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Painting a color portrait of stable orbits.

Painting a color portrait of stable orbits

Putting a satellite into a stable orbit is no simple matter. The Earth's bulging equator and other distortions in its gravitational field continually tug at the craft, often causing it to drift away from its planned orbit. Such deviations make satellite tracking difficult. They can also gradually shift a satellite into a position where it can no longer fulfill its mission.

To help aerospace engineers select orbits that stay put, a team of researchers has now developed a technique for visualizing the solutions of equations describing the motions of Earth-orbiting satellites. Using such mathematical "portraits" of orbits, engineers can readily identify equilibrium points and work out the precise conditions needed to lift a given craft into a stable orbit.

"People have had a rough idea of where these orbits are, but they've never had the kinds of tools that we've developed for finding them," says Shannon Coffey of the Naval Research Laboratory (NRL) in Washington, D.C.

An orbiting satellite traces out an ellipse, with the Earth at one focus of that ellipse. For many purposes, the most useful orbits are those in which the ellipse always points in a fixed direction as it sweeps over the Earth. In other words, the orbit's apogee -- its most distant point from the Earth's center -- would stay over, say, the Northern Hemisphere. In contrast, satellites in orbits for which the ellipse wobbles or tumbles would tend to drift excessively.

Initially, as reported in the Feb. 16 SCIENCE, Coffey and his colleagues applied their visualization technique to a simplified set of equations that included deviations caused only by the Earth's equatorial bulge. Now they can add in much smaller perturbations to get results useful to engineers planning satellite orbits that lie between 300 and 2,000 miles above the Earth's surface, says Andre Deprit of the National Institute of Standards and Technology in Gaithersburg, Md., who developed the technique with Coffey and NRL colleagues Etienne Deprit and Liam Healy.

"The next step would be to take into account the perturbations caused by the moon and the sun," Andre Deprit says.

"We have now come full circle," the researchers write in their report. "Analytical study of a dynamical system prompted graphical representations to support our results. Improvements in the visualization techniques revealed new phenomena, which brought us to refine our mathematical analysis."
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Title Annotation:satellite orbits
Author:Peterson, I.
Publication:Science News
Date:Feb 24, 1990
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