 data series from atmospheric entry to parachute
deployment begins at SPACECRAFT_CLOCK_START_COUNT=128278194.625
and ends at SPACECRAFT_CLOCK_START_COUNT=128278444.625. The MER-2
data series from atmospheric entry to parachute deployment begins
at SPACECRAFT_CLOCK_START_COUNT=126462085.625 and ends at
SPACECRAFT_CLOCK_START_COUNT=126462336.375.
SCLK_TIME equals the processed SPACECRAFT_CLOCK_START_COUNT
values. AXIAL_ACCELERATION equals -1 times the processed
BACKSHELL_IMU_ACCEL_Z values. The factor of -1 was introduced
for convenience. It ensures that AXIAL_ACCELERATION is positive,
rather than negative, at peak aerodynamic deceleration.
AXIAL_ACCELERATION can be positive, zero, or negative.
NORMAL_ACCELERATION equals the square root of the sum of the
squares of the processed BACKSHELL_IMU_ACCEL_X and
BACKSHELL_IMU_ACCEL_Y values. NORMAL_ACCELERATION can be positive or
zero, but cannot be negative. 1-sigma uncertainties in these
quantities are SIGMA_SCLK_TIME, SIGMA_AXIAL_ACCELERATION and
SIGMA_NORMAL_ACCELERATION.
Next, the trajectory was reconstructed. The total acceleration
acting on the spacecraft is the sum of aerodynamic and
gravitational accelerations. It is necessary to transform the
aerodynamic accelerations from a frame defined with respect to
the spacecraft to a frame defined with respect to Mars. It was
assumed that the aerodynamic acceleration consists of
AXIAL_ACCELERATION only, that the aerodynamic acceleration vector
is parallel to the velocity of the spacecraft with respect to
the atmosphere, and that the atmosphere rotates at the same
angular velocity as the solid body of Mars. Winds are thus
neglected. The spacecraft rotates about the axis of symmetry
on a timescale that is short compared to the timescale for
changes in accelerations normal to this axis. Therefore it is
reasonable to neglect NORMAL_ACCELERATION in the trajectory
reconstruction. The three components of the transformed
AXIAL_ACCELERATION are X_ACCELERATION, Y_ACCELERATION and
Z_ACCELERATION. 1-sigma uncertainties in these quantities
are SIGMA_X_ACCELERATION, SIGMA_Y_ACCELERATION and
SIGMA_Z_ACCELERATION.
Gravitational accelerations were calculated as follows:
g = grad(U) (1)
U = GM/r ( 1 + (Rref/r)^2 C20 P20(cos theta) ) (2)
P20(x) = sqrt(5) 1/2 (3x^2 - 1) (3)
where theta = colatitude
GM = 4.282E14 m^3 s^(-2)
Rref = 3394.2 km
C20 = -8.5791E-4
[TYLERETAL2000]
Entry states were determined as discussed in [WITHERS&SMITH2006A]
and [WITHERS&SMITH2006B].
The time, position, and velocity for MER-1 at atmospheric entry are:
SCLK_TIME = 128278194.625 s
RADIAL_DISTANCE = 3522200 m
LATITUDE = -2.9 degrees
LONGITUDE = 340.9 degrees east
Speed relative to Mars-centered inertial frame = 5700 m/s
Flight-path angle = 11.5 degrees
(angle below horizontal of velocity vector)
Flight-path azimuth = 86.5 degrees
(angle east of north of velocity vector)
X_POSITION = 3410501.1 m
Y_POSITION = 861754.30 m
Z_POSITION = -178198.42 m
X_VELOCITY = -2449.4191 m/s
Y_VELOCITY = 5131.4622 m/s
Z_VELOCITY = 398.04798 m/s
The time, position, and velocity for MER-2 at atmospheric entry are:
SCLK_TIME = 126462085.625 s
RADIAL_DISTANCE = 3522200 m
LATITUDE = -17.7 degrees
LONGITUDE = 161.8 degrees east
Speed relative to Mars-centered inertial frame = 5630 m/s
Flight-path angle = 11.5 degrees
(angle below horizontal of velocity vector)
Flight-path azimuth = 79.0 degrees
(angle east of north of velocity vector)
X_POSITION = -3307198.9 m
Y_POSITION = 567076.35 m
Z_POSITION = -1070865.2 m
X_VELOCITY = -176.76616 m/s
Y_VELOCITY = -5464.3396 m/s
Z_VELOCITY = 1344.1153 m/s
After the completion of this work, alternative entry states were
determined independently using SPICE kernels archived elsewhere
at the PDS. Software used in this independent determination is
archived in the EXTRAS directory of this PDS volume as file
meraltedlandtimes.pro. According to documentation associated with
those SPICE kernels, the UTC times of entry for MER-1 and MER-2 were
2004-01-25T04:48:41.720 and 2004-01-04T04:19:51.720, respectively.
