Data Set Overview ================== This dataset consists of data products derived from data collected by the Accelerometer (ACC) on Mars Odyssey (ODY) during its aerobraking in the martian atmosphere. The DATA/ directory contains four subdirectories: DATA/RAW/, DATA/PROF/, DATA/ANC/ and DATA/CALT/. DATA/RAW/ contains low rate and high rate data for each orbit. DATA/PROF/ contains density profiles for each orbit. DATA/ANC/ contains ancilliary information about each orbit. DATA/CALT/ contains densities and density scale heights at constant altitudes. Null values are 0 for numerical entries and YYYY-MM-DDTHH:MM:SS.SSS for time strings. Contents of DATA/RAW/ directory =============================== Filenames in the DATA/RAW/ subdirectory are ACCYYPXXX.ZZZ, where YY is either LO or HI, XXX is the orbit number and ZZZ is either LBL or TAB. If YY is LO, then the data file contains low rate data. If YY is HI, then the data file contains high rate data. Each data file contains data from one orbit. Each low rate data file contains time series of the following items. Time (UTC). TIME_LO_RAW Measured low-rate acceleration (m/s^2) in +X direction of M01_SPACECRAFT frame. AX_LO_RAW Measured low-rate acceleration (m/s^2) in +Y direction of M01_SPACECRAFT frame. AY_LO_RAW Measured low-rate acceleration (m/s^2) in +Z direction of M01_SPACECRAFT frame. AZ_LO_RAW Each high rate data file contains the following items. Time (UTC). TIME_HI_RAW Measured high-rate acceleration (m/s^2) in +X direction of M01_SPACECRAFT frame. AX_HI_RAW Measured high-rate acceleration (m/s^2) in +Y direction of M01_SPACECRAFT frame. AY_HI_RAW Measured high-rate acceleration (m/s^2) in +Z direction of M01_SPACECRAFT frame. AZ_HI_RAW No uncertainties are included in either type of data file. Production of files in the DATA/RAW/ directory ============================================== Low rate data have been delivered to the PDS Atmospheres Node in a non-standard format, but have not yet been peer-reviewed nor accepted into the PDS (ftp://atmos.nmsu.edu/odyssey/level0/data/). Acceleration measurements for orbit XXX were provided in an ASCII file (pXXXacc.txt) that contains time in YY/DOY-HH:MM:SS.SSS format and x, y, and z-axis accelerations in m s^(-2). There is no accompanying documentation, so the time standard and reference frame required to use the data have to be identified by other means. Many different time standards are used by spacecraft missions. These times were confirmed to be UTC times, not barycentric dynamical times or ephemeris times (ET), by reproduction of published plots of acceleration/density versus time since periapsis for P076 [TOLSONETAL2005]. We assumed that the x, y, and z-axes were those of the "M01_SPACECRAFT" frame defined by Navigation and Ancillary Information Facility (NAIF) SPICE kernel m01_v28.tf, which is identical to the Lockheed Martin (LMA) "mechanical coordinate system" for ODY [TAKASHIMA2002, NAIF2008B]. The "M01_SPACECRAFT" frame and LMA "mechanical coordinate system" are identical to the "spacecraft frame" described in the PDS instrument host file for ODY (versions created after 14 March 2003). The LMA "mechanical coordinate system" and a POST "body-frame coordinate system" are also defined in [CHAVIS&WILMOTH2005]. Accelerometer data were transferred from pXXXacc.txt to ACCLOPXXX.TAB without further processing. High rate data have been delivered to the PDS Atmospheres Node in a non-standard format, but have not yet been peer-reviewed nor accepted into the PDS (ftp:atmos.nmsu.edu/odyssey/level0/data/). Acceleration measurements for orbit XXX were provided in a MATLAB file (LOPXXX.mat). Some documentation was provided in Microsoft Excel and Word files. We extracted variables HiACCTime and HiACC from each orbit's LOPXXX.mat file. According to the documentation, HiACCTime is time expressed as UTC seconds past J2000. These were confirmed to be UTC seconds, not ET seconds, by reproduction of published plots of acceleration/density versus time since periapsis for P076 [TOLSONETAL2005]. According to the documentation, HiACC is x, y, and z-axis accelerations in m s^(-2). These accelerations are similar to the low-rate accelerations, which suggests that they are expressed in the same coordinate system. Therefore we again assumed that the x, y, and z-axes were those of the "M01_SPACECRAFT" frame defined by SPICE kernel m01_v28.tf, which is identical to the Lockheed Martin (LMA) mechanical coordinate system for ODY [TAKASHIMA2002, NAIF2008B]. Accelerometer data were transferred from LOPXXX.mat to ACCHIPXXX.TAB without further processing. Contents of DATA/PROF/ directory ================================ Filenames in the DATA/PROF/ subdirectory are ACCPROFPXXX.ZZZ where XXX is the orbit number and ZZZ is either LBL or TAB. Each data file contains data from one orbit. Each profile data file contains time series of the following items. UTC time. TIME_UTC Time after periapsis (seconds). TIME_AFTER_PERI Distance between the spacecraft and the center of mass of Mars (km). RADIAL_DIST Altitude of spacecraft above areoid (km). ALTITUDE Areocentric