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I Why are Lagrange points called libration points, and....

  1. Mar 21, 2017 at 12:29 AM #1
    Two questions about Lagrange points.

    (1) According to Wikipedia, "libration is a perceived oscillating motion of orbiting bodies relative to each other," whereas the Lagrange points are, with respect to two bodies, null points for a (real or hypothetical) third body with respect to the sum of the gravitational (or centrifugal: see next question) forces on that third body (assuming the third body's mass is negligible compared to each of the other two) . What do the two concepts have to do with one another so that they are considered identical? That is, (a) if something is at a Lagrange point, it is not oscillating, and (b) libration concerns the perception from an observer being on one of the two bodies bodies, whereas the Lagrange points concerns the state of an observer at a third point. I don't see the connection.

    (2) Some sites say the sum of the centrifugal forces, which is to say that there is no total inertia: the third body is motionless with respect to the two other bodies. In the situation in question, can you have one without the other: that is, where either (a) the sum of the gravitational forces is zero, but the sum of the centrifugal forces is not, or (b) the sum of the centrifugal forces is zero yet the sum of the gravitational forces is not? If either one of these is the case, then which one (gravitational or centrifugal) would be correct in the definition of Lagrange (or libration) points?
     
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  3. Mar 21, 2017 at 1:15 AM #2

    Bandersnatch

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    Bodies don't stay exactly in Lagrange points, but oscillate around them, as seen from one of the main bodies(i.e. in a rotating frame of reference). Look up e.g. 'tadpole orbit', which is an orbit of a body near L4 or L5.

    I'm sorry, I don't understand your second question.
     
  4. Mar 21, 2017 at 2:12 AM #3
    Thanks for the reply, Bandersnatch. That is a good answer to my first question.
    The second question could be asked another way:
    Which of the following would be the correct definition, or are they equivalent?
    (A) Lagrange (libration) points are, with respect to two bodies, null points for a (real or hypothetical) third body with respect to the sum of the gravitational forces on that third body (assuming the third body's mass is negligible compared to each of the other two) .
    (B) Lagrange (libration) points are, with respect to two bodies, null points for a (real or hypothetical) third body with respect to the sum of the centrifugal forces on that third body (assuming the third body's mass is negligible compared to each of the other two) .
     
  5. Mar 21, 2017 at 2:42 AM #4

    Bandersnatch

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    Neither of those is correct, unless I'm still reading it wrong. Neither just gravitational nor just centrifugal forces add up to zero.
    Lagrange points are either:
    a) (in an inertial frame of reference) points where gravitational forces from two massive bodies add up to a sufficient value to keep the third body in orbit with the same period as that of the orbit of the second body.
    b) (in a rotating frame) points where gravitational and centrifugal forces add up to zero.
     
  6. Mar 21, 2017 at 2:52 AM #5
    Many thanks for the excellent answers, Bandersnatch. :smile:
     
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