The Science Behind DANDE
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.
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.
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.
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.
Atmospheric Model Calibration
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.
Wind and Composition Measurements
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.