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Youe can not help men permanently by doing for them what they could and should do for themselves. ..."Abraham Lincoln(1809-1865, US President 1861-1865"

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 Author Topic: Restricted three-body problem – a satellite in the binary planet system (Eugene)  (Read 13533 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).

Fu-Kwun Hwang
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 « Embed this message on: October 21, 2007, 07:48:35 pm »

Original URL : http://faculty.ifmo.ru/butikov/Projects/Collection1.html

Examples:

1. Satellite orbiting a moon that circularly orbits a planet. This example shows a stationary motion of the satellite around the heavier component in the binary system whose components move in circles about the centre of mass. The motion can continue indefinitely.

2. Satellite orbiting a moon that elliptically orbits a planet. This motion can also be stationary and continue indefinitely. (Click also here  to see the applet.)

3. Satellite orbiting a moon and a planet by turn. At certain conditions the satellite in the binary system can change its primary from time to time. In this example the satellite ends this "game of space basketball" by crashing against the planet. (Click also here  to see the applet.)

4. Wandering satellite orbiting a moon and a planet by turn. In this example the satellite makes several transitions from orbiting the moon and the planet, and eventually hits the moon.  (Click also here  to see the applet.)

5. Periodic multi-petalled orbit of a satellite in the double planet system. The satellite of the heavier component can trace an almost closed orbit in the inertial plane moving synchronously with the other component of the binary system. (Click also here  to see the applet.)

6. Periodic orbit of a retrograde satellite in the double planet system. In this example the satellite of the lighter component traces an almost closed orbit moving synchronously with the other component of the binary system. (Click also here  to see the applet.)

7. Satellite at the triangular libration point. This example illustrates regular elliptical motion of a satellite at the triangular Lagrange point. The motion is unstable because of the large mass of the moon in this example. (For the Earth - Moon system m/M = 0.0123 < 0.04, so that the triangular libration point is stable.) (Click also here  to see the applet.)

8. Satellite at the outer collinear libration point. This example illustrates regular motion of a satellite at the outer collinear Lagrange point for the case of circular motions. The motion of the satellite is unstable: soon it leaves this point and orbits irregularly one of the bodies.  (Click also here  to see the applet.)

9. Satellite at the inner collinear libration point. This example illustrates regular motion of a satellite at the inner collinear Lagrange point for the case of circular motions. The motion of the satellite is unstable: soon it leaves this point and orbits irregularly one of the bodies.  (Click also here  to see the applet.)

10. Elliptical orbit at the outer collinear libration point. This example illustrates regular motion of a satellite at the inner collinear Lagrange point for the case of elliptical motions of the bodies. The motion of the satellite is unstable: soon it leaves this point and orbits irregularly one of the bodies.  (Click also here  to see the applet.)

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Youe can not help men permanently by doing for them what they could and should do for themselves. ..."Abraham Lincoln(1809-1865, US President 1861-1865"