latitude, degrees north, of spacecraft. LATITUDE Areocentric longitude, degrees east, of spacecraft. LONGITUDE Local true solar time at spacecraft (hours) LOCAL_SOLAR_TIME Solar zenith angle at spacecraft (degrees) SOLAR_ZENITH_ANGLE Ls of Mars (degrees). LS Component of the velocity of the spacecraft with respect to the atmosphere in the +X direction of the M01_SPACECRAFT frame (km/s). VRELX Component of the velocity of the spacecraft with respect to the atmosphere in the +Y direction of the M01_SPACECRAFT frame (km/s). VRELY Component of the velocity of the spacecraft with respect to the atmosphere in the +Z direction of the M01_SPACECRAFT frame (km/s). VRELZ Speed of the spacecraft with respect to the atmosphere (km/s). VREL Component of the angular velocity of the spacecraft about the +X axis of the M01_SPACECRAFT frame (radians/s). OMEGAX Component of the angular velocity of the spacecraft about the +Y axis of the M01_SPACECRAFT frame (radians/s). OMEGAY Component of the angular velocity of the spacecraft about the +Z axis of the M01_SPACECRAFT frame (radians/s). OMEGAZ Angle between the velocity of the spacecraft relative to the atmosphere and the -Y axis of the M01_SPACECRAFT frame (degrees). ALPHA Pitch angle (degrees). THETA Yaw angle (degrees). PHI Unaveraged measured acceleration in +Y direction of M01_SPACECRAFT frame after step 1 of data processing (meters/s^2). AY1AS1 Unaveraged measured acceleration in +Y direction of M01_SPACECRAFT frame after step 2 of data processing (meters/s^2). AY1AS2 7-point running mean aerodynamic acceleration in +Y direction of M01_SPACECRAFT frame after step 2 of data processing (meters/s^2). AY7AS2 39-point running mean aerodynamic acceleration in +Y direction of M01_SPACECRAFT frame after step 2 of data processing (meters/s^2). AY39AS2 Unaveraged aerodynamic acceleration in +Y direction of M01_SPACECRAFT frame after step 3 of data processing (meters/s^2). AY1AS3 One sigma uncertainty in AY1AS3 (meters/s^2). SAY1 7-point running mean aerodynamic acceleration in +Y direction of M01_SPACECRAFT frame after step 3 of data processing (meters/s^2). AY7AS3 One sigma uncertainty in AY7AS3 (meters/s^2). SAY7 39-point running mean aerodynamic acceleration in +Y direction of M01_SPACECRAFT frame after step 3 of data processing (meters/s^2). AY39AS3 One sigma uncertainty in AY39AS3 (meters/s^2). SAY39 Axial force coefficient corresponding to AY1AS3 (dimensionless). CY1 One sigma uncertainty in CY1 (dimensionless). SCY1 Axial force coefficient corresponding to AY7AS3 (dimensionless). CY7 One sigma uncertainty in CY7 (dimensionless). SCY7 Axial force coefficient corresponding to AY39AS3 (dimensionless). CY39 One sigma uncertainty in CY39 (dimensionless). SCY39 Density corresponding to AY1AS3 (kg/m^3). RHO1 One sigma uncertainty in RHO1 (kg/m^3). SRHO1 Density corresponding to AY7AS3 (kg/m^3). RHO7 One sigma uncertainty in RHO7 (kg/m^3). SRHO7 Density corresponding to AY39AS3 (kg/m^3). RHO39 One sigma uncertainty in RHO39 (kg/m^3). SRHO39 Production of files in the DATA/PROF/ directory =============================================== We extracted the low rate and high rate data from files in DATA/RAW/, then discarded some isolated data points. High rate data for hundreds of orbits contain gaps of >30s towards the end of the outbound leg. Data after these gaps were discarded. There is an additional gap of >5s towards the end of the outbound leg in high rate data for both P109 and P173. Data after these gaps were discarded. There is a gap of 3s between the last and penultimate data points in orbits 26, 27, 28, 38, 69, 74, 123, 155, 170, 179-189, 249, 273, 276, 285, 292, 297, 299, 301, 303, 305, and 306. The last data point was discarded in these orbits. Gaps of 1s-2s in the high rate data remain in about 20% of the orbits. These are short enough that their effects are minimal, so the data were not modified to correct for them. This completes step 1 (data cleaning) of the data processing. No data were delivered to the PDS for orbits 1, 2, 3, 5, and 327. The possibility that data were acquired, but omitted from the dataset delivered to the PDS, for these orbits can be excluded. During aerobraking operations, "Quick Look Reports" were generated by the ACC team within hours of each periapsis pass in support of mission operations. These reports summarized ACC measurements from a given aerobraking pass. No "Quick Look Reports" were generated for these orbits, which suggests that no useful data were received on the ground. Low rate data, but not high rate data, exist for orbits 4, 57, 158, 213, 255, 266, 289, and 336. The high rate data stream for orbit 137 begins well inside the atmosphere, close to periapsis, and contains measurements at 4 s intervals instead of the usual 1 s intervals. The low rate data for orbit 137 are normal. Data for orbits 4 (low rate only, periapsis altitude = 290 km) and 6 (low rate and high rate, periapsis altitude = 160 km) exist, but aerodynamic accelerations cannot be separated from non-aerodynamic accelerations when altitudes are so high and aerodynamic drag is so weak. Results