Use dimensional analysis to argue that the gravitational potential energy of a uniform-density sphere (mass M, radius R) must equal GM2 Ugrav = -(constant) where (constant) is some numerical constant. Be sure to explain the minus sign. The constant turns out to equal 3/5; you can derive it by calculating the (negative) work needed to assemble the sphere, shell by shell, from the inside out.
Use dimensional analysis to argue that the gravitational potential energy of a uniform-density sphere (mass M, radius R) must equal GM2 Ugrav = -(constant) where (constant) is some numerical constant. Be sure to explain the minus sign. The constant turns out to equal 3/5; you can derive it by calculating the (negative) work needed to assemble the sphere, shell by shell, from the inside out.
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Transcribed Image Text:Use dimensional analysis to argue that the gravitational potential energy
of a uniform-density sphere (mass M, radius R) must equal
GM2
Ugrav = -(constant)
where (constant) is some numerical constant. Be sure to explain the minus
sign. The constant turns out to equal 3/5; you can derive it by calculating
the (negative) work needed to assemble the sphere, shell by shell, from the
inside out.
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