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 Planets and Satellite Orbits: Conservation of Momentum 27 July 2006
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A couple of interesting facts:
Effective Gravity at the equator is higher due to the moment arm of the surface relative to the axis of rotation. The gravity of a planet can be estimated as gravity=gravitational_Constant*planet_massKG/(planet_radiusMeters^2) However, at the equator rotational momentum reduces the effective gravity on an object. For this reason, space launches require less energy if launched at the equator as opposed to other latitudes.
Planet to Sun Distances Increase Over Time because the sun radiaton of energy results in a slight loss of mass [e=mc^2]. Conservation of energy implies that as the sun emits a particle of mass, the momentum of the particle relative to the sun's rotational axis must increase. So in order to conserve angular momentum, the sun's rotation must slow slightly. [Seemingly similar to the electron quantum states] In reality, the sun is not a closed system. As a sun loses mass, conservation of momentum can also be accomplished by planets gaining mass and planets increasing orbit distances or axis momentum. For this reason it seems logical that over time the universe will expand to a point where all matter is distributed to the corners of the universe and motion is non-existent. However, the laws observed today cannot be extrapulated to such simple conclusions and a 4 dimensional closed system may not be reality. |
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Angular momentum is calculated by multiply mass by velocity by distance.
*5061 is 50% of 6376 **5095 is 50% for 6376+1737 [earth+moon] ***0.000289 days/revolution equals 25 seconds per revolution. If earth and moon were joined billions of years ago, it is unlikely that the earth could spin at a rotational rate of once every 25 seconds. This rate exceeds the escape velocity of the planet. The Kinetic energy could have been increased over time once via natural nuclear reactions in the earth (volcanoes would vent gas). Over time, the planet's surface might reach escape velocity near the equator. When this event occurred, the moon might break off from the earth. As the moon moved farther and farther away from earth, the earth days would lengthen.
Gravity is therefore driven by mass density. A mass with an infinitely small radius may create a nearly infinite gravitational force at it's surface. This type of characteristic may be present in black holes. However, the tendency for oblateness competes with gravity and may decrease densities over time.
which reduces to: T = 769337.588 * SQRT(R^3 / M) where units are seconds, meters, and kgs.
Orbital_Velocity_Meters_Per_Second = 1.15E+10 / SQRT(Distance_To_Sun_In_Meters)
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