課程名稱︰力學上 課程性質︰物理系必修 課程教師︰陳俊瑋 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰99年1月11日-99年2月1號 考試時限（分鐘）：30240分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1)(25points) Look at Fig8-12 (p.310) of textook. (a) Work out the energy gained by the spacecraft A when it flies by a large body B. The initial velocities of A and B are VA and VB respectively when they are infinitely apart. The mass of A is mA and the mass of B is mB. The closest distance between A and B is d (b) If one can charge the direction of VA and the size of d,what is strategy to gain the maximun energy? Assume mA<<mB and the momentum of A is much smaller than B for part (b). 2)(25points)(a) Compute the geodesics on an ellipsoid which satisfies x^2/a^2 + y^2/b^2 + z^2/c^2 = 1 . (b) Plot the ellipsoid and its geodesics for a few cases using Mathematica or any computer software. 3)(25points) Testing the gravitational 1/r^2 law. If the gravitational force between two point particles is F(r)=[-GMme^(-δr)]/(r^2) , where 0<δ<<1, M and m are the two particle masses and r is the distance between the two. (a) Use the technique in 8.9 to work out the precession for orbits of small eccentricity ε(ε<<1). You only need to expand to the first power of δand the first power of ε. (b) Compare with the precession rate data in Table 8-2 of P.316. What have you larned from this? 4)(25points) Write an eassy (3 pages, typed, in Englisg) about the aspects of sending an astronaut to land on Mars and come back to the Earth safety. Discuss what it takes to make this happen. --

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