Johannes Kepler (1571 to 1630) was the grandfather of orbital mechanics. Using data originally collected by Tycho Brahe (1546 to 1601), he defined the concepts that are still being used today when referring to satellite orbits. His brilliant mind developed three basics laws of orbital motion:
KEPLER LAW #1: All planets have elliptical orbits; the Sun being one of the foci. All satellite orbits are elliptical.
KEPLER LAW #2: All planets sweep out equal areas in equal times as they orbit the Sun. If you were to determine the area swept out by the motion of a satellite within a specific span of time, you would find that the areas measured will be identical wherever the satellite is in its orbit.
KEPLER LAW #3: The cube of a planet orbit's semi-major axis is directly proportional to the square of its orbit period. In other words:
a^{3} a T^{2}
Since Newton's Laws of Gravitation were not yet known, Kepler could not have derived the full equation. However, Issac Newton (and Cavendish) completed the equation:
a^{3} = GMT^{2} / 4p^{2} = kT^{2}
where G = The Gravitational Constant;
M = The Mass of the Earth;
T = The
Period
of the Satellite Orbit; and
k = GM / 4p^{2}
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Kepler's Laws Was Last Modified On May 23, 2010 |