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My question involves Lagrange points. I have finished my mechanics physics class, and we talked about gravitation, tides, and finally Lagrange points were referenced at the end of the semester. When you see a picture of Lagrange points you usually see the sun-earth system with five points (areas). I was wondering if you were to take a line through the center of mass of the sun and earth, and then rotate this plane of points around this axis. The L1, L2, and L3 would stay in the same place, but the L4 and L5 would rotate around making a doughnut Lagrange circle. Does this exist?
- Tom (age 18)
that's an interesting thought. As you say, it's obvious that three of the points are just points since if you rotate the Earth-Sun about its spatial symmetry axis, they don't move. However, the orbital system of the Earth-Sun doesn't have that symmetry axis, because the plane of the rotation is distinct. In other words, if you added little velocity arrows to the positions of the Earth and Sun you'd no longer have a figure that could be rotated about an axis without changing. The last two points are confined to that orbital plane.
L4 and L5 are not really exact points but are areas with a finite spread. Any object within these areas are, more or less, stable. The objects can and do wander around a bit. Take a look at the Wiki article at: http://en.wikipedia.org/wiki/Lagrangian_point
and the animated cartoon at :
(published on 03/02/12)
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