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Hi Mo-o,

Thanks for posting this question. At a Lagrange point, the centrifugal forces have the same strength as the gravitational forces, but they are opposite in direction. Therefore, no force is experienced at these points. In a system of two orbiting masses, there are five Lagrange points for a third body whose mass is much smaller. Click here for a nice reference and more background information.

If you mean a particle with negative mass by "particle that deflects/repels gravity" that repels a 'usual particle' (with positive mass) then the Lagrange points are not altered - provided that the magnitude (the absolute value) of the negative mass is much smaller than the other two masses. The Lagrange points do not depend on the mass of the third body or even on its sign.

Two of the five Lagrange points are stable. That means that a body nearby will be attracted by that point. Differently spoken, a body slightly moved away from one of these Lagrange points will experience a pull back to it, similar to elongating a spring. The other three points are unstable. The third body will be driven away from that point if it loses its position. All these considerations are independent of the sign of the third mass.

I hope I could help you,

Michael

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