69th International Astronautical Congress, Bremen, Germany. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. IAC{18{C1.9.5 Mars Optimal Aerobrake Maneuver Estimation Bruno V. Sarli NASA/GSFC Science Collaborator, Catholic University of America, [email protected] Ariadna Farres NASA/GSFC Science Collaborator, University of Maryland Baltimore County, [email protected] David C. Folta Aerospace Engineer, NASA Goddard Space Flight Center, [email protected] Abstract Mars science satellites often perform orbit changes to obtain different measurements, ground tracks or relay operations. Large reductions in semi-major axis and eccentricity can be done efficiently using the atmospheric drag, a.k.a aerobrake. Aerobraking is one of the most challenging planetary orbit maneuvers in terms of planning and operations. The most important consideration for aerobraking is maintaining the spacecraft's periapsis within an allocated atmospheric density corridor, which is accomplished by raising or lowering periapsis through one or a series of very small and short maneuvers. These maneuvers must be performed as efficiently as possible due to propellant constraints. Work herein details a fast and accurate method to calculate the required impulsive velocity changes in the orbit to guarantee that the spacecraft remains in a prescribed density corridor. The method makes use of the orbit's state transition matrix to map the solution space around the reference orbit. It evaluates the most efficient maneuver epochs to target a given periapsis change with a linear optimal control for single or multiple maneuvers. A fast calculation of the maneuver allows for a more comprehensive evaluation of the trade space, and the selected maneuver may be re-targeted later with a higher-fidelity model. Comparisons against fully propagated models and direct method optimizations demonstrate the new method's performance. 1. Introduction complex evolution with variations coming from So- lar cycles, Martian albedo and seasons, as well as Aerobraking is the process of using high atmo- atmospheric winds and dust storms. The range that spheric drag, together with maneuvers made by an defines the mission's density corridor incorporate fac- attitude control system, to change a spacecraft's or- tors such as maximum structural acceleration given bit.1 Generally, the atmospheric brake is used to de- by the drag force acting on the vehicle, and the ve- crease apoapsis without relying exclusively on propel- locity changes that would result in an orbit escape or lant. However, chemical maneuvers are necessary to entry. keep the spacecraft in an allowed density atmospheric Aerobrake maneuver schemes are challenging for corridor, in which the changes to the orbit are accept- many reasons. Perhaps the most important from a able. The chemical maneuvers are short enough and flight dynamics perspective is the need to accurately small enough that they may be considered impulsive. account for orbital perturbations. Particularly for Due to the ever diminishing quantity of propellant re- Martian missions, higher-order gravitational pertur- maining in the spacecraft, the maneuvers need to be bations, perturbing gravitating third bodies and at- as efficient as possible in order to maximize the mis- mospheric drag must all be accounted for in order to sion's operational lifetime. Another important fac- accurately predict the evolution of the spacecraft's tor for the evaluation of an aerobrake scheme is the orbit. Moreover, the inclusion of drag effects requires planetary environment through which the spacecraft consideration of the spacecraft's attitude and the dy- will go, which defines the density profile. Particu- namics of the Martian atmosphere, which adds con- larly, Mars is the focus of this study. Several factors siderable complexity to the problem's modeling. affect the Martian atmospheric density, which has a A method to calculate an optimal aerobrake ma- IAC{18{C1.9.5 Page 1 of 10 69th International Astronautical Congress, Bremen, Germany. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. neuver scheme that minimizes the propellant con- with a fast computation time. The goal is to allow sumption is the main goal of this study. Herein, the the analysis of numerous aerobrake maneuver plans impulsive maneuvers are targeted to keep the orbit's to minimize the propellant usage and provide various periapsis within the defined density corridor. The operational scenarios, such as to be proactive and proposed method uses the spacecraft orbit's state permit quick assessment of aerobrake maintenance transition matrix (STM), propagated with several options, contingencies, variations in maneuver plans, perturbation models, to evaluate the stability of the minimal maneuvers, maneuver timing, multiple ma- spacecraft's final position with respect to the velocity neuvers, etc. throughout the trajectory. The most unstable points To model the dynamics of a