for orbits 1-336 used the following data streams: no results for orbits 1, 2, 3, 4, 5, 6 and 327; results based on low rate data for orbits 57, 137, 158, 213, 255, 266, 289 and 336; and results based on high rate data for all other orbits. Interpretation of the ACC measurements requires knowledge of ODY's position, velocity and orientation. The position, velocity, and orientation of ODY in an inertial reference frame during aerobraking were obtained from SPICE kernels m01_ab.bsp, m01_sc_ab0110.bc, m01_sc_ab0111.bc, m01_sc_ab0112.bc, m01_sc_ab0201.bc, and m01_sc_ab0202.bc [NAIF2008A]. The position and orientation of Mars in an inertial reference frame were obtained from SPICE kernels de414.bsp and pck00008.tpc. Time-related SPICE kernels naif0008.tls and orb1_sclkscet_00129.tsc were also used in this work. The velocity of the martian atmosphere, assuming that it rotates with the solid body of the planet, in an inertial reference frame was calculated using these SPICE kernels. The velocity of the atmosphere relative to the spacecraft and of the spacecraft relative to the atmosphere can be determined from this information. Spacecraft altitude was defined as the magnitude of vector P, which is defined as vector A minus vector B. Vector A is the vector position of ODY relative to the centre of mass of Mars. Vector B is the vector position of a point on a pre-defined martian areoid relative to the centre of mass of Mars and vector A is parallel to vector B. In this work, the MOLA 0.25 x 0.25 degree areoid was used [SMITHETAL2003]. Periapsis is defined in this work as the point of minimum altitude, not minimum radial distance. SPICE kernels for ODY's orientation are not available on 28 November 2001, which encompasses aerobraking passes on orbits 58 and 59. ODY's attitude on these orbits was assumed to be phi = 0 degrees and theta = -4 degrees, where phi and theta are defined later [TOLSONETAL2005]. This attitude, the nominal trim attitude, is consistent with ODY's average attitude for neighbouring orbits. Figures of orbit number, periapsis latitude, altitude, local solar time (LST) and Ls are contained in [TOLSONETAL2005] and [TOLSONETAL2007]. Ls is the aerocentric longitude of the Sun, a measure of the martian season. Ls is 0 degrees at the northern spring equinox, 90 degrees at the northern summer solstice, 180 degrees at the northern autumn equinox and 270 degrees at the northern winter solstice. These figures show that the ODY ACC measurements separate naturally into two subsets - dayside and nightside. In this work, "dayside" corresponds to 12 hours < LST < 24 hours and "nightside" corresponds to 0 hours < LST < 12 hours. The boundary between dayside and nightside is not the same as the terminator that separates the sunlit and shadowed hemispheres. Sub-solar latitude changed from -24.9 degrees N to -20.1 degrees N during ODY aerobraking, so all latitudes poleward of 65.1 degrees N (69.9 degrees N) were in darkness in the polar night at the start (end) of aerobraking. We wish to derive atmospheric densities, rho, from aerodynamic accelerations, vector aaero. Measured accelerations, vector ameas, are not identical to vector aaero. They are related by: vector ameas = vector aaero + vector abias + (1) vector agg + vector athr + vector omega x (vector omega x vector r) + vector omega-dot x vector r Vector abias represents the effect of sensor bias, vector agg, which is called the gravity gradient term, represents the effect of differences between the acceleration due to gravity at the sensor and at the spacecraft's centre of mass, vector athr represents the effect of reaction control system (RCS) thruster firings, vector omega is the angular velocity of the spacecraft, vector r is the position of the accelerometer with respect to the spacecraft's centre of mass, vector omega-dot is the rate of change of vector omega, and the last two terms represent the effects of angular motion of the sensor about the spacecraft's centre of mass. The derivation of atmospheric densities uses only the y-axis component of vector aaero, so we focus on the y-axis component of Equation 1. We now address each term in Equation 1. The two angular acceleration terms can, in principle, be calculated. SPICE orientation information is sufficient to determine vector omega and vector omega-dot. However, we do not know vector r accurately. The positions of the accelerometer and the centre of mass were measured before launch. The accelerometer has not moved since then, but the centre of mass has. Fuel consumption causes a secular change in centre of mass position. Accelerations experienced during aerobraking cause the fuel to slosh back and forth in the tanks, which also alters the centre of mass position. Rapid changes in vector r could introduce an additional term, a Coriolis term, into Equation 1. According to [TOLSONETAL2005], the accelerometer position is (x,y,z) = (0.164, -0.544, 1.137) metres relative to the centre of mass. However, the reference frame for this position is not defined. The frame suggested by Figure 1 of [TOLSONETAL2005] is not consistent