Doppler shift as Computational Tool, Mars Pathfinder – by Albert
Lim
Doppler shifts are common among research in establishing the expanding
Universe ( e.g. Hubble ) and the motion of galaxies, rotation of stars, binaries and
studies of spectroscopic binaries etc. However, even closer to home, Doppler shift can
also be used as powerful computational tools to study the interior of planets as the
below example shows.
Mars Pathfinder - Background Information
On 4th December 1996, a Delta II - 7925 launch vehicle with a payload
assist module (PAM) propelled the Mars Pathfinder into Earth's orbit and on its 7 month
long journey to explore Planet Mars. About 30 hours after launch, Pathfinder will be
asked to determine its orientation in space by locating specific stars and adjust its
position to be in a direct line of sight to the Earth. A series of 4 Trajectory Correction
Manoeuvres or TCMs had also to be performed to put Pathfinder on course to Mars. Tracking,
telemetry and command operations were conducted using the Deep Space Network(DSN) - NASA's
international network of antennas that supports interplanetary spacecraft missions managed
and operated by Jet Propulsion Laboratory (JPL). The DSN essentially consist of 3 deep-space
communications facilities placed approximately 120 degrees apart around the world (in
California, Spain and Australia) to permit constant link to the spacecraft as the Earth
rotates.
On 4th July 1997, Mars Pathfinder - the second of NASA's low cost, quick
Discovery class missions, successfully entered the Martian atmosphere, landed and deployed
a small rover named Sojourner which explored an area approximately 200 square meters
on the surface of Mars. Pathfinder utilise a combination of an 11 meter (36 foot ) parachute,
rocket braking systems and air bags to cushion the impact to achieve this historic and
novel soft, upright landing at a site in the Ares Vallis region ( 19.33N 33.55W ) at
2.58 am true local solar time.
Pathfinder's lander had operated nearly 3 times its designed lifetime
of 30 sols (i.e. Martian days / 1 sol = 24.6 Earth hours ), while the Sojourner rover
operated 12 times its designed lifetime of 7 sols on the surface of Mars. Pathfinder
collected data from 3 science instruments and 10 technology experiments for nearly 3
months and returned 2.6 billion bits of information ( new data ) including over 16,000
lander and 550 rover images, 16 chemical analyses of rocks and soil and 8.5 million individual
temperature, pressure and wind measurements. A record 566 million "hits" were
registered during the first month of the mission making the Pathfinder landing by far
the largest Internet event in recorded history. The lander has since been named the Sagan
Memorial Station in honour of Carl Sagan.
The last successful data transmission cycle from Pathfinder was completed at 3.23am Pacific
Daylight Time on Sept 27th 1997 which was sol 83 of the mission.
Who proposed the use of Doppler shift as computational tool for Pathfinder ?
Dr. William Folkner, an interdisciplinary scientist at JPL who was part
of the Pathfinder Science Team was the first to propose the use of Doppler measurements
and ranging techniques to determine the variations in the rotation of Mars and hence
determine properties of its interior and climate.
He proposed studies to determine optimal times for Doppler tracking measurements to be
acquired from Mars Pathfinder and modification of software to include Pathfinder tracking
data with the earlier Viking lander data combined to establish the precession constant
and seasonal rotation variations of Mars.
The Viking lander data has given an estimate of the Martian precession
constant with 5% uncertainty and detection of annual rotation-rate variations with 20%
uncertainty. Viking results alone Dr. Folkner argued were not accurate enough to place
meaningful constraints on the interior structure of Mars. By combining Viking and Pathfinder's
new data, the precession constant can be determined to about 1% or better and enable
scientist to refine the moment of inertia of Mars and place significant constraints on
models for the composition of the mantle. At that time, it should be remembered that
the moment of inertia was called “the single most important number about Mars
that we don’t know”.
In addition, Doppler tracking data from the lander can be used to investigate
possible changes in the gravitation constant G, place tighter constraints on parameters
( such as the PPN parameter
γ ) that describe the theory of gravity and to determine masses of some of the
asteroids that perturb the orbit of Mars.
What significance is there for Doppler shift data for Pathfinder ?
How can this Doppler shift data from the Doppler Tracker be used ?
Mission scientist can use Doppler shifts in radio communication signals
and ranging from Pathfinder to measure the rotation of Mars. This can be achieved through
daily Doppler tracking and less frequent 2-way ranging during communication sessions.
