Advaced Celestial Mechanics Questions II

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Advaced Celestial Mechanics Questions II

• Problems and Questions

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Question 15

• Derive the Hamiltonian of an asteroid in the
  three-body problem
• and use the generating function
• to transform the Hamiltonian to a rotating
  coordinate frame

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Question 16

• The Hamiltonian of an asteroid in a rotating
  coordinate frame is
• Derive equations of motion

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Question 17

• Starting from the equations of motion in the
  restricted circular three-body problem,
• derive the Jacobian integral. How does it help to
  describe the motions? Define Lagrangian points.

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Question 18

• Derive Hills equations starting from the
  equations of motion for a satellite

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Question 19

• Using Hills equations
• describe the stability of satellite orbits.

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Question 20

• Show that in three-body scattering the binary
  energy change is
• and calculate delta v.

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