with either the "M01_SPACECRAFT" frame or the "body coordinate system" [NAIF2008B, TAKASHIMA2002, CHAVIS&WILMOTH2005]. According to [CHAVIS&WILMOTH2005], the accelerometer position at the midpoint of aerobraking was (x,y,z) = (-0.629, -0.0172, 1.1) metres relative to the centre of mass in the "body coordinate system." This is (x,y,z) = (0.0172, 0.629, -1.1) metres relative to the centre of mass in the "M01_SPACECRAFT" frame. It is likely that the frame used by [TOLSONETAL2005] differs from the "M01_SPACECRAFT" frame by a factor of -1, which makes their accelerometer position (x,y,z) = (0.164, -0.544, 1.137) metres relative to the centre of mass. We do not correct vector ameas for the two angular acceleration terms, therefore angular accelerations influence the uncertainty in vector ameas. Vector athr is "two orders of magnitude less than the periapsis drag effect" [TOLSONETAL2005]. The typical acceleration at periapsis is 2E-2 m s^(-2), so the thruster term is on the order of 2E-4 m s^(-2). The nominal impulse, I, generated by a single RCS thruster firing is approximately I = 0.00804038 t + 0.02125765, where t is the duration of the thruster firing in milliseconds and I is in N-sec [MASE&BURKHART2000]. There are four RCS thrusters, labelled RCS1 to RCS4. The change in ODY's velocity due to an RCS thruster firing, vector Delta-v, equals I x vector e / m where m is ODY's mass and vector e is a unit vector. For RCS1, vector e = (-X, Y, -Z). For RCS2, vector e = (-X, -Y, -Z). For RCS3, vector e = (X, -Y, -Z). For RCS4, vector e = (X, Y, -Z). X = 0.8926, Y = 0.4162, and Z = 0.1736 [MASE&BURKHART2000]. These unit vectors are in the "M01_SPACECRAFT" frame. Thruster firings for orbit XXX are reported in ASCII files (pXXXthot.txt) that accompany the low rate accelerometer data. The cumulative times that each thruster has fired for are listed as functions of time. Typical thruster firings last for 0.1 sec, much less than the typical interval between cumulative times in pXXXthot.txt (1-10 sec). Since the times of thruster activity cannot be resolved, their contributions cannot be removed from the measured accelerations. Also, the actual impulse produced by a thruster will differ from the nominal impulse. Past experience has shown that determination of thruster impulse to within 50% is difficult [TOLSONETAL2005]. We do not correct vector ameas for thruster activity. Vector agg is on the order of 1E-6 m s^(-2) [CANCROETAL1998]. This is much smaller than vector athr, so we neglect it. When ODY is far outside the atmosphere, vector ameas = vector abias. Pre-entry and post-exit measured accelerations can be used to estimate instrument bias. Scatter in ameas,lo,y (the y-component of the low rate measured acceleration) was large enough that estimates of abias,lo,y could not be distinguished from zero. ameas,lo,y was not corrected for bias. abias,hi,y was calculated from pre-entry and post-exit accelerations. The pre-entry value of abias,hi,y was assumed to be the mean of all ameas,hi,y measurements from 10s after the start of the data stream to 60s later. The post-exit value of abias,hi,y was assumed to be the mean of all ameas,hi,y measurements from 70s before the end of the data stream to 60s later. These time ranges were chosen to ensure that aerodynamic accelerations and any transients associated with the beginning/end of the data stream were negligible. The typical pre-entry bias was -2.4E-4 m s^(-2) and the typical post-exit bias was -2.2E-4 m s^(-2). abias,hi,y was assumed to vary linearly with time during an aerobraking pass. The post-exit bias was assumed to equal the pre-entry bias for orbits 84, 91, 93, and 95 due to lack of adequate post-exit data. We correct vector ameas for bias for high rate data only. Thus aaero,lo,y = ameas,lo,y and aaero,hi,y = ameas,hi,y - abias,hi,y. This completes step 2 (data correction) of the data processing. We next formed 7-point and 39-point running means of aaero,lo,y and aaero,hi,y, effectively 7-s and 39-s averages, and labelled them aaero,lo,y,7; aaero,lo,y,39; aaero,hi,y,7 and aaero,hi,y,39. This reduced the noise in the accelerations at the expense of spatial resolution. The duration of the 39-point time series is shorter than the duration of the 7-point time series, which is shorter than the duration of the unaveraged time series, because a 7-point running mean cannot be calculated for the first three data points in a series of measurements. The noise inherent in aaero,lo,y; aaero,hi,y; aaero,lo,y,7; aaero,hi,y,7; aaero,lo,y,39 and aaero,hi,y,39 was estimated based on the standard deviation of selected pre-entry measurements. Measurements from 30s after the start of the time series to 60s later were used for aaero,lo,y; aaero,lo,y,7 and aaero,lo,y,39. Measurements from 10s after the start of the time series to 200s later were used for aaero,hi,y. Measurements from 10s after the start of the time series to 100s later were used for aaero,hi,y,7. Measurements from 30s after the start of the time series to 60s later were used for aaero,hi,y,39. The start times of these time series were chosen to