JOURNAL OF SPACECRAFT AND ROCKETS Vol. 42, No. 4, July–August 2005 Trajectory and Attitude Simulation for Aerocapture and Aerobraking Mrinal Kumar ∗ and Ashish Tewari † Indian Institute of Technology, Kanpur 208 016, India A combined strategy of aerocapture and aerobraking is presented to achieve a near-circular orbit, starting from a hyperbolic trajectory, without requiring an orbital insertion burn. Aerothermodynamic force, moment, and heat flux calculations employ a Maxwellian free-molecular flow model, with Knudsen-number-based interpolations for the transition regime. The six-degree-of-freedom motion model, including quaternion-based attitude dynamics, al- lows stability and sensitivity analyses for the atmospheric passes. A spacecraft model with two large panels suitable for Earth aerocapture is considered. Minor orbit-correction burns at the apoapsis are provided after each pass for manipulating the periapsis for the next pass to meet the desired aerobraking corridor. It is observed that an initial orbit of eccentricity 1.6 and relative entry velocity of 12 km/s at 300-km altitude can be reduced to an orbit with an eccentricity of 0.02, using a total of six atmospheric passes, without exceeding the peak convective heat flux constraint for the spacecraft or requiring an orbit insertion burn. This result has considerable importance for low-Earth-orbit space-tug captures and Mars missions, wherein the strategy proposed will lead to significant savings in spacecraft propellant mass during the orbit insertion and, subsequently, orbit circularization. Nomenclature A = reference area a c = thermal accommodation coefficient C p = pressure coefficient C τ = tangential stress coefficient c = reference length d ∞ = freestream dynamic pressure e = orbital eccentricity F = external force vector, ∈ℜ 3 × 1 J = inertia tensor of the spacecraft, ∈ℜ 3 × 3 J 11 , J 22 , J 33 = principal moments of inertia of the spacecraft Kn = Knudsen number M = external moment vector, ∈ℜ 3 × 1 m = mass of the spacecraft ˆ n i = unit normal vector of the i th surface panel p, q , r = angular velocity components about the X , Y , and Z body axes Q = convective heat load on the spacecraft ˙ Q = convective heat flux ˙ Q max = maximum convective heat flux q 0 , q 1 , q 2 , q 3 = quaternion components used to describe body orientation R = distance of spacecraft center of mass from the planet’s center r i = position vector of the i th panel centroid relative to the center of mass of the spacecraft, r i ∈ℜ 3 × 1 S(ω) = skew-symmetric matrix, ∈ℜ 3 × 3 s = molecular speed ratio T W / T ∞ = ratio of wall temperature to freestream temperature V = spacecraft velocity measured in the planet fixed coordinate system X fo , Y fo , Z fo = forces along the wind axes α = angle of attack Received 17 December 2003; revision received 8 May 2004; accepted for publication 1 June 2004. Copyright c  2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose- wood Drive, Danvers, MA 01923; include the code 0022-4650/05 $10.00 in correspondence with the CCC. ∗ Undergraduate Student, Department of Aerospace Engineering. † Associate Professor, Department of Aerospace Engineering; ashtew@ iitk.ac.in. Senior Member AIAA. β ∞ = parameter analogous to an inverse continuum speed of sound, s = V β ∞ γ = flight-path angle, defined as the inclination of the velocity vector with respect to the instantaneous local horizon, positive above the horizon ˜ γ = specific heat ratio of air, 1.4 δ = longitude, positive toward east  = inclination of an elemental panel with respect to flow direction θ 1 , θ 2 = deployment angles of the left and right panels of the spacecraft λ = latitude, positive above the equator ρ ∞ = freestream density σ N = normal momentum accommodation coefficient σ T = tangential momentum accommodation coefficient ς = angle of sideslip χ = heading angle, defined as the azimuth of the velocity vector’s projection on the local horizontal plane, positive toward north  = rotational rate of the planet ω = angular velocity vector of the spacecraft, ∈ℜ 3 × 1 Superscripts ∗ = inertial frame · = time derivative Introduction M ODERN spacecraft mission design has grown in sophistica- tion with every passing year. Several novel techniques have been incorporated into mission profiles and have proved beneficial to the overall mission structure. Aerobraking 1−4 is one such revo- lutionary technique, which was executed for the first time by the Magellan spacecraft 5 in 1992, although not as a part of the planned mission. Aerobraking is a method of reducing the spacecraft ve- locity by making it pass through the higher reaches of a planetary atmosphere, thereby using the concomitant drag as an “aerodynamic brake.” The reduction in speed leads to a reduction in the orbit size when the spacecraft emerges from the atmosphere after the pass. Aerobraking had to wait until 1997 to become an integral part of a mission, when the Mars Global Surveyor (MGS) achieved a near- circular orbit, starting from the highly eccentric orbit resulting from 684