**Team Number: **081

**School Name: **Santa Fe High School

**Area of Science: **Astronomy

**Project Title: **Mathematical Applications in the Determination of Orbits of Satellites

Problem Definition:

Astronomers are frequently called upon to calculate the path a body in space will take based on the gravitational pull of another body on it coupled with its pull on the other body. This helps scientists to plan specific actions concerning the body, because they know exactly where it is at a certain time. Theycan then conduct experiments on it, or just predict where it is a certain time. They can conduct experiments on it, or just predict where it will land up in space. Out program, on a two dimensional Cartesian plane, willchart the path a body will take when pulled by the gravity of another body.

Problem Solution:

We plan to solve this problem using Microsoft Visual C++. First we will
have to set up a visual graphics screen that can be exited with the press
of a certain key. We will program in one body, and calculate its
gravitational pull, using simple vector physics coupled with Kepler's and
Newton's laws. Then the second body will be programmed in. Finally,
both bodies will be allowed to interact with each other. The visuals of
what is happening will be shown from an overhead view.

Progress to Date:

So far we have created all the visuals and have started on the
gravitational program. To date, we have a fixed body of set mass, with
another, also of set mass orbiting around it. The user can select the
location and starting velocity of the second body, and can then watch the
path it takes. Each real time second is equivalent to the earth year.
Our progress seems to be running smoothly with our mentor. We our
learning to use and apply new formulas, and different applications for
our program. Our teamwork seems very strong, and our progress rate shall
take us beyond our expected gaols with our project.

Expected Results:

The program will be able to calculate and graphically show the path of a
body moving through space with gravitational influences acting on it in a
2 dimensional plane. The program will be capable of predicting the
trajectory and path of a body moving in space depending on mass,
position, and gravitational influences acting on it. To complexity our
program, we cound attempt to refine our result by creating 3 dimensional
plane as opposed to the previous 2 dimensional plane. Also, the use
ofmultiple orbiting bodies could add to a more sophisticated program.
This program can be very useful to astrophysicists, or any other
scientists who seek to predict the path of a body moving through our
solar system. For commercial use, one could use this program to
calculate the trajectories of satellites thus avoiding collisions with
others that might be orbiting around that same body.

WORKS CITED:

" The Motion of Comets."

"Orbital Phisics Equations."

"Solar System Backround." World Book Encyclopedia 1994 ed.

"Summary of Kepler's Laws."

**Team Members**

**Sponsoring Teacher(s)**

**Project Mentor(s)**

- Robert Carlos