According to the SPICE kernels, the position and velocity of MER-1
at the time of entry were:
SCLK_TIME = 128278194.142 s
RADIAL_DISTANCE = 3522201.3 m
LATITUDE = -2.9091901 degrees
LONGITUDE = 340.90205 degrees east
Speed relative to Mars-centered inertial frame = 5698.6452 m/s
Flight-path angle = 11.469960 degrees
Flight-path azimuth = 86.503350 degrees
According to the SPICE kernels, the position and velocity of MER-2
at the time of entry were:
SCLK_TIME = 126462085.048
RADIAL_DISTANCE = 3522202.1 m
LATITUDE = -17.749196 degrees
LONGITUDE = 161.77632 degrees east
Speed relative to Mars-centered inertial frame = 5627.5267 m/s
Flight-path angle = 11.494375 degrees
Flight-path azimuth = 79.025420 degrees
These alternative entry states, which are very similar to those
obtained by [WITHERS&SMITH2006A, WITHERS&SMITH2006B], were not
used to produce these datasets.
After determination of the entry states, as described in
[WITHERS&SMITH2006A, WITHERS&SMITH2006B], the equations of
motion were integrated forwards in time from the initial position
and velocity using the total acceleration, which produced a time
series of position and velocity (X_POSITION, Y_POSITION, Z_POSITION,
RADIAL_DISTANCE, LATITUDE, LONGITUDE, X_VELOCITY, Y_VELOCITY,
Z_VELOCITY). This reconstructed trajectory extends from the time of
atmospheric entry to parachute deployment.
The derived velocity values are archived as X_VELOCITY,
Y_VELOCITY and Z_VELOCITY. 1-sigma uncertainties in these
quantities are SIGMA_X_VELOCITY, SIGMA_Y_VELOCITY and
SIGMA_Z_VELOCITY. The derived position values are archived
as X_POSITION, Y_POSITION and Z_POSITION. 1-sigma uncertainties
in these quantities are SIGMA_X_POSITION, SIGMA_Y_POSITION and
SIGMA_Z_POSITION. The derived position values are also archived in
a spherical polar coordinate system as RADIAL_DISTANCE, LATITUDE
and LONGITUDE. 1-sigma uncertainties in these quantities are
SIGMA_RADIAL_DISTANCE, SIGMA_LATITUDE and SIGMA_LONGITUDE. The
speed of the spacecraft relative to the atmosphere, which is
assumed to rotate with the same angular velocity as the solid
body of Mars, is important for the atmospheric structure
reconstruction. These values are archived as VREL and their
1-sigma uncertainties are archived as SIGMA_VREL. Uncertainties
were found using a Monte Carlo uncertainty analysis.
Atmospheric density is related to aerodynamic deceleration by
the drag equation.
m az = rho A vrel^2 CA / 2 (4)
where m is spacecraft mass
az is AXIAL_ACCELERATION
rho is atmospheric density
A is the reference area of the spacecraft
vrel is VREL, the speed of the spacecraft with respect to the
atmosphere
CA is the axial force coefficent, usually on the order of 2
A for both Spirit and Opportunity was that of a disk of diameter
2.648 m [SCHOENENBERETAL2005B]. m was 827.0 kg for Spirit and
832.3 kg for Opportunity [DESAI&KNOCKE2004].
