課程名稱︰星系天文物理
課程性質︰天文所必修
課程教師︰闕志鴻
開課學院：理學院
開課系所︰天文物理所
考試日期（年月日）︰103/11/14
考試時限（分鐘）：110(+15)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.The Plummer-Kuzmin model of a disk uses two identical point masses located
at the opposite sides and at some distance b away from a mid plane.
(a) Derive the potential of the Plummer-Kuzmin disk. (10%)
(b) What is the surface density of the disk? (15%)
2.(a) Please derive the epicyclic frequency of a disk.(We assume the potential
V(R) is -a/R, where a is a positive constant.)(10%)
(b) Lindblad resonances are related to the epicyclic frequency. Why do
Lindblad resonances occur?(10%) Why are there inner and outer Lindblad
resonances?(5%) Are there more than two Lindblad resonances in a disk of a
given potential?Why?(5%)
3.Near the Lagrangian point, one can derive a set of two equations describing
the particle orbit in the rotating frame. What are these two equations?(15%)
What is the condition of a stable Lagrangian point?(15%)(Please derive both)
4.The Homoeoid theorem refers to an axisymmetric 3D ellipsoidal mass shell.
What must this ellipsoidal mass shell be to satisfy this theorem?(10%) What
is the theorem?(5%)