ensure that transients associated with the beginning of the data stream did not affect any of the calculated noise values. The end times of these time series were chosen to ensure that aerodynamic accelerations did not affect any of the calculated noise values. These time series were made as long as possible to increase the accuracy of the noise calculation. Noise levels depend on the number of samples acquired per second: 200 for orbits 1-136, 50 for orbits 137-268 and 20 for orbits 269-330. The ratio of noise levels in aaero,hi,y for orbits 269-330 to orbits 1-136 is 6.05, significantly greater than the square root of the ratio 200/20, or 3.16, that would occur for samples from a Gaussian distribution. The ratio of noise levels in aaero,hi,y for orbits 137-268 to orbits 1-136 is 3.28, significantly greater than the square root of the ratio 200/50, or 2, that would occur for samples from a Gaussian distribution. The ratio of noise levels in aaero,hi,y for orbits 269-330 to orbits 137-268 is 1.84, close to the square root of the ratio 50/20, or 1.58, that would occur for samples from a Gaussian distribution. This suggests that scatter in aaero,hi,y for orbits 137-330, but not for orbits 1-136, can be considered to be Gaussian noise. Useful data are data that are clearly dominated by aerodynamic acceleration, not other factors such as instrument noise, the effects of thrusters, and the effects of angular accelerations. We process the dataset to remove those data points that are not useful. Accelerations due to thrusters are on the order of 2E-4 m s^(-2). Let the magnitudes of the y-component of the two angular acceleration terms in Equation 1 be Y1 and Y2 respectively. We estimate Y1 and Y2 using angular rate information from SPICE and vector r. We tested two values for vector r, both assumed to be in the M01_SPACECRAFT frame, vector r = (0.164, -0.544, 1.137) metres [TOLSONETAL2005] and vector r = (0.0172, 0.629, -1.1) [CHAVIS&WILMOTH2005]. Differences in Y1 and Y2 are relatively small, and we adopted the value derived from [TOLSONETAL2005]. Data points that were smaller than a threshold were deemed to be not useful. The threshold was calculated for each time step and each of the six sets of accelerations (aaero,lo,y; aaero,lo,y,7; aaero,lo,y,39; aaero,hi,y; aaero,hi,y,7 and aaero,hi,y,39). The threshold was the largest of (A) the relevant noise level, (B) 2E-4 m s^(-2), (C) Y1 and (D) Y2. Angular accelerations determine threshold values near periapsis when accelerations significantly exceed threshold values. Further from periapsis, the time at which accelerations cross the threshold is controlled by either the effects of thrusters (aaero,lo,y,7; aaero,lo,y,39; orbits 7-136 of aaero,hi,y; aaero,hi,y,7 and aaero,hi,y,39) or by noise (aaero,lo,y and orbits 137-336 of aaero,hi,y). Thus the vertical range of ODY density profiles is not affected by angular accelerations or choice of vector r. Data points that were smaller than their corresponding thresholds were discarded. This sometimes resulted in large gaps in the time series of retained data points, which is not desirable. To correct this, additional data points were discarded as necessary to ensure that the time series of retained data points was continuous. For example, suppose that data points at t < -100s did not exceed their thresholds, data points at -100s < t < -90s exceeded their thresholds, data points at -90s < t < -80s did not exceed their thresholds, data points at -80s < t < +100s exceeded their thresholds and data points at t > +100s did not exceed their thresholds. Data points at -80s < t < +100s would be retained, but all other data points would be discarded, including data points at -100s < t < -90s. Each retained data point was assigned an uncertainty equal to its corresponding threshold. This completes step 3 (data selection) of the data processing. The atmospheric density, rho, satisfies: m x |aaero,y| = 0.5 rho V^2 Cy A (2) where m is the spacecraft mass, aaero,y is the y-component of the aerodynamic acceleration, V is the scalar speed of the spacecraft relative to the atmosphere, or vice versa, Cy is an aerodynamic coefficient, and A is a reference area connected with Cy [WITHERSETAL2003A]. Similar equations exist for all directions. We use the y-axis in the M01_SPACECRAFT frame since acceleration measurements along this axis, which is close to the velocity of the spacecraft relative to the atmosphere, have the greatest signal-to-noise ratio. m decreased monotonically from 460.8 kg at the start of aerobraking to 451.7 kg at the end (pers. comm, Mase, 2006). Uncertainty in the absolute mass is 3 kg, although the change in mass from one orbit to the next orbit is known much more accurately (<1 g). A is 11.03 m^2 [CHAVIS&WILMOTH2005]. V is known from SPICE information. The product rho x Cy can be found using measured or known quantities (m, aaero,y, V, and A) at each time step along an aerobraking pass. Next, rho and Cy are determined from the product rho x Cy. ODY's Cy, typically about 2, is a function of density and the attitude of the spacecraft with respect