def findTerminalThrust():
# above the top of the atmosphere, there is no limit!
if alt >= TOA: return 1e30
v_term = planet.terminalVelocity(alt, dragCoefficient)
a = timestep * timestep
v_noTX = v_nothrust[0] * cos(phi) + v_nothrust[1] * sin(phi)
b = 2 * timestep * v_noTX
c = v_noTX - v_term * v_term
soln = physics.quadratic(a,b,c)
return max(soln)
def determineOrbit(self, h, velocity):
"""
Given distance from the planet's core, and current velocity vector,
return the apsides in meters from the planet's core.
If one of them is negative, the orbit is hyperbolic.
h is in meters relative to the core
velocity is in polar coordinates (m/s, radians) where the angle is
relative to the tangent to the surface.
"""
# http://forum.kerbalspaceprogram.com/showthread.php/36178-How-to-predict-my-apoapsis-given-altitude-and-velocity
# Plugging in Horn Brain's derivation (which is the same as Jason
# Patterson's, but seems a bit easier to follow):
# We use two equations, twice each:
# vis viva: v^2 = mu (2/r - 1/a) where a is the semimajor axis
# momentum: p = r v cos(theta) where theta is the angle of v to
# the surface tangent.
# Momentum is preserved, so p is the same value at all points of
# the orbit.
#
# Steps:
# 1. vis viva with r=h, v=v, solve for 1/a.
# 2. momentum from the parameters: p = rv cos theta
# 3. momentum at the apses to relate r_apsis and v_apsis
# 4. vis viva with r being the apses.
# Substitue 1/a from before, and substitute v_apsis from
# momentum.
# 5. Solve quadratic equation:
# 0 = (1/a) r_apsis^2 - 2 r_apsis + p^2 / mu
#
# We get two solutions, which are the apoapsis and periapsis
# (measured from the center of the planet), in that order.
#
(v, theta) = velocity
ainv = (2 / h) - (v*v / self.mu)
p = h * v * cos(theta)
return quadratic(ainv, -2, p*p / self.mu)