# Optimizing Trajectories**Team:** 38
**School:** HOMESCHOOL, MANZANO, PIUS
**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.
** Progress **
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.
** References **
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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