It's not where the gravity of one large object equals the gravity of the other. The five Lagrange points in a two object system are points where the forces from the two objects add together to result in a centripetal acceleration, which cause a third object place there to orbit at the same rate as the smaller of the original two.
Ok -- Newton's 1st & 2nd laws tell you that if you have unbalanced forces acting on an object (like a moon), that will result in an acceleration on that object. Acceleration is change in velocity, i.e. speed and direction. A moon going around in an orbit is constantly changing direction and needs a particular centripetal acceleration to stay in that orbit.
In celestial mechanics, Lagrange points come up in the three-body problem, where you have two large bodies (eg Sun and planet, planet and large moon) and one small object (a Trojan asteroid, spacecraft, new Saturn moon).
Lagrange points are the five places relative to the two large objects, where the third object will be held at the same position - relative to those two objects - in its orbit. In other words, there will be a net force on the third object that will result in it accelerating around the largest object at the same rate as the second largest object.*
A Lagrange point is stable if an object near by the L point will tend to be pulled towards or orbit around that point if it's a bit off the exact point. The L point is unstable if the object tends to be pulled further away from it once it wanders a little away.
The L1 point (in between the two large bodies), L4 and L5 points (60 deg ahead and behind the orbiting large body) are stable, the L2 and L3 points are unstable. Many of our solar observing spacecraft get sent to orbit the L1 point.
*(Center of mass discussion left out for relative simplicity)
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See my other post in this thread:4 &threshold=1&commentsort=0&tid=160&tid=14&mode=thr ead&pid=11786996#11787170
http://science.slashdot.org/comments.pl?sid=14072
In celestial mechanics, Lagrange points come up in the three-body problem, where you have two large bodies (eg Sun and planet, planet and large moon) and one small object (a Trojan asteroid, spacecraft, new Saturn moon).
Lagrange points are the five places relative to the two large objects, where the third object will be held at the same position - relative to those two objects - in its orbit. In other words, there will be a net force on the third object that will result in it accelerating around the largest object at the same rate as the second largest object.*
A Lagrange point is stable if an object near by the L point will tend to be pulled towards or orbit around that point if it's a bit off the exact point. The L point is unstable if the object tends to be pulled further away from it once it wanders a little away.
The L1 point (in between the two large bodies), L4 and L5 points (60 deg ahead and behind the orbiting large body) are stable, the L2 and L3 points are unstable. Many of our solar observing spacecraft get sent to orbit the L1 point.
*(Center of mass discussion left out for relative simplicity)