to its velocity relative to the atmosphere. Spacecraft attitude can be expressed as two angles, phi and theta. If the velocity of the atmosphere relative to the spacecraft is vector U = scalar U x vector u, where vector u is a unit vector expressed in the M01_SPACECRAFT frame, then pitch (theta) and yaw (phi) angles are defined by [TAKASHIMA2002]. ux = cos(theta) sin(phi) (3) uy = cos(theta) cos(phi) (4) uz = - sin(theta) (5) Values of Cy for various rho, phi, and theta have been determined by numerical simulation. These values constitute the "aerodynamic database." The aerodynamic database was reported in [TAKASHIMA&WILMOTH2002] and provided to us by R. Mase (pers. comm., 2006). Uncertainties in Cy are estimated to be 3% [CHAVIS&WILMOTH2005]. Inputs to the numerical simulations ranged from 1E-4 kg km^(-3) to 1E4 kg km^(-3) for rho, from -60 degrees to +60 degrees for phi, and -60 degrees to +60 degrees for theta. These ranges encompassed all conditions encountered during aerobraking. We found the unit vector u as a function of time for each aerobraking pass. Angles phi and theta were then determined using Equations 3-5, also as functions of time for each aerobraking pass. At each time step in each aerobraking pass, the simulated value of Cy was found as a function of rho using the aerodynamic database. The simulated value of the product rho x Cy was also found as a function of rho. rho x Cy is a single-valued function of rho for any specified phi and theta, which enables both rho and Cy to be found from rho x Cy. At each time step in each aerobraking pass, the observed value of the product rho x Cy and the simulated function rho x Cy(rho) were compared to determine the value of rho. The value of Cy followed trivially. This technique is also discussed by [TAKASHIMA&WILMOTH2002] and [TOLSONETAL2005]. This process was applied to aaero,lo,y; aaero,hi,y; aaero,lo,y,7; aaero,hi,y,7; aaero,lo,y,39 and aaero,hi,y,39 to obtain rho,lo; rho,hi; rho,lo,7; rho,hi,7; rho,lo,39 and rho,hi,39. Uncertainties in each of these densities were found using [BEVINGTON1969]. (sigma,rho / rho)^2 = (sigma,m / m)^2 + (sigma,Cy / Cy)^2 + (6) (sigma,a / a)^2 where sigma,rho is the uncertainty in density rho and sigma,a is the uncertainty in the corresponding acceleration a. Derived densities that were smaller than their uncertainties were discarded. This sometimes resulted in large gaps in the time series of retained densities, which is not desirable. To correct this, other derived densities were discarded as necessary to ensure that the time series of retained densities was continuous. For example, suppose that densities at t < -100s did not exceed their uncertainties, densities at -100s < t < -90s exceeded their uncertainties, densities at -90s < t < -80s did not exceed their uncertainties, densities at -80s < t < +100s exceeded their uncertainties and densities at t > +100s did not exceed their uncertainties. Densities at -80s < t < +100s would be retained, but all other densities would be discarded, including densities at -100s < t < -90s. This completes step 4 (density derivation) of the data processing. Each aerobraking pass has up to six derived density profiles: rho,lo; rho,hi; rho,lo,7; rho,hi,7; rho,lo,39 and rho,hi,39. Each derived density value has an associated altitude. Derived densities rely on knowledge of the speed and direction of the spacecraft relative to the atmosphere. The velocity of ODY in an inertial frame is determined from SPICE information. The velocity of the atmosphere in an inertial frame is determined from the assumption that the atmosphere rotates at the same angular velocity as the solid planet. This assumption is not accurate. Models predict zonal and meridional winds of about 100 m s^(-1) at aerobraking altitudes [BOUGHERETAL1999, BOUGHERETAL2000, BOUGHERETAL2002]. These speeds are consistent with results from the first efforts to determine winds from aerobraking measurements [BAIRDETAL2007, CROWLEY&TOLSON2007]. If, instead of assuming solid body rotation for the atmosphere, we assume that there is a zonal wind of 100 m s^(-1), then derived densities are altered by <1%. A meridional wind of 100 m s^(-1) alters derived densities by about 5%. Data users should be aware of this potential source of error, which is not included in the derived uncertainties (Equation 6) because the accuracy of wind predictions has not been quantified. Contents of DATA/ANC/ directory =============================== Filenames in the DATA/ANC/ subdirectory are ACCANCPXXX.ZZZ where XXX is the orbit number and ZZZ is either LBL or TAB. Each data file contains data from one orbit. Each ancilliary data file contains the following items. Orbit number (dimensionless). ORBIT_NUMBER_ANC The time of periapsis (UTC). PERI_TIME_ANC Distance between the spacecraft and the center of mass of Mars at periapsis (km). PERI_RADIUS_ANC Altitude of spacecraft above areoid at periapsis (km). PERI_ALT_ANC Areocentric latitude, degrees north, at spacecraft at periapsis. PERI_LAT_ANC Areocentric longitude, degrees east, at spacecraft at periapsis. PERI_LON_ANC Local