To do so, he proposed in a work called Tahrlr al-Majisti, which was completed in 1247, that the oscillatory motion be produced by the combined uniform circular motions of two identical circles, one riding on the circumference of the other.
32.
He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:
33.
:The video was tldr, but the prof may have made the same mistake I made when reading this question, which was reading " uniform circular motion " and thinking " simple harmonic motion " . talk ) 00 : 27, 31 July 2008 ( UTC)
34.
In contrast, the examples in Centrifugal force ( rotating reference frame ) describe motion as seen strictly from a rotating frame, and, moreover, that article is devoted to objects in uniform circular motion, not in general planar motion . talk ) 04 : 32, 11 October 2008 ( UTC)
35.
Therefore, it cancels out the ubiquitous centrifugal force found in the first example, and goes a step further to provide exactly the centripetal force demanded by uniform circular motion, so the rotating observer calculates there is no need for tension in the string " the Coriolis force looks after everything.
36.
Because the planetary spheres each move unfalteringly for all eternity in uniform circular motion with a given rotational period relative to the supreme diurnal motion of the sphere of fixed stars ( or First Heaven ), they must each love and desire to mimic different unmoved movers corresponding to the given periods.
37.
Nasir al-Din al-Tusi ( 1201 1274 ), a Persian astronomer and mathematician who died in Baghdad, authored the " Treasury of Astronomy ", a remarkably accurate table of planetary movements that reformed the existing planetary model of Roman astronomer Ptolemy by describing a uniform circular motion of all planets in their orbits.
38.
In the case of rotation around a fixed axis of a rigid body that is not negligibly small compared to the radius of the path, each particle of the body describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varying with the position with respect to the axis.
39.
To generate a uniform circular motion, use a uniformly increasing time parameter t and set x = x0 + r cos ( w t ) and y = y0 + r sin ( w t ) for some radius r, angular speed w, and center point ( x0, y0 ) . 169.230.94.28 02 : 37, 9 July 2007 ( UTC)
40.
From that, Newton's Law of Universal Gravitation, and the equation for uniform circular motion ( I'm making the simplifications that ( 1 ) the moon's orbit is circular, and ( 2 ) the Moon orbits the Earth, rather than both orbiting a common centre of mass ), you should be able to get an equation relating the mass, orbital velocity and orbital radius of a satellite.
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