These can determine the position of the lander to a position of 100 meters - this
position can be established to an accuracy a few meters within a few months in the months.
The last such positional measurement was done by Viking over 20 years ago. In the meantime,
the pole of the planet has undergone precession - that is, the tilt of the planet has
wobbled. If the exact location of the Mars Pathfinder lander was known, the orientation
and precession rate ( i.e the regular motion or change of the Martian poles with respect
to the ecliptic ) can be calculated. These data can then be compared to those of Viking landers
20 years ago - the difference between the 2 positional measurements should yield the
rate of precession. Knowing the precession rate allows scientist to directly calculate
the moment of inertia. These provides the constraints ( since it is a function of the
distribution of mass within Mars ) scientist are looking for to establish the density
of the Martian rock with depth. So indirectly, Doppler computation can provide valuable
information about the interior of Mars.
Given 4 parameters, the core size, mass and mantle of Mars can be determined.
The combination of Pathfinder Doppler data with earlier data from Viking landers can
determine the third parameter - the moment of inertia - through Doppler data calculations
to yield Mar’s precession rate. While a forth parameter is needed to complete the
interior model, this can be achieved through future Doppler tracking since presence of
a fluid core may be detectable through its effects on Mars’ nutation. For now,
if Pathfinder can determine the moment of inertia of Mars - it is by itself already a
significant constraint on possible models for Mars’ interior.
How Doppler shift data was acquired in Pathfinder mission ?
Because this rotational and orbital dynamics experiment was based on
the measuring of Doppler range to the Pathfinder using radio link, Pathfinder was equipped
with special 2 way transponder in the X-band.
The Mars Pathfinder utilises the Cassini-designed Deep Space Transponder (DST).
DST is capable of generating 2 way X-band Doppler and range data via the DSN. Two way
( or coherent ) Doppler is produced by measuring the received frequency of the downlink
carrier and comparing it with the uplink carrier frequency which is known and stable.
Because the lander moves in relation with the tracking station, the velocity between
the two causes a shift in observed frequency known as Doppler shift - measuring
this shift can establish the exact location of the Mars Pathfinder. Typical Doppler noise
at X-band is 0.003 - 0.006 Hz for a 60-second count. Similar Doppler techniques are used
by the navigation team of Pathfinder to determine the actual trajectory and its orbit
for navigational purposes.
In operation, DSN transmit a signal to Pathfinder. The spacecraft tracks
the phase of the uplink signal and generates a phase-coherent downlink signal. The DSN
then compares the received frequency with the same reference reference frequency from
which the uplink was generated. The spacecraft transponder turn around ratios for X band
up and down link are 880 / 749 in the below specially allocated frequency range :
X-band
uplink : 7145
- 7190 MHz
X-band
downlink : 8400
- 8440 MHz
DSN reports Doppler data in the form of a continuous phase count which
is equivalent to integration of biased Doppler frequency over time.
Mars rotation about its poles causes a signature in the Doppler data
with a daily minimum when the lander is closest to the Earth. Changes in daily signature
reveal information about the planet’s interior through its effect of precession
and nutation.
Outcome from Doppler Tracking / rotational and orbital dynamics experiment
Daily Doppler tracking and two way ranging during communications sessions
provided data to calculate very precise position of the lander. These allow calculation
of precession rate and the moment of inertia of Mars. The calculated precession
rate is consistent with the hypothesis that the non-hydrostatic component of inertia
at 0.3653 + / - 0.0056 and is due to the Tharsis bulge.
From Pathfinder’s determination of the moment of inertia, we know
that Mars must have a central metallic core of between 1,300 and 2,400 km in radius.
We know also know that if the iron-enriched Sherottite meteorites are typical of the
mantle composition of Mars, then the mantle must be warmer than Earth’s at the
same pressure levels. Scientist for the first time now can put constraints on interior
temperatures of Mars.
Pathfinder also detected an annual variation in the planet’s rotation
rate which can be explained by the seasonal exchange of carbon dioxide between the atmosphere
and the ice caps.
Long term signatures in Doppler data were detected and attributed to
perturbations caused by asteroids. The masses of asteroids were also calculated and determined
from Pathfinder Doppler data.
Because of Pathfinder, scientist can now also understand how Mars has
evolved over time much better. This was expressed clearly by Dr. David Baltimore who
is president of the California Institute of Technology which manages JPL for NASA. I
am confident astronomers from all over the world would agree to that.
