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Background
The
characterization of drag forces on spacecraft is an
important area of research with applications in precision
orbit determination, formation flying, re-entry dynamics,
laser communication, collision avoidance, and improving our
understanding of atmospheric and space-weather science.
All of these areas depend on the improvement of neutral
atmosphere models.
Space Environment
The
"neutral" in "neutral atmosphere" refers to non-ionized
particles, and the thermosphere is the region where these
particles affect LEO spacecraft. The thermosphere
extends from an altitude of approximately 80 km to 750 km,
and consists mainly of atomic oxygen along with trace
amounts of molecular nitrogen and molecular oxygen.
The thermosphere and its relation to the lower-atmospheric
regions is illustrated in the figure . It is collisions with particles in
the thermosphere, especially atomic oxygen, which account
for atmospheric drag on spacecraft in LEO.
Density Variability
The largest
variations in drag are caused by variations in atmospheric
density, which can be correlated to local time (sun angle),
solar and geomagnetic activity, latitude, and altitude.
 The
dominant characteristic of the density distribution is the
day-night cycle. On the day side, the atmosphere is
heated by solar radiation and expands, causing a significant
increase in density and therefore in drag. During
solar maximum the difference between the night and day time
density at 400 km altitude can be as much as 80%. Other
significant periodic variations are correlated to the time
of year and the 27-day rotation of the sun. In
addition, an order of magnitude change in density is linked
to the eleven-year solar sunspot cycle. The next solar
maximum will peak around the year 2012, and will be
associated with increased geomagnetic and neutral atmosphere
activity. This peak will coincide with the expected
launch for Nanosat V, and would be an ideal window for
achieving the DANDE mission science objectives.
Variations
in density are not necessarily uniform. Fluctuations
are characterized as either small-scale (100-500 km) or
large-scale (1,000-4,000 km), and can have amplitudes as
high as 20% of the day-night variation. There exist
many possible causes of density fluctuations which remain to
be studied. Some examples of density changes relevant
to the DANDE mission are the effect of global weather on
large-scale waves at high latitudes, and the effect of
geomagnetic activity on winds in the thermosphere. The
small-scale changes are especially important for validating
and improving physics-based models of the thermosphere.
Challenges
The
challenges in understanding and modeling the atmosphere are
numerous. The following is just a short list of
difficulties facing researchers at the Air Force, NOAA, the
University of Colorado at Boulder and other institutions:
- Few
spacecraft measure physical density de-coupled from wind
and drag coefficient effects
- Little
in-situ accelerometer data available presently in altitudes of 350
km and below
-
Accelerometer data alone cannot distinguish density
variations from wind velocities
-
Thermospheric wind models have large uncertainties
- There
are no simultaneous measurements of along-track and
cross-track wind, composition, and acceleration
available
- There
is a poor understanding of the dynamics of thermospheric
density fluctuations
-
Obtaining precise acceleration measurements is expensive
and only available from missions which are not optimally
suited for density analysis
The DANDE
mission will be able to solve many of these problems, but
first it is important to understand what relevance the above
list has to neutral-atmosphere science and related
technologies. Providing a low-cost way to calibrate models
empirically and to study the atmosphere so that models may
be improved is of great interest to any LEO mission with
precise orbit-determination needs. In fact, the Air
Force Modified Atmospheric Density Model initiative has
shown that the error growth rate in the propagation of
satellite orbits could be reduced significantly by
calibrating the model with empirical data obtained from
tracking a set of satellites. Better drag models lead
to improved accuracies in missions performing rendezvous,
formation-flying, station-keeping, and remote-sensing tasks.
Also, the huge uncertainties in re-entry predictions and
orbit lifetime analysis are strongly related to the
uncertainty in the drag model and to the lack of in-situ
data. In-situ data are density measurements obtained
from a satellite at specific points in its orbit and can be
related to a density value at a certain time, altitude, and
latitude. In-situ data is sparse at lower altitudes
with no spacecraft gathering data at 300 km or below.
Average densities are those obtained from the analysis of
reference orbits, represent the average density over a
certain fraction of an orbit, and are the type of
measurements most readily available to the Air Force
calibration effort. The advantage of certain types of
in-situ data reflects improvements in both scientific
observation and in calibration usefulness.