satellite around Mars, within the trajectory define the most efficient ma- it is necessary to consider the main forces affecting neuver timings to change the final position; however, its motion. In this paper, the following are consid- these points may not necessarily be in the desired ered: (a) the gravity field of Mars using the Mars-50C direction (periapsis in this case). Nevertheless, this harmonics up to degree and order 50;4 (b) the atmo- region of the orbit is generally known for most cases spheric drag using Mars GRAM-2005;5 (c) the solar because perturbations are small and corrections fre- radiation pressure (SRP) using the cannonball model quent - making the orbit quasi-Keplerian within these (spacecraft's attitude evaluation is out of the scope regions. For maneuvers that raise or lower the peri- of this work); and, (d) the point mass gravity pertur- apsis, as is the case for aerobrake, these multiple rev- bations from the Sun, Jupiter, Phobos and Deimos. olution orbits with small second-order perturbations State propagation is performed using the General will have the most efficient maneuver point at or very Mission Analysis Tool (GMAT).6 GMAT is an open- near the apoapsis. Once the number and time of the source tool for space mission design and navigation impulses are defined, a linear optimal control policy that has been developed at NASA Goddard Space is derived using the STM.2 This strategy defines the Flight Center. The tool enables trajectory optimiza- optimal direction and magnitude of each impulse to tion and mission design regimes ranging from low target the desired orbital parameters. Earth orbit to lunar applications, interplanetary tra- The Mars Atmosphere and Volatile EvolutioN jectories and other deep space missions. Two of this (MAVEN) mission, currently in orbit around Mars, tool's capabilities are of particular interest here: easy, is used here as an example for the method's applica- flexible computation of trajectories around Mars us- tion.3 The spacecraft routinely performs deep dives ing high-fidelity force models and the ability to gen- in the Martian atmosphere to gather atmospheric sci- erate the STM through the propagation of the vari- ence data, making it a suitable test case. ational equations.7 This propagation of the STM Section 2 details the aerobrake scheme, including using a high-fidelity model allows for mapping the the dynamic model used in this paper. Section 3 region around a reference orbit with a good represen- describes the method used in this work, detailing the tation of the second-order effects already described mathematics behind it. An example of the mission's above. While this study uses GMAT, the method- aerobrake scenario is shown in Section 4. ology presented in this paper is independent of the force-model and numerical integration tools. As long 2. Problem Modeling as the reference orbit and the STM are provided, the methodology presented here can be applied. Aerobrake analysis primarily involves maneuver design and operational verification. This analysis is 3. Aerobrake and Maneuver Models currently centered on the use of high-fidelity prop- agators employed for all mission maneuvers. These The aerobrake analysis proposed here combines are typically slow in computing a single solution and the computation of a reference orbit and a high- are not suitable for large scale trade studies or large fidelity propagated STM associated with this orbit. Monte Carlo runs. The method developed in this These are used in a targeting scheme that is able study aims to improve the computational speed in to minimize the propellant with single or multiple analyses that trade multiple solutions as a first un- maneuvers. In this section, different parts of the derstanding of the scenario which informs the high- methodology are presented. fidelity tools. In addition, it helps to establish orbit designs and procedures for the mission's aerobrake 3.1 Problem Base Formulation support models. It is, however, important to comply To fix notation, let x_ = f(t; x) be the equations with high-fidelity operational modeling for accuracy of motion for the force model, where x = [r; v] is IAC{18{C1.9.5 Page 2 of 10 69th International Astronautical Congress, Bremen, Germany. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. a 6 × 1 vector. In order to compute the trajectory where and its associated STM from the force model's Jaco- ΦRR ΦRV Φ(tf ; ti) = : [5] bian matrix, it is necessary to integrate the extended ΦVR ΦVV system: Hence, having computed the STM throughout a full trajectory, a quick analysis can be done by solving x_ (t) = f(t; x(t)); x(t0) = x0; [1] Eq. 4 for the different points in the trajectory. This Φ(_ t) = AΦ(t); Φ(t0) = I6×6; provides a relation between the maneuver epoch and where t0 is the initial epoch, x0 is the initial state, the jj∆vjj cost for a given change in the final position, A = Dfx is the Jacobian of the force model and I6×6 δrf .