Created
June 28, 2009 23:53
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type Point = (Double, Double) | |
type Vector = Point | |
distance :: Point -> Point -> Double | |
distance (x1, y1), (x2, y2) = sqrt ((x2-x1)**2 + (y2-y1)**2) | |
-- Compute the normalized tangent vector from two points | |
normalizedVector :: Point -> Point -> Vector | |
normalizedVector (x1, y1) (x2, y1) = (xv / l, yv / l) | |
where | |
xv = x2 - x1 | |
yv = y2 - y1 | |
l = distance (0, 0) (xv, yv) | |
mu :: Double | |
mu = 6.67428e-11 * 6.0e24 | |
times :: Double -> Vector -> Vector | |
times v (x, y) = (v*x, v*y) | |
-- vec is the result of computing normalizedVector on the first two points that | |
-- were observed (don't fire the rockets before observing!) | |
delta1 :: Double -> Double -> Vector -> Vector | |
delta1 r1 r2 vec = (lhs*rhs) `times` vec | |
where | |
lhs = sqrt (mu / r1) | |
rhs = (sqrt (2 * r2 / (r1 + r2))) - 1 | |
-- same note as above | |
delta2 :: Double -> Double -> Vector -> Vector | |
delta2 r1 r2 vec = (lhs*rhs) `times` vec | |
where | |
lhs = sqrt (mu / r2) | |
rhs = 1 - (sqrt (2 * r1 / (r1 + r2))) |
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