Comprehensive Literature Review: Spacecraft Trajectory in Aerobraking

This literature review explores the trajectory of spacecraft during aerobraking, a technique used to slow spacecraft using atmospheric drag. It highlights the importance of trajectory control to prevent excessive deceleration and heating. The review covers the historical application of aerobraking, including missions like Hiten, Magellan, and ExoMars, emphasizing the shift towards autonomous systems to reduce costs. It discusses the forces involved, including aerodynamic, thruster, and gravitational forces, and provides equations for calculating drag and lift. The review also covers trajectory control techniques, such as PID controllers, and emphasizes the need for accurate modeling to manage thermal loads. The document references various studies and research papers, providing a comprehensive overview of the subject.

Trajectory of Spacecraft in Aerobraking 1
LITERATURE REVIEW ON TRAJECTORY OF SPACECRAFT IN AEROBRAKING
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Literature Review on Trajectory of Spacecraft in Aerobraking
Aerobraking is a technique used to slow down a spacecraft by the help of the atmosphere
or other planet’s outer gas layers. This happens when the maneuver of the spacecraft reduces the
apoapsis (an elliptical orbit’s high point) as the vehicle flies through the atmosphere at periapsis
(the orbit’s low point) (Kaelberer, Kopman, Brain, Perin, & Valentine, 2017). Aerobraking
technology is very important in modern-day spacecraft industry as it improves vehicle
performance, increases scientific payloads available for missions and elongates mission duration
by simply reducing fuel loads. The first application of aerobraking was in 1991 by the Institute
of Space and Astronautical Science of Japan when they were launching spacecraft Hiten. During
this mission, the spacecraft maneuvered through the atmosphere of the earth over the Pacific
Ocean at an altitude and speed of 125.5 kilometers and 11 kilometers per hour respectively.
Application of aerobraking in this mission saw an apogee decline of 8,665 kilometers. In 1993,
Magellan spacecraft also used aerobraking maneuver on a mission to Venus (dos Santo, Rocco,
& Carrara, 2014). Since then, there are several other spacecraft missions that have used
aerobraking and the technology has continued to gain popularity and relevance across the world.
Today, aerobraking is mostly used to reduce the amount of fuel needed to send a spacecraft to its
anticipated orbit around the moon o target planet with a considerable atmosphere. Instead of
decelerating the spacecraft using propulsion system, aerobraking uses aerodynamic drag to
decelerate the spacecraft (Spencer & Tolson, 2007).
Despite the numerous potential benefits of aerobraking, it is very important to investigate
and establish the trajectory of a spacecraft in aerobraking. The trajectory must be controlled so as
to prevent excessive deceleration loads especially on the spacecraft crew and to ensure that the
spacecraft mission’s target objectives are achieved. It also helps in avoiding excessive heating

Trajectory of Spacecraft in Aerobraking 3
(Jah, Lisao II, Born, & Axelrad, 2006). Generally, orbital spacecrafts are usually not designed
with thermal protection systems or aerodynamics in mind. This means that unless their projector
is controlled, orbital spacecrafts can traverse through undesired parts of the atmosphere.
Therefore it is very important to ensure that the spacecraft in aerobraking maneuvers through the
upper section of the moon or plant’s atmosphere and at the same time keep the heating and
aerodynamic loads to considerably low levels throughout the passes. In most cases, the
spacecraft in aerobraking is maintained within the desired periapsis control trajectory by using
lesser propulsive maneuvers at apoapsis, which regulates the altitude at periapsis.
The National Aeronautics and Space Administration (NASA) has been conducting
studies to establish the actual costs and risks of aerobraking with an aim of modifying the orbit
of spacecraft in aerobraking and ensuring that it has smaller orbital period, reduced apoapsis
altitude and lower energy (reduced propellant). Originally, the key drawbacks of aerobraking
operations included: longer time, large ground staff and continuous DSN (deep space network)
coverage. NASA embarked on a mission to reduce the cost of aerobraking operations by
developing AA (autonomous aerobraking). Today, aerobraking operations are automated, which
has helped in reducing cost of these operations and also improving safety of spacecraft staff
(Prince, Powell, & Murri, 2011). In the recently completed maneuver by ExoMars Trace Gas
Orbiter (TGO) of ESA (European Space Agency) and Roscosmos (Russian space agency),
aerobraking was used to facilitate the orbit’s alteration in the most economical way. ExoMars
was launched in March 2016 and arrived at Mars in October 2016. However, the spacecraft’s
orbit was highly elliptical and remained at an altitude ranging between 200km and 98,000 km,
which was absolutely inappropriate for the mission. To overcome this challenge, an autonomous
aerobraking system was integrated to the system in March 2017 and it successfully decelerated

