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]