As the spacecraft traveled through the atmosphere to its landing site, the Atmospheric Structure Investigation/Meteorology package (ASIMET) measured aerodynamic accelerations on the lander throughout the entry using onboard accelerometers. In addition, sensors directly measured pressures and temperatures during the parachute descent phase, which began at about 8.5 km above the landing site. This data set contains the profiles of atmospheric density, pressure, and temperature derived from the accelerations measured prior to parachute release.
A first description of the ASIMET results can be found in [SCHOFIELDETAL1997]. The ASI experiment is described in the same reference.
The tabular file is formatted so that it may be read directly into many database management systems (DBMS) or spreadsheet programs on various computers. All fields in the table are separated by commas, and are right justified. The 'start byte' and 'bytes' values listed in the PDS label do not include the commas between fields. The records are of fixed length, and the last two bytes of each record contain the ASCII carriage return and line feed characters. This allows the table to be treated as a fixed length record file on computers that support this file type and as a normal text file on other computers.
The PDS label is object-oriented. The object to which the label refers (the TABLE) is denoted by a statement of the form:
^object = location
^TABLE = 'EDL_DDR.TAB'
The detached label file is a stream format file, with a carriage return (ASCII 13) and a line feed character (ASCII 10) at the end of each record. This allows the file to be read by the MacOS, DOS, UNIX, and VMS operating systems.
The second column shows the elapsed time, in seconds, since the spacecraft passed the altitude of 3,597.2 km. The first data point in the file is at time = 34.156 seconds, with a corresponding SCLK of 1246726312.75. At that time, the equivalent UTC time was 16:51:46.440, July 4, 1997.
The third column shows the altitude of the spacecraft above the landing site, in kilometers. Note that the radius of Mars at the landing site is 3389.72 km [FOLKNERETAL1997B].
Column four shows the planetocentric latitude, in degrees, of the spacecraft at the time the sample was acquired.
The fifth column contains the east longitude, in degrees, of the spacecraft.
The sixth column contains the calculated atmospheric density, in kilograms per meter cubed.
The seventh column contains the calculated atmospheric pressure, in millibars.
The eighth column contains the calculated atmospheric temperature, in Kelvin.
Column nine contains the mean molecular weights (amu) that were used to evaluate the atmospheric temperatures. These mean molecular weights were derived from molecular weight as a function of pressure measured by the Viking 1 Upper Atmosphere Mass Spectrometer [SEIFF&KIRK1977].
The tenth column shows the width of the uncertainty envelope in the positive direction, of the atmospheric density. It is measured in kilograms per meter cubed. The value in the sixth column plus the value in this column gives the upper boundary of the density uncertainty envelope.
The eleventh column shows the width of the uncertainty envelope in the negative direction, of the atmospheric density. It is measured in kilograms per meter cubed. The value in the sixth column plus the value in this column gives the lower boundary of the density uncertainty envelope.
The twelfth column shows the width of the uncertainty envelope in the positive direction, of the atmospheric pressure. It is measured in millibars. The value in the seventh column plus the value in this column gives the upper boundary of the pressure uncertainty envelope.
The thirteenth column shows the width of the uncertainty envelope in the negative direction, of the atmospheric pressure. It is measured in millibars. The value in the seventh column plus the value in this column gives the lower boundary of the pressure uncertainty envelope.
The fourteenth column shows the width of the uncertainty envelope in the positive direction, of the atmospheric temperature. It is measured in Kelvin. The value in the eighth column plus the value in this column gives the upper boundary of the temperature uncertainty envelope.
The fifteenth column shows the width of the uncertainty envelope in the negative direction, of the atmospheric temperature. It is measured in Kelvin. The value in the eighth column plus the value in this column gives the lower boundary of the temperature uncertainty envelope.
A full description of the data and the procedure used to generate the atmospheric structure profiles on this CD can be found in [ HREF="ref:htm#MAGALHAESETAL1999">MAGALHAESETAL1999]. The procedure for the reconstruction of planetary atmospheric structure from accelerometer data was first described by [SEIFFETAL1973], and a more detailed description of the procedure appeared in [SEIFF&KIRK1977]. The analysis of the Mars Pathfinder ASI data has utilized the same basic deterministic approach, but the analysis algorithm and software were independently developed to refine and extend the atmospheric structure reconstruction procedure used previously. The reconstruction procedure used to derive the profiles in this file can be divided into four general steps. First, the trajectory of the lander was reconstructed using the measured accelerations, a model for the gravity field of the planet, the equations of motion of the lander, and an initial condition provided by the Navigation Team. Second, the atmospheric density profile was derived from the measured aerodynamic decelerations and the aerodynamic characteristics of the Pathfinder lander. Third, an atmospheric pressure profile was derived by integrating the equation of hydrostatic equilibrium using the density profile. Fourth, an atmospheric temperature profile was derived from the ideal gas law using the density profile, pressure profile, and a model for the variation of mean molecular weight with pressure.
