# CU Boulder AeroSpace Ventures: Vishal Ray, Satellite Drag Coefficient Modeling

Hi, everyone, I’m Vishal. I’m a graduate student in
the Celestial and Spaceflight Mechanics Laboratory led
by Dr. Daniel Scheeres. In this lab, we do a lot of work surrounding small bodies and
Space Situational Awareness. My work concerns the development
of drag coefficient models that can be incorporated into the estimation framework
for orbit prediction. So we have, in the previous presentations, we have looked at the problem surrounding atmospheric density prediction
and how it’s very dynamic. The other side of the
problem is the interaction of the atmosphere with the
satellite, which is also dynamic. And this interaction parameter, represented by the drag coefficient, depends on various factors,
such as atmospheric parameters, like molecular composition and temperature of the atmosphere, and the satellite-specific factors, like temperature of the wall,
mass of the satellite surface, and the satellite orientation. Now, in order to demonstrate the variation of drag coefficient with
the satellite orientation, let’s look at an animation. So this animation basically
shows the rotation of a cubical satellite and how it affects the drag coefficient. The right-hand-side
plot shows the variation of the drag coefficient over a surface. So basically the drag
coefficient is not constant. And this can be modeled using gas-surface interaction models, which are basically analytical
physics-based models, but we know that they’re
not used in operations. Why? This is because the inputs and parameters that are used in these
models are not constant, and they vary over time. And these cannot be estimated in the real life and real tracking process because of observability issues. So what we basically do is
assume it to be a constant and decouple it with the
cross-sectional area, which is actually a part
of the drag coefficient. So our proposal is to use dynamic models for the drag coefficient using
Fourier series expansions. Now this approach has been used for solar radiation pressure coefficient and thermal radiation
pressure coefficient, and worked pretty well. So the main principle is that the Fourier coefficients
are orthogonal to each other and can be estimated in the
tracking process in situ. So we take two approaches to this problem. First is we do a Fourier series
expansion in the body frame, and this helps the model to respond to changes in the satellite orientation. The second approach is to do an expansion around the true anomaly of the satellite, which is basically a periodic model in the orbit frame of the satellite. So this response to change is
in the atmospheric parameters. Now we develop the theory, validated these models using simulations, and I show a case for the
processing of real data from a NASA satellite at 400 kilometers. So in this case, you can
see how the constant model, which is called the cannonball drag model, leads to an error of
around nine kilometers at the end of the prediction of nine days. And our Fourier series models
are able to reduce the error compared to the constant model. So, by the end of nine
days, the body-fixed model is able to reduce the errors by 33%, and if you look at the
end of two, three days, the errors are actually reduced by 50%. So these models can be used in the orbit determination process, and they are not computation
intensive at all. So the Fourier coefficients are basically, for the body-fixed model, it’s around five coefficient
that we had to estimate, along with the position and velocity. Okay, one slide is nothing. Anyway, the application of these models is not limited to applications
in the lower orbit. So we haven’t made any
inherent assumptions about the physics and
chemistry of the atmosphere, so they can be applied to atmospheres around other celestial bodies, like missions to Venus, Mars, or Titan. And the other important part is the, okay, that’s a really bad slide. Anyway, so the other important
part of the applications is to the atmospheric physics community, where the space weather
picture comes into being. So atmospheric density has been calibrated using satellite drag since along because the global coverage
that the satellites provide. But this process of inversion of atmospheric density from satellite drag is directly affected by
drag coefficient errors, so any errors in the drag coefficient directly translates to
biases in the density models, which potentially affects
all the other applications. Again, for orbit prediction. So any improvements in the
drag coefficient models will directly lead to improvements in the atmospheric density calibration as well as orbit prediction, which basically forms a cycle, and they’re correlated to each other. So that’s where I stop. Thank you. We can talk on the break. [audience applauding]