# AiS Challenge Team Interim

Team Number: 030

School Name: Farmington High School

Area of Science: Orbital Mechanics

Project Title: In Orbit

With hundreds of functional artificial satellites, powering today's world of technology, an important issue faced by many scientists, is the problem of the mechanics of orbit. The objective of this experiment is to scientifically determine the changes of orbits of objects in space. A study of orbital mechanics must be conducted in order to achieve this goal. Physics, in collaboration with Calculus, will be used to calculate differential equations for each position. Velocity and acceleration will be determined in order to sufficiently represent the circular and non-circular positions of each object. It is hypothesized that C++ will successfully be used to graphically demonstrate the orbits of these objects.

Although only elliptical orbits in space exist, the purpose of this project is to successfully model the circular and non-circular orbits of satellites in space. It will be conducted through the execution of a program that uses centripetal and tangental equations for velocity and acceleration, and equations for the periods of orbits, t. Using these equations, a useful program has been formulated to accurately model the the circular orbit of a satellite. With the aid of the program, one is able to vary the position of the satellite in its orbit, determine the period of the satellite's orbit, as well as both the centripetal and tangental acceleration or velocity at any time or position. Only relatively small amounts of progress, however, have been made on the development of a similar program for the non-circular orbits of such satellites. It is also desired to create a similar program, using the information from the previous program that models the satellite's circular and non-circular orbits, to successfully create a circular orbit of a satellite from an elliptical model. Such a program will be created by altering the period of the orbit to shoot the satellite from a elliptical orbit to a perfectly, nonexsistent, circular orbit. The development of a program to model the non-circular orbit of a satellite is still in progress, however, and is yet to be entirely useful.

Difficulties have been encountered in several aspects. The applications of Calculus and Physics in modeling the desired data have been troubling. It is difficult to accurately and successfully model the non-circular orbit of a satellite, while simultaneously using the formulas of physics to determine exact periods, velocities, and accelerations. Despite the presence of various tribulations, development on the program has been successful and the sought purpose will be achieved.

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