With knowledge of the external forces acting on the spacecraft, the velocity and position of the probe were determined by integrating the equations of motion starting with an initial condition provided by the Navigation Team. The equations of motion written in a planet-centered spherical coordinate system rotating with the planet were used for the computations. The acceleration due to gravity was not directly measured by the accelerometers during passage through the atmosphere. To include the effects of gravity, we have used a gravity model that includes the first zonal harmonic coefficient J2 in the normalized spherical harmonic expansion of the gravity field (cf. [HUBBARD1984]). For Mars J2 = 8.759 x 10-4 [SMITHETAL1993]. Higher order harmonics are of much smaller magnitude [SMITHETAL1993] and are not important over the short time interval of EDL. The aerodynamic drag on the vehicle was directly obtained from the three-axis science accelerometer measurements. Due to the small angle of attack alpha (= angle between the symmetry axis of the entry vehicle and the direction of the relative velocity vector) during the Pathfinder entry (cf. [BRAUNETAL1995]) and due to the close proximity of the z-axis accelerometer to the axis of symmetry, the measured z-axis accelerations during entry were very close (generally within 0.02%) to the true deceleration along the flight path.
Initial conditions for the integration were provided by the Mars Pathfinder Navigation Team in the form of an entry velocity and entry location at a prescribed time. This so-called 'entry state' is based on observations of range and rate of motion along the line-of-sight derived from radiometric tracking of the spacecraft combined with trajectory solutions based on high-order models of the gravitational forces on the vehicle from solar system bodies (cf. [KALLEMEYNETAL1996]). The 'entry state' for 4-July-1997 16:51:12.28 UTC with 1-sigma uncertainties listed is r = 3597.2±1.7 km, theta = 23±0.04 degrees N Areocentric latitude, phi = 343.67±0.01 degrees East Longitude, VR = 7444.7±0.7 m/s, gamma = 16.85±0.02 degrees, psi = 255.41±0.02 degrees. r is the radial distance from the center of mass of the planet. VR is the entry speed, gamma is the flight path angle below horizontal, and psi is the flight path azimuth measured clockwise from North (all in a Mars-fixed, ie rotating, coordinate system). This initial state was marched forward in time using a fourth and fifth order Runge-Kutta-Fehlberg integrator with automatic step-size control.
Atmospheric density rho is related to the aerodynamic deceleration of a spacecraft through the aerodynamic drag equation:
-2m Av
rho = ----- ------ (1)
C_D A V_R**2
where Av is the acceleration along the flight path relative to the
atmosphere, V_R is the probe velocity relative to the atmosphere, m is
the probe mass, C_D is the drag coefficient of the probe, and A is the
probe's cross-sectional area. The drag coefficient C_D varies during
the entry, and this variation can be accounted for iteratively using
aerodynamic databases compiled from pre-flight experiments and
numerical simulations, as discussed further below. V_R was set equal
to the velocity relative to the surface of the planet (V), which was
derived from the trajectory reconstruction, since the Pathfinder
lander's velocity was very much greater than expected wind magnitudes
during the time interval covered by this file. During the entry
phase, the total mass of the Mars Pathfinder entry vehicle was m =
585.3 kg and it's area was A = 5.526 m2. During the
parachute descent phase, the total mass was initially decreased by the
mortar firing (0.5 kg) and later by the separation of the heatshield
(74 kg). The total area of the parachute was approximately 121
m2. The aerodynamic drag coefficient C_D of the lander is needed in order to evaluate atmospheric densities from the observed decelerations and the reconstructed trajectory, as shown in eq. 1. The aerodynamic properties of the Mars Pathfinder entry vehicle were determined from experimental data and computational fluid dynamic simulations, and these data have been used to create an aerodynamic database [BRAUNETAL1995]. C_D varies during the entry and depends on the velocity of the vehicle, the angle of attack alpha, the Knudsen number (Kn), and Mach number (Mach). Since Kn depends on the atmospheric density and Mach depends on the atmospheric temperature, an iterative procedure was required to accurately determine the atmospheric density and aerodynamic coefficients. Initial density, pressure, and temperature profiles were evaluated by assuming a constant value of C_D. From these profiles, Kn and Mach as a function of time were determined and used to evaluate improved values of C_D from the aerodynamic database. The resulting new density, pressure, and temperature profiles were then used as a basis for the next iteration. This procedure was continued until successive iterations yielded minor change in the atmospheric structure. Two iterations beyond the initial profiles were found to yield excellent convergence.
