An Elementary Treatise On Dynamics, Containing Applications to Thermodynamics, With Examples

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20. Prove by Newtonian methods that, if two bodies attract one another according to any law, they describe similar figures about their centre of inertia and about one another.
Neglecting the obliquity of the ecliptic, and the inclination and the eccen- tricity of the lunar orbit, show that, if we take the Sun's distance as 390 times that of the Moon, the Earth's mass as 79 times that of the Moon, and the lunar synodic period as 30 mean solar days ; then the solar day is, to a near approxi- mati
...on, shorter at full Moon that at new Moon by one 468,000th part of a mean solar day. Camb. Trip., 1882.
21. A material particle, moving freely in a plane, being supposed to describe a conic under the action of a central force emanating from any point in the plane ; show that the force varies directly as the distau ce from the point, and inversely as the cube of its distance from the polar of the point with respect to the curve.
22. In free motion in a plane under the action of a central force varying according to any law, state and prove the effect on the trajectory (and on the motion in it) of an additional force emanating from the same centre, and varying inversely as the cube of the distance.


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