Spacecraft and Aircraft Dynamics - Lecture 5 - Illinois Institute of ...

Example ContinuedGiven the true anomalies, f 1,2 , we want to find the associated times, t 1,2 .• Only solve for t 2 , get t 1 by symmetry.• First find Hyperbolic Anomaly,(√ ( e−1H 2 = tanh −1 e+1 tan f22• Now use Hyperbolic anomaly to find mean anomalyM 2 = esinh(H 2 )−H 2 = .0085) ) = .1173◮ This is the “easy” direction.◮ No Newton iteration required.• t 2 is now easy to findt 2 = M 2√−a 3µ = 1076.6Finally, we conclude ∆t = 2∗t 2 = 2153s = 35min.So the spacecraft survives.M. Peet Lecture 5: Spacecraft Dynamics 19 / 26