Coupling
between the thermosphere, the ionosphere, and the
magnetosphere relates the uncertainties in modeling one
region to uncertainties in modeling the others. This
in turn has a direct effect on the modeling of communication
effects due to charged particles in the ionosphere and to
the magnetic field models often used for navigation.
One hindrance in improving the models is the
characterization of density-variation structures on various
scales. While numerous missions have been flown to
measure certain aspects of these variations, very few have
been able to obtain simultaneous measurements of drag, wind,
and composition and none of these were able to distribute
the measurements. Obtaining acceleration-derived data
alone is insufficient as the resulting measurement contains
a component of the atmospheric wind velocity which can lead
to a density error of as much as 40%. In fact, much
work can be done in the development of wind models alone to
help reduce the uncertainties in the orbit-determination
problem. The CHAMP and GRACE
spacecraft for example, have provided years of unprecedented
in-situ accelerometer measurements but were not designed to
measure density and cannot distinguish between wind induced
and density-variation induced accelerations.
In addition to this, the lack of distributed, in-situ
measurements limits the temporal resolution of data at any
point over the earth to the orbital period of the satellite
and prevents obtaining better information related to the
dynamics of the thermosphere.
In-situ
density data may be obtained from acceleration measurements
by using the relations expressed in the following equation:
Where Cd
is the coefficient of drag, adrag is the
drag acceleration, A is the effective cross-sectional
area, m is the mass of the
spacecraft, Vi is the in-track component
of the spacecraft velocity with respect to the atmospheric
velocity or wind, and finally ρ is the atmospheric
density. Accelerometers on the
GRACE spacecraft
can provide accelerations with a resolution of 1x10-10
m/s2 but are unable to distinguish between
acceleration changes due to density variation or atmospheric
wind velocity. This problem is especially relevant
during geomagnetic storms when wind velocities can be as
high as 2 km/s. Another problem is that these
spacecraft are constantly thrusting and
affecting/interrupting the acceleration measurements.
Moreover, spacecraft with "long" shapes such as CHAMP and
GRACE suffer coefficient of drag uncertainties up to 30%.
These examples illustrate just some of the difficulties in
determining density from acceleration. For drag
measurements, the spacecraft needs to have a well determined
cross sectional area to determine the coefficient of drag.
A spherical spacecraft like DANDE has a uniform cross
sectional area and a coefficient of drag that does not vary
with attitude, which is ideal for this type of measurement.
Finally, the determination of density is sensitive to errors
in velocity determination, as this component of the equation
is squared. The DANDE design will address all these
problems in measurement and the characterization of density.
A number of
spherical spacecraft have been flown to calibrate
atmospheric models above 400 km. The deployment of spherical
spacecraft into the region below 350 km, along with in-situ
composition, density and wind data, would greatly complement
existing data for the Air Force High Accuracy Satellite Drag
Model (HASDM). DANDE will be capable of providing a
calibration reference at the desired altitude range, as well
as complementing this with in-situ instrument observation of
density, composition, and winds. This will allow
scientists to evaluate the accuracy of density models and
improve them accordingly. Improved models will allow
better orbit determination, which is crucial to supporting
such operations as satellite life and re-entry prediction,
laser communications, formation flying, and collision
avoidance warnings for the International Space Station.
The
S3-1 satellite measured accelerations, composition, and
wind from 1974 to 1975 during sunspot minimum, and provided
very useful data. However, not until recently have
techniques for simultaneously analyzing the data from
several instruments improved enough to meet the needs of
separating wind effects from density variations. DANDE
will improve on the S3-1 set, and fly during a more active
geomagnetic period. The DANDE mission will take place
in 2010, which is during the maximum activity period of the
sun's 11-year cycle. A major benefit to this date is
that DANDE will provide data to better study wind and
density fluctuations during geomagnetic storms, which occur
more frequently during solar maximum
One of
DANDE's goals is to provide the above listed science
products at a relatively low cost. To accomplish this
goal, the DANDE team is making use of inexpensive (but
skilled) student engineers, adapting inexpensive
commercial-off-the-shelf technologies for spaceflight, and
following good systems engineering practices.
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