Find the Lead Pursuit Line to Reach a Planet

[GrantB]

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.

 

[Bobbywhy]

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.

 

[GrantB]

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.

 

[Bobbywhy]

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.”