Atmospheric pressure (p) was derived from the density by integrating the equation of hydrostatic equilibrium from an initial altitude z0 down to each value of altitude z. z0 = 140 km was used since at this altitude the density measurements are well above the instrument's threshold value, which is determined by the digital resolution. The initial value p(z0) for the integration is estimated by using rho(z0) and d[rho]/dz at z0 to derive a density scale height and hence temperature, which can be used with the ideal gas law and an estimate of the mean molecular weight to derive a starting pressure. The temperature profile was derived from the density and pressure profiles by using the ideal gas law and a model for the variation with pressure of the mean molecular weight.
We have assumed that the atmosphere is well mixed below ~100 km altitude with a mean molecular weight of 43.49, which is based on Viking Lander mass spectrometer measurements [OWEN&BIEMANN1976]. At higher altitudes photodissociation and diffusive separation lead to a gradient with altitude of the mean molecular weight. We have created a model for the variation of molecular weight with pressure based on the Viking 1 Upper Atmosphere Mass Spectrometer results [NIER&MCELROY1977, SEIFF&KIRK1977]. The mean molecular weights in column 9 are derived from this model.
Address: Planetary Data System, PDS Operator
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109Phone: (818) 354-4321 Email: pds_operator@jpl.nasa.gov WWW URL: http://pds.jpl.nasa.gov/
The temperatures have been evaluated using a molecular weight model based on the Viking 1 Upper Atmosphere Mass Spectrometer results [NIER&MCELROY1977, SEIFF&KIRK1977], as discussed above. Although the season, landing site coordinates, and solar cycle phase were very similar for the Pathfinder and Viking 1 landings, the Local Solar Time of the two landings were quite different. The NCAR Mars Thermospheric General Circulation (MTGCM) models of the upper atmosphere (cf. [BOUGHERETAL1990]) indicate that substantial diurnal variation in the molecular weight profile can occur (Bougher, personal communication). To estimate the uncertainties in the temperatures due to possible diurnal variations in the molecular weights, we have evaluated temperatures using molecular weight profiles from the MTGCM (Bougher, personal communication) runs for local times around the Pathfinder landing. To the extent that the MTGCM and Viking 1 profiles bound the possible range of molecular weights, the uncertainty ranges from ~4 Kelvin near 140 km altitude down to zero at altitudes near and below 100 km. Note that these uncertainties are much smaller than the error envelopes included in the file.
| Lyle Huber | - | PDS Atmospheres Node, New Mexico State University |
| Julio Magalhaes | - | MPF ASI/MET Team, NASA Ames Research Center |
| Jim Murphy | - | MPF ASI/MET Team & PDS Atmospheres Node, New Mexico State University |
| Tim Schofield | - | MPF ASI/MET Team Lead, Jet Propulsion Laboratory |
| Rob Sullivan | - | MPF Participating Scientist, Cornell University |
| Betty Sword | - | PDS Central Node Data Engineer, Jet Propulsion Laboratory |
| John Wilson | - | Non-MPF scientist, Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University |
After accelerometer gain state changes, very brief transients were produced in the accelerometer data as expected based on tests of the accelerometers and associated electronics prior to launch. The extent of these transients were defined by careful inspection of the data near the time of the gain change and by extrapolating data acquired immediately prior to the gain change to define the end of the transient. The time constant for the transients was far less than one second. Inspection of the data using the procedure mentioned above showed that the effects of the transients were generally undetectable within about 1 second of the gain change. The values in the transient were then replaced by interpolation between the values acquired before the gain change and the values acquired about 1 second after the gain change. Since the rise and fall of the peak deceleration pulse due to the atmosphere varies approximately exponentially with time, extrapolation and interpolation through the transients was performed using the logarithm of the accelerations for gain changes occurring during the deceleration pulse.
Only two data values were missing from the accelerometer measurements; one z-axis measurement (at SCLK 1246726322.53) and one x-axis measurement (at SCLK 1246726361.41). These two points were replaced by using linear interpolation across the adjacent points.