Story: I have x and y positions of a spaceship as it moves through space to some goal location at [1000, 700].
A record of its movement is given by:
x = [800, 850, 900, 950, 1000] y = [600, 625, 650, 675, 700]
with each observation of its position recorded 4 seconds apart.
Now let's say there is also a stationary object (let's say it's a planet) at [894, 444]. I'd like to quantify the 'pull' of this object on the spaceship as it moves through space. The captain of the spaceship is assumed to fight this force to make sure she arrives at her goal location.
If the force is weak, then there should be no record of her making small corrections. If the force is strong, then there should be a clear record of her correcting course.
Real problem: I have a log of eye movements. I am trying to quantify the 'pull' of an irrelevant object in space as eyes move towards a goal location.
As I only have a math background, my initial instinct was to use regression to compute a fit for the above data (to get a polynomial model of the points), compute the curvature (ϰ) of this fitted function and look to see if the maximal curvature occured at roughly the same place as the object as the eyes moved towards a goal.
...but this seems to miss the point in my mind. How else can I accomplish this?