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Lead Pursuit Line

  1. Dec 6, 2011 #1
    Suppose you are at a point (x0,y0) in space. There is a planet at position (x1,y1) orbiting in a circle a distance r away from the orbit center (x2,y2).

    The planet has constant angular velocity as it orbits. You move at a constant speed towards the planet, and want to move in a straight line.

    How do you determine how to reach the planet, traveling only in a straight line?

    Thanks.
     
    Last edited: Dec 6, 2011
  2. jcsd
  3. Dec 6, 2011 #2

    Bobbywhy

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    GrantB, when you say "You move at a constant velocity from the planet,..." does that mean you are moving AWAY from the planet? Then you want to determine how to reach the planet, so I am confused.

    So, I am guessing you may get some insight on the problem by considering this:

    "Basic fighter maneuvers (BFM) are tactical movements performed by fighter aircraft during air combat maneuvering (also called ACM, or dogfighting), in order to gain a positional advantage over the opponent."

    http://en.wikipedia.org/wiki/Basic_fighter_maneuvers

    This article includes the Lead Persuit attack course, which you mention in the thread title, but do not mention in the post itself.
     
  4. Dec 6, 2011 #3
    Sorry, it was a mistype.

    It should say:

    The planet has constant angular velocity as it orbits. You move at a constant speed towards the planet, and want to move in a straight line.

    So, you want to get to the planet, and you are at an arbitrary point a distance d from the planet, moving only in a straight line.

    Thanks, and sorry for the mistype.
     
  5. Dec 6, 2011 #4

    Bobbywhy

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    I think your problem of intercepting a moving planet can be solved by using the methods of missile guidance trajectories. Here is an article you may be able to use. See:

    www.jhuapl.edu/techdigest/TD/td2901/Palumbo_Homing.pdf

    “Figure 2. Planar engagement geometry. The planar intercept problem is illustrated along with most of the angular and Cartesian quantities necessary to derive modern guidance laws.”
     
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