true solar time at spacecraft at periapsis (hours). PERI_LST_ANC Solar zenith angle at spacecraft at periapsis (degrees). PERI_SZA_ANC Ls of Mars at periapsis (degrees). PERI_LS_ANC Mass of spacecraft at periapsis (kg). SCT_MASS_ANC Reference area of spacecraft at periapsis (m^2). SCT_AREA_ANC Data rate, 0=LO or 1=HI (dimensionless). DATARATE_ANC Bias in AY_RAW_HI calculated from pre-entry data (m/s^2). PREBIAS_ANC Bias in AY_RAW_HI calculated from post-exit data (m/s^2). POSTBIAS_ANC Noise in AY1AS2 (m/s^2). AY1AS2NOISE_ANC Noise in AY7AS2 (m/s^2). AY7AS2NOISE_ANC Noise in AY39AS2 (m/s^2). AY39AS2NOISE_ANC Production of files in the DATA/ANC/ directory ============================================== File ACCANCPXXX.TAB was produced alongside file ACCPROFPXXX.TAB, where XXX is the orbit number. Quantities were calculated as described in the DATA/PROF/ section. Thus files ACCANCP004.TAB and ACCANCP006.TAB were not produced, despite the existence of ACC data for orbits P004 and P006, because no valid density measurements were obtained for those orbits. Future data users may desire ancilliary information for these aerobraking passes, which we report here. Ancilliary information for orbit P004: ORBIT_NUMBER_ANC 004 PERI_TIME_ANC 2001-299T10:16:52.093 PERI_RADIUS_ANC 3672.7110 PERI_ALT_ANC 291.91641 PERI_LAT_ANC 67.249424 PERI_LON_ANC 352.23104 PERI_LST_ANC 18.279167 PERI_SZA_ANC 114.33280 PERI_LS_ANC 259.87815 SCT_MASS_ANC 460.80000 SCT_AREA_ANC 11.03000 DATARATE_ANC 0.00000 PREBIAS_ANC Not calculated POSTBIAS_ANC Not calculated AY1AS2NOISE_ANC Not calculated AY7AS2NOISE_ANC Not calculated AY39AS2NOISE_ANC Not calculated Ancilliary information for orbit P006: ORBIT_NUMBER_ANC 006 PERI_TIME_ANC 2001-300T23:18:34.727 PERI_RADIUS_ANC 3539.2647 PERI_ALT_ANC 158.63646 PERI_LAT_ANC 67.494803 PERI_LON_ANC 170.98553 PERI_LST_ANC 18.216111 PERI_SZA_ANC 114.07077 PERI_LS_ANC 260.85521 SCT_MASS_ANC 457.80000 SCT_AREA_ANC 11.03000 DATARATE_ANC 1.00000 PREBIAS_ANC Not calculated POSTBIAS_ANC Not calculated AY1AS2NOISE_ANC Not calculated AY7AS2NOISE_ANC Not calculated AY39AS2NOISE_ANC Not calculated Contents of DATA/CALT/ directory ================================ Filenames in the DATA/CALT/ subdirectory are PPPQQQ.ZZZ where PPP is either IN or OUT, QQQ is 100, 110, 120, 130, 140, 150 or 160, and ZZZ is either LBL or TAB. QQQ gives the value of the reference altitude in km. Each data file contains data from multiple orbits. Each constant altitude data file contains the following items. Orbit number (dimensionless). ORBIT_NUMBER_CALT Time (UTC) when spacecraft is at reference altitude. TIME_UTC_CALT Areocentric latitude, degrees north, of spacecraft at reference altitude. LATITUDE_CALT Areocentric longitude, degrees east, of spacecraft at reference altitude. LONGITUDE_CALT Local true solar time at spacecraft at reference altitude (hours). LST_CALT Solar zenith angle at spacecraft at reference altitude (degrees). SZA_CALT Ls of Mars when spacecraft is at reference altitude (degrees). LS_CALT Fitted atmospheric density at reference altitude (kg/m^3). RHO_CALT One sigma uncertainty in RHO_CALT (kg/m^3). SRHO_CALT Fitted density scale height at reference altitude (km). DSH_CALT One sigma uncertainty in DSH_CALT (km). SDSH_CALT Fitted temperature at reference altitude (K). TEMP_CALT One sigma uncertainty in TEMP_CALT (K). STEMP_CALT Reduced chi-squared for fit (dimensionless). REDCHISQD_CALT Number of data points used for fit (dimensionless). NPTS_CALT Production of files in the DATA/CALT/ directory =============================================== The 1-second sampling rate (<1 km vertical resolution) in the derived density profiles is not necessary for many studies of large-scale atmospheric processes. Another dataset of reduced size, called the constant altitude dataset, was generated from rho,39 data to support such studies. Orbits for which rho,hi,39 data were available used rho,hi,39 data. Orbits for which rho,hi,39 data were not available used rho,lo,39 data. rho,39 measurements for a given orbit were first split in two. All densities before periapsis, including the periapsis density, were assigned to the inbound leg. All densities after periapsis, including the periapsis density, were assigned to the outbound leg. Each leg was processed separately. Target altitudes were defined as 100 km, 110 km, 120 km, 130 km, 140 km, 150 km, and 160 km. Periapsis never reached 90 km. If density measurements existed more than 3 km below the target altitude and more than 3 km above the target altitude, then we proceeded to determine constant altitude data products for that target altitude. We assume that densities, rho, within 5 km of the target altitude, z0, satisfy: rho = rho0 x exp( -(z-z0) / Hrho ) (7) where rho0 is the density at z0 and Hrho is the density scale height between z0 - 5 km and z0 + 5 km. Equivalently: ln rho = ln rho0 + (-1 / Hrho) x (z-z0) (8) Defining y = ln rho, x = z - z0, a = ln rho0 and b = -1/Hrho, we have: y = a + b x (9) Values of x, the independent variable, are known exactly. Values of y, the dependent variable have uncertainties