Motion of planets

# Motion of planets - Motion of planets Suppose a planet with...

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Motion of planets Suppose a planet with mass m is in a circular orbit around the sun, whose mass is M. The radius of the orbit is r. The gravitational force between the sun and the planet is given by This is the force that keeps the planet in its circular orbit and its magnitude should therefore be equal to the centripetal force F C : This implies that or This shows that for circular orbits, the square of the period of any planet is proportional to the cube of the radius of the orbit ( law of periods ). The constant depends only on the mass of the sun (M) and the gravitational constant (G). In reality none of the planets carry out a circular orbit; their orbits are elliptical. The general equation of an ellipse is given by (see Figure 14.7) The parameter a is called the semi-major axis of the ellipse (if a > b). It corresponds to the longest distance between the center of the ellipse (x=0,y=0) and the trajectory. The parameter b is called the semi-minor axis of the ellipse (if a > b). It corresponds to the shortest distance

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## This document was uploaded on 11/25/2011.

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Motion of planets - Motion of planets Suppose a planet with...

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