A similar equation relates NORMAL_ACCELERATION and the normal
force coefficient CN, so
CN/CA = NORMAL_ACCELERATION / AXIAL_ACCELERATION
Atmospheric density can be derived from measured aerodynamic
decelerations using the drag equation. However, this will not
work at very high altitudes when densities and aerodynamic
decelerations are very small. Acceleration measurements are
dominated by errors and offsets at very high altitudes, implying
unphysical negative densities. Also, this will not work at very
low altitudes, after parachute deployment. The aerodynamic
behavior of the parachute-backshell-lander system is very complex
and it is not possible to determine CA accurately. Without an
accurate CA, the drag equation cannot be used to determine
atmospheric density from aerodynamic decelerations. So the
atmospheric structure reconstruction cannot be performed over
the entire trajectory.
Atmospheric pressure is related to atmospheric density by the
equation of hydrostatic equilibrium.
dp/dr = rho x (gr + cr) (5)
where p is pressure
r is radial distance
gr, which is negative and a function of position, is the radial
component of equation 1
cr is the radial component of - Omegavec x (Omegavec x rvec)
Omegavec is the angular vector for the rotation of Mars
rvec is the spacecraft's position vector
Atmospheric temperature is related to atmospheric pressure and
density by the ideal gas law.
mu p = rho R T / NA (6)
where mu is the mean molecular mass of the martian atmosphere
(43.49 g/mol, [MAGALHAESETAL1999])
R is the universal gas constant
T is temperature
NA is Avogadro's number
If the appropriate value of CA can be determined at each timestep,
then the atmospheric density can be found at each timestep using
known quantities and equation 1. Next, atmospheric pressure can be
found at each timestep using equation 5 if a boundary condition is
specified. The commonly-accepted boundary condition is that
p0 = rho0 g0 H0, where H is the measured density scale height at
the top of the atmosphere and the subscript 0 refers to values at
the top of the atmosphere. This can also be expressed as a
temperature, T0 = mu g0 H0 / R. Once atmospheric pressure and
atmospheric density are known, atmospheric temperature can then
be found at each timestep using equation 6.
Two atmospheric structure reconstructions were performed for each
spacecraft. One considered uncertainties, began at about 100 km
altitude and ended at parachute deployment. The other did not
consider uncertainties, began at about 120 km altitude and ended
at parachute deployment. The reasons for this are related to the
Monte Carlo uncertainty analysis and will be described shortly.
The atmospheric structure reconstruction that did not consider
uncertainties was performed first and is described next.
The MER-1 atmospheric structure reconstruction that did not
consider uncertainties used data between 128278199.625 and
128278444.625 seconds, inclusive. The MER-2 atmospheric structure
reconstruction that did not consider uncertainties used data
between 126462095.625 and 126462336.375 seconds, inclusive.
CA is a function of attitude, spacecraft shape, atmospheric
density, and speed of the spacecraft relative to the atmosphere.
Since the MER entry capsule is axisymmetric, the dependence on
attitude can be expressed in terms of the angle of attack, alpha,
which is the angle between the symmetry axis and the velocity of
the spacecraft with respect to the atmosphere. Alpha is small,
usually less than 5 degrees. MER project engineers estimated the
likely entry trajectory and atmospheric structure before entry
occurred. They used numerical simulations to determine CA as a
function of alpha, or CA(alpha), and CN as a function of alpha, or
CN(alpha), at a finite number of points along this trajectory.
This set of simulated coefficients is called the aerodynamic
database. Values of CA(alpha) and CN(alpha) between the simulated
points can be found by interpolation. Interpolation required the
velocity of the spacecraft relative to the atmosphere, the Mach
number and the Knudsen number.
Ma = vrel / sqrt( gamma p / rho ) (7)
Kn = 1 / ( sqrt(2) pi d^2 n D ) (8)
where Ma is Mach number
Kn is Knudsen number
vrel is VREL, the speed of the spacecraft with respect to the
atmosphere
gamma is the ratio of the heat capacity at constant pressure to the
heat capacity at constant volume of the martian atmosphere
pi is 3.14...
d is the diameter of an atmospheric molecule
n, which satisfies n = NA rho / mu, is the atmospheric number density
D, which satisfies pi D^2/4 = A, is the reference diameter of
the spacecraft
Values corresponding to pure CO2 were used for gamma and d, so
gamma = 1.4 [ATKINS2002] and d = 4.46E-10 m [SCHOENENBERETAL2005B].
