Page 40 - Intro to Space Sciences Spacecraft Applications

Orbital Principles
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can heliocentric hypothesis but was still saddled with the religious-backed
belief in the perfection of the heavens, which called for purely circular
motions of the planets. For nine years, Kepler struggled to fit the observed
motions of the planet Mars into different models of combinations of circu-
lar paths. It was only after finally trying an oval-shaped path that Kepler
found that the orbit of Mars fit extremely well into an ellipse. Kepler sum-
marized his findings in his famous three “laws” which will be examined in
this chapter. Kepler showed that these relationships held not only for the
paths of the planets around the sun, but for the paths of the four moons
recently discovered circling the planet Jupiter by Galileo. We will use these
same relations to describe the motion of earth-orbiting satellites.
Galileo Galilei was well known, even in his own time, as a capable sci-
entist and experimenter in many fields. In his quest for knowledge,
Galileo employed a systematic approach to his studies that laid the foun-
dation for what is now known as the scientific method of investigations.
His study of the motions of bodies led to the understanding of friction,
inertia, and the acceleration of falling bodies. Galileo was the first to use
a combination of lenses to make telescopic observations, and with these
crude devices he made some astounding discoveries, including the exis-
tence of the moons around Jupiter now known as the Galilean moons. It
was the combination of Galileo’s experiments in general motions and
Kepler’s findings in planetary motions that gave Newton the tools he
needed to explain, not just describe, the mechanics of orbits.
Sir Isaac Newton’s status as a genius is obvious considering the great leap
of understanding in many different areas attributed to the seventeenth-centu-
ry physicist. By his time, people had had over 50 years to mull over the find-
ings of Kepler and others concerning planetary motions. It is important to
recognize that Kepler’s “laws” were derived empirically, simply describing
the characteristics of the planetary motion recorded by Brahe. Yet no one had
come up with a plausible explanation as to why the planets followed the par-
ticular paths around the sun that Kepler’s relationships indicated, and there
was great debate among the scientific investigators of the time. Sir Edmund
Halley, a friend of Newton’s, nonchalantly mused on the topic one day, and
to his amazement Newton replied that he had come up with an explanation
some 20 years earlier but had not bothered to publish the results. At Halley’s
urging and expense, Newton published his findings which included his three
laws of motion and his description of gravitational force.
Newton and Kepler formulated their “laws” based on the motions of the
planets around the sun, but these relationships describe orbital motions