2. The Trojan asteroids occupy the L4 point in the three-body equilibrium configuration, where the...

Question

2. The Trojan asteroids occupy the L4 point in the three-body equilibrium configuration, where the other two bodies are Jupiter and the Sun.
a) Show that for the in-plane motion of a Trojan two stable oscillations are possible, one with period very close to that of Jupiter and the other with period of approximately 147 years.
b) For the long-period motion (T = 147 years) find approximately the ratio of the amplitudes of the oscillatory motion (in the vicinity of L4) components in the x and y directions. The x direction is along the line joining Jupiter and the Sun; the y direction is normal to x but in the plane of Jupiter's orbit about the Sun.

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David · Accepted Answer

Problem
Solution  
(a) The above three body problem is the motion of a small object moving under the gravitational effect of 
a planet and the Sun.

2. The Trojan asteroids occupy the L4 point in the three-body equilibrium configuration, where the other two bodies are Jupiter and the Sun. a) Show that for the in-plane motion of a Trojan two stable...

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