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The Two Body Problem - Harvard University

Copyright 2004 6 The Two Body Problem The classical Problem of celestial mechanics, perhaps of all Newtonian mechanics, involves the motion of one body about another under the influence of their mutual gravitation. In its simplest form, this Problem is little more than the generalization of the central force Problem , but in some cases the bodies are of finite size and are not spherical. This may complicate the Problem immensely as the potential fields of the objects no longer vary as the inverse square of the distance.

This is often defined to be that point where the force of gravity can be considered to be acting. Mathematically that would mean that all torques produced by gravity would vanish about that point so that ×∑ =∑ × =∫ [×ρ( ) ] = ii rg fi ri fi V r r g dV 0 r r r r r rr. (6.1.2) In a Cartesian coordinate frame this could be expressed in ...

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7 Probability Theory and Statistics - Harvard University

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generate an event E, then the probability of E occurring is P(E) = m/n . (7.1.1) Consider the probability of selecting a diamond card from a deck of 52 playing cards. Since there are 13 diamonds in the deck, the probability is just 13/52 = ¼. This result did not depend on there being 4

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