Classical Mechanics: Body/Space Cone Angle Relation

Rahat
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please help me and send me the derivation of relationship between body cone angle and space cone angle.thanx
 
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It's given a gas of particles all identical which has T fixed and spin S. Let's the density of orbital states and for , zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate and we have...
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