The aerodynamic database has been published in graphical form in
[SCHOENENBERETAL2005B]. Several different flight regimes are
encompassed by the aerodynamic database: free molecular flow,
transitional flow, hypersonic continuum flow, and supersonic
continuum flow.
Although the aerodynamic database has been published in graphical
format in [SCHOENENBERETAL2005B], it is not yet possible for
it to be published in tabular format (personal communication,
Desai, 2008).
First, preliminary profiles of atmospheric density, pressure,
and temperature were obtained using CA=2. As outlined in
[WITHERSETAL2003B, WITHERS&SMITH2006A, WITHERS&SMITH2006B],
an iterative procedure was used to determine rho, alpha, CA and
CN at each timestep. Results for alpha are unreliable when the
ratio NORMAL_ACCELERATION / AXIAL_ACCELERATION is inaccurate,
which occurs at high altitudes. Alpha and CN were set equal to zero
for times before 128278242.125 s (MER-1) or 126462133.125 s
(MER-2) (about 80 km). Densities from the upper ten km of the
profile were used to find H0 and to provide the upper boundary
condition for the equation of hydrostatic equilibrium. Pressures
and temperatures were then obtained.
The results of this atmospheric structure reconstruction are
archived as CA, CN, ALPHA, MA, KN, RHO, PRESS and TEMP.
Uncertainties were obtained using a Monte Carlo technique. The
Monte Carlo technique generated an ensemble of values of
AXIAL_ACCELERATION for each timestep using the quoted nominal
values and their uncertainties. If values from near 120 km were
used, then some of these accelerations were negative, which
correspond to unphysical negative densities. In order to minimize
the occurrence of negative densities, the atmospheric structure
reconstruction that considered uncertainties began at about 100 km,
not 120 km. The MER-1 atmospheric structure reconstruction that
considered uncertainties used data between 128278219.625 and
128278444.625 seconds, inclusive. The MER-2 atmospheric structure
reconstruction that considered uncertainties used data between
126462110.625 and 126462336.375 seconds, inclusive. An ensemble of
values for T0 was used as the upper boundary condition in the
equation of hydrostatic equilibrium. This ensemble was generated
using the value of T0 from the atmospheric structure reconstruction
without uncertainties (160 K for both MER-1 and MER-2) and an
assumed uncertainty of 50 K. Atmospheric structure reconstructions
were performed as above using these ensemble inputs. Their standard
deviations were used to generate uncertainties for the archived
data products. This is an abbreviated description of the error
analysis, see [WITHERS&SMITH2006B] for further information.
Derived values of atmospheric density, atmospheric pressure,
and atmospheric temperature are archived as RHO, PRESS and TEMP,
respectively. 1-sigma uncertainties in these quantities are
archived as SIGMA_RHO, SIGMA_PRESS and SIGMA_TEMP. Derived values
of CA, CN, alpha, Ma, and Kn are archived as CA, CN, ALPHA,
MA and KN, respectively. 1-sigma uncertainties in these quantities
are archived as SIGMA_CA, SIGMA_CN, SIGMA_ALPHA, SIGMA_MA and
SIGMA_KN.
Each run of a Monte Carlo error analysis leads to slightly
different uncertainties. Different runs were used to generate
the data products archived here and the data products published
as supplemental information to [WITHERS&SMITH2006A]. The Monte
Carlo techniques were only used to generate those data products
whose names begin with 'SIGMA_'. Data products such as LATITUDE and
RHO were produced without consideration of uncertainties, so they
do not change from one run of the data processing software to the
next.
Not all data products are defined at all timesteps. Data
products derived in the atmospheric structure reconstruction are
not defined above about 120 km and uncertainties in these data
products are not defined above about 100 km. Uncertainties in
alpha and CN are also not defined above about 80 km, where alpha
and CN are assumed to be zero. Such data products are given the
null value -1 in the data files.
