def invE(self,offsetArcLength=None,arcLengthArg=None,rtnIter=False):
"""Find eccentric anomaly corresponding to the input arc length"""
### Parse arguments
assert not (offsetArcLength is not None and arcLengthArg is not None)
if arcLengthArg is None: arcLengthTarget = self.arcChf + offsetArcLength
else : arcLengthTarget = float(arcLengthArg)
### Initial estimate of Eccentric Anomaly
### - highest positive or negative multiple of halfpi that gives
### an arc length less than or equal to targetLength
nQuad = int(arcLengthTarget / self.quadArc)
arcLengthGuess = nQuad * self.quadArc
if arcLengthGuess > arcLengthTarget:
nQuad -= 1
arcLengthGuess -= self.quadArc
eaGuess0 = eaGuess = nQuad * halfpi
eaGuess0PlusTwoPi = eaGuess0 + twopi
deltaArc = arcLengthTarget - arcLengthGuess
tol = self.aChf * 1e-9
itter = 0
while abs(deltaArc) > tol:
itter += 1
### Vector from primary focus to Ecc. Anom. guess
cosea = math.cos(eaGuess)
sinea = math.sin(eaGuess)
x = self.aChf * cosea
y = self.bChf * sinea
### Delta-[x,y] of tangent at (x,y) for distance of deltaArc
delx = -self.aChf * sinea
dely = self.bChf * cosea
fac = deltaArc / sp.vnorm(sp.vpack(delx,dely,0.))
delx *= fac
dely *= fac
### Delta-vector tangent at (x,y) for distance of deltaArc
### - [X,Y,Z] = [x+delx, y+dely, 0]
### - scale X by 1/a and Y by 1/b to get Eccentric Anomaly
eaGuess = sp.recrad(sp.vpack((x+delx)/self.aChf
,(y+dely)/self.bChf
,0.
)
)[iRA]
while eaGuess0 > eaGuess: eaGuess += twopi
while (eaGuess0PlusTwoPi) <= eaGuess: eaGuess -= twopi
arcLengthGuess = self.E(eaGuess)
deltaArc = arcLengthTarget - arcLengthGuess
return rtnIter and (eaGuess,itter,) or eaGuess
utcPRG = spice.et2utc(et,'ISOC',3,99)
mtxJ2kToBF = spice.tipbod('J2000', targetID, et)
velocityPRG_BF = spice.mxv(mtxJ2kToBF,state[3:])
V_prg,ra,Theta = spice.recrad(velocityPRG_BF)
Theta_deg = Theta * dpr
print((dt,dt/et,utcPRG,V_prg,Theta_deg))
import matplotlib.pyplot as plt
days = 7
hours = xrange(-24*days,24*days + 1)
speeds = [ spice.vnorm(spice.spkezr(spacecraft,et+(hour*3600.),'J2000','NONE',target)[0][3:]) for hour in hours]
Vmin = min(speeds)
plt.axhline(y=V_prg,label='V_prg = %.3fkm/s' % (V_prg,))
plt.axhline(y=Vmin,label='Vmin = %.3fkm/s' % (Vmin,))
plt.plot(hours,speeds,'r',label='%s-relative speed' % (target,))
plt.title('Perigee at %s (UTC); Theta=%.3fdeg' % (utcPRG,Theta_deg,))
plt.xlabel('t - T_prg, h')
plt.ylabel('%s-relative speed, km/s' % (target,))
plt.legend()
plt.show()
