# 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]