Acronyms
========
AAT Atmospheric Advisory Team
AIAA American Institute of Aeronautics and Astronautics
B-IMU Backshell IMU
DIMES Descent Image Motion Estimation System
EDL Entry, Descent and Landing
ET Ephemeris Time
HASI Huygens Atmospheric Structure Instrument
IDL Interactive Data Language, a computer programming language
IMU Inertial Measurement Unit
ITAR International Traffic in Arms Regulations
JPL Jet Propulsion Laboratory
Ls The angle between the Mars-Sun line and the Mars-Sun
line at the northern hemisphere vernal equinox, known as
the areocentric longitude of the Sun
LST Local Solar Time
MER Mars Exploration Rover
MGS Mars Global Surveyor
NASA National Aeronautics and Space Administration
OPP Opportunity
PAET Planetary Atmosphere Experiments Test
PDS Planetary Data System
R-IMU Rover IMU
SCLK Spacecraft Clock
SPI Spirit
SPICAM Spectroscopy for the Investigation of the Characteristics
of the Atmosphere of Mars
SPICE An information system provided by the Navigation and
Ancillary Information Facility
TES Thermal Emission Spectrometer
TIRS Transverse Impulse Rockets System
UTC Coordinated Universal Time
|
| CONFIDENCE_LEVEL_NOTE |
Data Coverage and Quality
=========================
Data coverage is excellent. The only minor gaps in the data
series are discussed above. None of the values of
SPACECRAFT_CLOCK_START_COUNT, BACKSHELL_IMU_ACCEL_X,
BACKSHELL_IMU_ACCEL_Y and BACKSHELL_IMU_ACCEL_Z were identified
as erroneous. Uncertainties in the values of
BACKSHELL_IMU_ACCEL_X, BACKSHELL_IMU_ACCEL_Y,
BACKSHELL_IMU_ACCEL_Z and other IMU measurements from PDS
volume MERIMU_1001 [KASSETAL2004] are discussed in
[WITHERS&SMITH2006B].
Limitations and Caveats
=======================
The entry states used to generate this archived data volume are
not as accurate as they could be. They were determined as
described in [WITHERS&SMITH2006A, WITHERS&SMITH2006B],
rather than being taken from SPICE kernels. Uncertainties in the
entry state were assumed to be the same as for Mars Pathfinder
[MAGALHAESETAL1999]. There is no evidence to support this
assumption. The PDS volume MERIMU_1001 [KASSETAL2004] contains
information on spacecraft attitude during entry. This
reconstruction does not use that information and instead made
several assumptions concerning spacecraft attitude. Use of the
archived attitude quaternions led to a realistic reconstructed
trajectory for Spirit, but not Opportunity
[WITHERS&SMITH2006A, WITHERS&SMITH2006B]. These attitude
quaternions were derived from angular rate data recorded by
gyroscopes and an initial attitude. It is possible that the
initial attitude for Opportunity, but not Spirit, was unreliable,
thereby contaminating the entire time series of attitude
quaternions. The archived angular rate data from the gyroscopes
are useless, because the orientation of the gyroscope axes with
respect to the spacecraft coordinate frame has not been
published [WITHERS&SMITH2006A, WITHERS&SMITH2006B].
