Matter And Motion

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With respect to the centre of mass it is The total acceleration of the planet towards the centre of mass [in describing an arc PQ] is S TJV S+PTb U and the impulse on the planet whose mass is P is therefore sp STPTb UV ' Let t be the time of describing PQ, then twice the h a 2 b and UV = 2acot = 2a -% t = 477 ~- 2 t.
Hence the force on the planet [being impulse divided by time] is sp ^ This then is the value of the stress or attraction between a planet and the sun in terms of their masses P and
..., their mean distance a, their actual distance r, and the periodic time T.
135. INTERPRETATION OF KEPLER'S THIRD LAW To compare the attraction between the sun and different planets, Newton made use of Kepler's third law.
Law III. The squares of the periodic times of differ- ent planets are proportional to the cubes of their mean a 3 c distances. In other words yr 2 is a constant, say 2 .
SP i Hence F = c --.
vin] UNIVERSAL GRAVITATION in In the case of the smaller planets their masses are o so small, compared with that of the sun, that p may be put equal to i, so that F = c -% or the attraction on a planet is proportional to its mass and inversely as the square of its distance.


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