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Supercomputing Challenge

Optimizing Trajectories

Team: 38


Area of Science: Math, Space Science

Interim: Supercomputing Challenge Interim Problem Definition
We are developing an algorithm that finds gravity assist routes that have an efficient time to fuel ratio. By analyzing maneuvers common to efficient routes it should be possible to narrow down which routes will be most efficient.
The n-body problem of many bodies' gravitational fields effecting an object can be expressed geometrically by a three dimensional graph of the intensity of gravity at any point. These dynamic gravitational effects can greatly change the path of an object, and it is possible to exploit unusual planetary movements for the greatest effect on the object.
There are several complexities in this process, such as rounding issues and checking the answer. Also, assuming you have a rocket with a limited amount of fuel it will be complicated to decide when the rocket is allowed to use fuel to optimize its affect.

Computational Solution
We are attempting to develop and efficient algorithm to utilize maneuvers that are common to many gravity assisted motion problems. We expect to develop an algorithm that will weight these maneuvers according to their probable effectiveness on the outcome of the route and then calculate the top routes and compare them, re-weighting the effective maneuvers.

We have a scale model of the solar system that orbits correctly and the Lagrange points for the earth/moon system. Lagrange points, or liberation points are important to this process because they are 'decision' points for the object- the slightest movement in any direction will cause a cascade effect on the object's eventual position. We have also developed an intuitive interface for displaying the results of the computation.
Here is some of the math we have been researching for Lagrange poins. Here is the Mathematica model, with a slight simplification, of the Earth/Moon L1 point, where F is the Earth's mass, M is the Moon's mass, and x is the distance of the L1 point from the moon on the line from the moon to the earth.

Other Lagrange points are combinations of this equation focused on different areas.

Expected Results
Reducing the number of routes needed to calculate the most efficient outcome will make this problem possible to solve.

Martin Lo Publications
Wikipedia on the n-body problem
Lagrange Point explanation
Detailed Explanation on Gravity
Liberation Points

Team Members:

  Erika DeBenedictis
  Brian Lott
  Kristin Cordwell

Sponsoring Teacher: NA

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