Find the Lead Pursuit Line to Reach a Planet

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Discussion Overview

The discussion revolves around determining a trajectory to intercept a planet that is orbiting in a circular path with constant angular velocity. The scenario involves moving from a point in space towards the planet while traveling in a straight line, raising questions about the necessary calculations and methods to achieve this interception.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant describes the initial scenario involving a point in space and a planet orbiting at a distance, seeking a method to reach the planet while moving in a straight line.
  • Another participant expresses confusion regarding the movement direction and suggests considering tactical maneuvers from air combat as a potential analogy for the problem.
  • A later post clarifies the initial misunderstanding about movement direction and reiterates the goal of reaching the planet from an arbitrary distance while maintaining a straight-line path.
  • Another participant proposes that the problem can be approached using missile guidance trajectory methods, referencing a specific article that discusses planar engagement geometry and guidance laws.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to solve the problem, with multiple perspectives and methods being suggested without resolution.

Contextual Notes

The discussion includes potential ambiguities regarding the definitions of movement direction and the assumptions underlying the trajectory calculations. The applicability of missile guidance methods to the problem remains to be fully explored.

GrantB
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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:
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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.
 
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.
 
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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