If the trajectory and atmospheric structure are reconstructed
using the alternative (SPICE) entry states, rather than the
[WITHERS&SMITH2006A] entry states, changes are small. In this
discussion, the 'difference' in a reconstructed quantity is
the value of that quantity for the reconstruction that used the
alternative (SPICE) entry state minus the value of that quantity
for the reconstruction that used the [WITHERS&SMITH2006A] entry
state. The 'relative difference' is the ratio of the 'difference'
to the value of that quantity for the reconstruction that used the
[WITHERS&SMITH2006A] entry state. For MER-1, the difference in
altitude, which is about +1 m at entry and +450 m at parachute
deployment, varies approximately linearly with altitude. The
difference in latitude is -0.01 degrees. The difference in
longitude is +0.02 degrees at entry and -0.04 degrees at parachute
deployment. It varies approximately linearly with time. The
difference in speed of the spacecraft relative to the atmosphere
is -1.38 m/s at entry and -1.74 m/s at parachute deployment. The
relative difference in density is less than 0.1% above 30 km
and less than 1% at all altitudes. The relative difference in
pressure is less than 0.5% at all altitudes. The difference in
temperature varies smoothly between -0.5 K at 80 km and -1.5 K at
parachute deployment. For MER-2, the difference in altitude, which
is about +2 m at entry and +100 m at parachute deployment, varies
approximately linearly with altitude. The difference in latitude
is -0.05 degrees. The difference in longitude is -0.02 degrees
at entry and -0.03 degrees at parachute deployment. The difference
in speed of the spacecraft relative to the atmosphere is between
-2.25 m/s and -2.45 m/s. The relative difference in density is less
than 0.1% above 50 km and less than 1.2% at all altitudes. The
relative difference in pressure is less than 0.5% at all altitudes
below 110 km. The difference in temperature is between 0 K and
-0.2 K at all altitudes between 30 km and 110 km. The difference
in temperature is between -0.2 K and -1.5 K at all altitudes
between 30 km and parachute deployment. The alternative (SPICE)
entry states occur about 0.5 s before the [WITHERS&SMITH2006A]
entry states. This was neglected in the comparison.
There is an inconsistency between the trajectory reconstruction
and the atmospheric structure reconstruction. The trajectory
reconstruction assumes an angle of attack of zero and neglects
normal accelerations. The atmospheric structure reconstruction
determines the value of the angle of attack, which was typically
on the order of a few degrees. If the angle of attack is fixed
at 0 degrees or at 2 degrees in both the trajectory reconstruction
and the atmospheric structure reconstruction, then changes in the
inferred trajectory and atmospheric structure are generally small.
The changes in density and temperature at parachute deployment
are <2% and <3K. However, if the angle of attack is fixed at 5
degrees, then the density and temperature at 30 km change by
<1% and <3K, whereas the density, temperature, altitude, and
atmosphere-relative speed at parachute deployment change by 7%,
about 20 K, 0.2 km, and 20 m/s. These changes are similar for
both Spirit and Opportunity.
Wind speeds were assumed to be zero in the trajectory
reconstruction and the atmospheric structure reconstruction.
Since neither the mean nor the standard deviation of the zonal
and meridional wind speeds for the entries of Spirit and
Opportunity were known as functions of altitude, non-zero
wind speeds were not considered in the trajectory and
atmospheric structure Monte Carlo error analysis.
If the zonal wind is fixed at +30 m/s eastward throughout the
atmosphere, then the density and temperature at 30 km change
by +2% and -2K. The density, temperature, altitude, and
atmosphere-relative speed at parachute deployment change
by +15%, -20K, +0.4 km, and -30 m/s. If the wind direction
is reversed, then the sign of these changes is also reversed.
These changes are similar for both Spirit and Opportunity.
Three parts of the entry state were determined indirectly in
[WITHERS&SMITH2006A, WITHERS&SMITH2006B]: flight path azimuth,
latitude, and longitude. Changes in latitude and longitude at
entry by approximately 1 degree merely translate the entire
trajectory horizontally, with negligible change in the inferred
atmospheric structure. Changes in the flight path angle at entry
by approximately 5 degrees change the latitude at 30 km and
parachute deployment by approximately 1 degree; changes in
longitude are much smaller. Changes in the inferred atmospheric
structure at 30 km are negligible, but changes in density and
temperature at parachute deployment are 2% and 3K. These changes
are similar for both Spirit and Opportunity.
The IMU data archived in PDS volume MERIMU_1001 [KASSETAL2004]
are stated in that volume's DATASET.CAT file to be those
transmitted from the spacecraft. That is, they have not undergone
additional calibration. Recalibration of the MER IMU data began in
2004 and so these data should be considered preliminary (Desai,
personal communication, 2004). At the time of writing, January
2008, that work is ongoing (Desai, personal communication, 2008).
These recalibrated data will be delivered to the PDS in 2008
(Desai, personal communication, 2008). The reconstructed
trajectory and atmospheric structure archived here and based
on preliminary IMU data may in the future be superceded by
reconstructions based on the more accurate recalibrated IMU data.
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