sigma,y = sigma,rho / rho. We use standard least-squares techniques, Equation 6-12 of [BEVINGTON1969] as implemented by the IDL POLY_FIT procedure, to determine best-fit values of a and b, and uncertainties sigma,a and sigma,b. Then we have [BEVINGTON1969]: rho0 = exp(a) (10) sigma,rho0 = sigma,a x rho0 (11) Hrho = -1 / b (12) sigma,Hrho = Hrho x Hrho x sigma,b (13) Assuming an isothermal atmosphere, temperature, Trho, and its uncertainty, sigma,Trho, were estimated from the fitted density scale height, Hrho, using: Trho = ( mu g Hrho ) / kB (14) sigma,Trho / Trho = sigma,Hrho / Hrho (15) where mu is mean molecular mass, assumed to be 43.49 daltons, g is the acceleration due to gravity, and kB is Boltzmann's constant. The assumed mu, which corresponds to Viking Lander measurements at the surface, is an overestimate [OWEN1992, MAGALHAESETAL1999]. Light species such as O are more abundant in the thermosphere than near the surface. Data users who wish to make a different assumption concerning mu can simply multiply our Trho and sigma,Trho by the ratio of their desired mean molecular mass to 43.49 daltons. g is given by: g = GM / (Rref + z)^2 (16) where Rref is the mean equatorial radius of the MOLA areoid used in this work, 3396 km, G is the gravitational constant, and M is the mass of Mars [SMITHETAL2003]. GM = 4.2828382332E13 m^3 s^(-2) [TYLERETAL2000]. No fitted rho, Hrho, or Trho had a smaller absolute value than its uncertainty. One set of results for Hrho and Trho was negative (orbit 12, outbound 130 km, Hrho = -75 km, sigma,Hrho = 29 km, Trho = -1340K, sigma,Trho = 480K). Recall that aerobraking passes are not vertical; they span significant horizontal extent. Densities do decrease with altitude at 130 km on the outbound leg of this aerobraking pass, presumably due to some kind of wave in the atmosphere, so this negative scale height is formally accurate. However, this illustrates that caution should be used when interpreting scale heights derived from non-vertical density profiles. Fitted values of rho cannot be negative, due to the exponential fitting approach. Results were obtained at 110 km and 120 km for almost all orbits, at 100 km for >50% of orbits, and at 140 km outbound for >20% of orbits. Results at 150 km and 160 km are essentially non-existent. Accelerations were measured at 140 km on outbound legs at daytime LSTs more frequently than at 140 km on inbound legs, and the difference between daytime and nighttime densities at 140 km explains why there are so many more outbound 140 km measurements than inbound 140 km measurements. Acronyms ======== AASTEX AASTeX is a LaTeX-based package that can be used to mark up manuscripts for American Astronomical Society (AAS) journals ACC Accelerometer ASCII American Standard Code for Information Interchange ET Ephemeris Time IDL Interactive Data Language, a computer programming language IMU Inertial Measurement Unit LMA Lockheed Martin Astronautics 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 MGS Mars Global Surveyor MHSA MGS Mars Horizon Sensor Assembly MOLA Mars Orbiter Laser Altimeter MTGCM Mars Thermospheric General Circulation Model NAIF Navigation and Ancillary Information Facility NASA National Aeronautics and Space Administration ODY 2001 Mars Odyssey PDS Planetary Data System POST Program to Optimize Simulated Trajectories SPICE An information system used for mission design and for planning observations SZA Solar Zenith Angle TES Thermal Emission Spectrometer UTC Coordinated Universal Time " CONFIDENCE_LEVEL_NOTE = " Data Coverage and Quality ========================= Geographical coverage is described by [TOLSONETAL2005]. Vertical extent is approximately 90 km to 160 km. Gaps in time series data have been discussed earlier in this file. No erroneous data points remained after step 1 of the data processing. Uncertainties in measured accelerations have been inferred from the available data and documentation. Additional information may exist that could improve the accuracy of the uncertainties. As discussed earlier in this file, low rate accelerometer data, which are noisier than high rate accelerometer data were used for orbits that lacked high rate accelerometer data. Estimated effects of thrusters and angular accelerations have been used to truncate data series, but have not been removed. Attitude information was not available for orbits P058 and P059, so the nominal attitude was assumed. Uncertainties are reported for all data products. Limitations and Caveats ======================= The effects of winds on the speed of the spacecraft relative to the atmosphere have not been included. These may affect densities by 5%. These density profiles are not vertical profiles, they have significant horizontal extent. That affects interpretation of apparent vertical trends. Waves in density profiles can prevent fitted densities and density scale heights from representing the mean state of the atmosphere. For example, an unusually large density scale height may be caused by a wave, not high temperatures and associated small changes in background density with altitude. "