Problem Set 5.3: For a near circular orbit with a potential: (r, z) = -GM[R² + {a + (z² + b²)¹/²3²]-1/² which is expressed in the cylindrical coordinates of r and z. Consider the orbit when z=0, calculate the epicycle frequency a and vertical frequency 3, and derive an expression for the azimuthal motion (orthogonal to r and z) with respect to orbital motion whose angular frequency is wc.
Problem Set 5.3: For a near circular orbit with a potential: (r, z) = -GM[R² + {a + (z² + b²)¹/²3²]-1/² which is expressed in the cylindrical coordinates of r and z. Consider the orbit when z=0, calculate the epicycle frequency a and vertical frequency 3, and derive an expression for the azimuthal motion (orthogonal to r and z) with respect to orbital motion whose angular frequency is wc.
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![Problem Set 5.3: For a near circular orbit with a potential:
(r, z) = -GM[R² + {a + (z? + b?)/23²]-1/2
which is expressed in the cylindrical coordinates ofr and z. Consider the orbit
when z=0, calculate the epicycle frequency a and vertical frequency B, and
derive an expression for the azimuthal motion (orthogonal to r and z) with
respect to orbital motion whose angular frequency is wc.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7aba6a51-dfe7-492f-b3c0-bc77d87f7364%2F1da15f57-1ea8-400a-a2b8-db02ca42dfc7%2Fm23zkcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem Set 5.3: For a near circular orbit with a potential:
(r, z) = -GM[R² + {a + (z? + b?)/23²]-1/2
which is expressed in the cylindrical coordinates ofr and z. Consider the orbit
when z=0, calculate the epicycle frequency a and vertical frequency B, and
derive an expression for the azimuthal motion (orthogonal to r and z) with
respect to orbital motion whose angular frequency is wc.
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