We are trying to find some optimal trajectories that NASA is interested in.
They want to send some spacecraft missions to Jupiter, to Jupiter’s moon.
This grant, it's a collaboration with Georgia Institute of Technology,
and with Jet Propulsion Laboratory.
It has two objectives. One, it’s research, and one,
it’s training of students and young scientists.
Well I’ve liked astronomy since I was a kid.
Enough to get my Master degree in mathematics,so this is a perfect stream for me to enter.
This particular three body problem is the sun, Jupiter,
and a comet that has been observed near both the sun and Jupiter called Oterma.
We want to know, how does Oterma move under the influence of gravity?
I’m working on the trajectory design of a spacecraft close to the asteroid.
There are locations in space where
the gravitational forces almost cancel each other,
and so the spacecraft would be at an equilibrium.
It’s possible to find routes, that they do not need any fuel for the spacecraft
to follow those particular routes.
Sometimes they are called gravitational super highways.
But when you make a transition from one highway to another, you have to spend some fuel.
And the idea is how to do it in an optimal way.
This Arnold Diffusion Problem, it’s really how to
make large changes with small perturbations.
Like when you’re pushing a swing. If you do it with proper timing,
the amplitude of the swing grows bigger and bigger.
So now instead of pushing the swing, you have the thrusters of the spacecraft,
but you have to do it at the proper timing in order to maximize the effect.
I like it because before I did this I was more, like, very theoretical math.
There’s a lot of theory behind it, 
but it’s also kind of interesting because we’re talking about real life things.
I think it’s quite exciting to see that abstract mathematics,
that you are actually teaching in the classroom, has such powerful applications.
I think this connection between research and teaching, it’s very important.