Trajectory of Spacecraft in Aerobraking 4
the spacecraft, after taking more than 950 orbits (Szondy, 2018). This is a confirmation that
aerobraking technology is practical, beneficial and is steadily revolutionizing the spacecraft
mission industry (Assadian & Pourtakdoust, 2010). Researchers and scientists behind this
mission also emphasized on the importance of accurate computation of spacecraft trajectory as
any miscalculation can result into burning up of the entire spacecraft immediately it gets into the
undesired part of the atmosphere. The aerobraking trajectory of ExoMars is as shown in Figure 1
below
Figure 1: ExoMars Aerobraking (Daniel, 2018)
Forces
The best way to analyze the trajectory of a spacecraft in aerobraking is by determining
the aerodynamic characteristics of the spacecraft as it maneuvers through the atmosphere. One of
the approaches of doing this is by estimating the velocity and position of the spacecraft at instant
time. According to a study carried out by (Zhang, Han, & Zhang, 2010), rarefied aerodynamic
characteristics of a spacecraft in aerobraking can be simulated using direct simulation Monte
Carlo (DSMC) technique. This study focused on analyzing aerodynamic and flow field

Trajectory of Spacecraft in Aerobraking 5
characteristics distribution under different free stream densities. The results obtained showed that
it is very important to establish the effects of spacecraft yaw, planetary atmospheric density and
pitch attitudes on trajectory of spacecraft in aerobraking so as to keep the trajectory under
control. For the spacecraft in aerobraking to maintain good performance throughout its
trajectory, pitch attitude must be controlled appropriately.
Another study was conducted to show how aerobraking and aerocapture can be combined
so as to attain a near-circular orbit without the need for an orbital insertion burn. In this study, a
Maxwellian-free molecular flow model was used together with interpolations based on Knudsen
number to determine aerodynamic force, het flux and moment of the spacecraft model. To
achieve the desired aerobraking trajectory, the researchers manipulated periapsis for each pass
using the given apoapsis. The researchers found that an initial orbit with a relative speed of 12
km/s and eccentricity of 1.6 moving at an altitude of 300 km can be moderated to an orbit with
an eccentricity of 0.02, without exceeding the spacecraft’s maximum allowable convective heat
flux constraint or necessitating an orbit insertion-burn (Kumar & Tewari, 2005). These findings
are very essential especially for Mass emissions and space-tug capture with low-earth orbits as
they can be used to save significant amount of spacecraft propeller mass.
To develop trajectory of a spacecraft in aerobraking, the key forces acting on the
spacecraft must be determined. These forces are: aerodynamic forces (F), thrusters force (Ts) and
gravitational force (mg). All these force are caused by the interaction between the spacecraft and
the atmosphere. Aerodynamic forces’ magnitude is largely determined by the position of the
spacecraft in the space. The aerodynamic forces can be categorized into two: drag force (FD) and
lift force (FL), which are determined using Equation 1 and 2 below (dos Santo, Rocco, & Carrara,
2014)

Trajectory of Spacecraft in Aerobraking 6
FD= 1
2 ρSV ² Cd ……………………………………………….. (1)
FL= 1
2 ρSV ²Cl ……………………………………..…………. (2)
Where ρ = atmosphere density, V = spacecraft velocity in relation to atmosphere, Cd = drag
coefficient and Cl = lift coefficient on the projected space area, S.
Lift force can be divided into lateral lift force (FB) and altitude lift force (FA). These two are
calculated using equation 3 and 4 below
FA=1
2 ρSV ² CA ……………………………………………….. (3)
FB= 1
2 ρSV ² CB ……………………………………………….. (4)
Where CA = altitude lift and CB = lateral lift. The constants can be calculated using different
methods, including Impact Method, as follows:
CD = 2sin3 α = Cp sinα, CL = 2sinα cosα CA = CL cosα, CB = CL sinα.
Where α = attack angle, which is measured the spacecraft’s longitudinal axis and velocity in
correlation with the atmosphere, and Cp = pressure coefficient. CD can also be determined using
Newtonian impact theory.
The aerodynamic forces’ magnitude and direction can be calculated using equation 5 and 6
below
FD=−FD ^V ………………………………………………….. (5)
FL=FA ^N + FB ^H …………………………………………….. (6)

Trajectory of Spacecraft in Aerobraking 7
Where ^V = velocity in correlation with atmosphere vector; ^N = altitude vector, and ^H = angular
momentum vector.
Atmospheric density values are provided by the U.S. Standard Atmosphere model. The
spacecraft’s velocity can be calculated using equation 7 below (Kuga, Rao, & Carrara, 2008)
V = ˙r−ω x r= [ ˙x +ωy
˙y−ωx
˙z ] ……………………………………. (7)
Where ˙r = velocity vector in correlation with inertial system and ω = angular velocity vector of
the rotation of earth.
Trajectory control system
Trajectory deviation of a spacecraft in aerobraking can be controlled using different
techniques (Jiang & Rui, 2015). The choice of method used should be dependent on factors such
as practicality, cost of implementation, accuracy qualities and speed, among others (Rahimi,
Kumar, & Alighanbari, 2013). One of the most common technique used is proportional integral
derivative (PID) controller system. This system used sensors and actuators that collect data,
interprets the data, sends signals and initiate actions that maintain the spacecraft within the
desired atmosphere space. The control actions of the PD controller are computed using different
equations, such equation 8 below (dos Santos, Kuga, & Rocco, 2013).
c ( t ) =Kpe ( t ) + KI ∫e ( t ) dt+ KD de(t )
dt ………………………. (8)
Where KI = integral gain, Kp = proportional gain, KD = derivative gain, and e(t) = position error

Trajectory of Spacecraft in Aerobraking 8
The state of the spacecraft is usually described using coordinates whose measurements are taken
from an inertial frame that is positioned on the earth.
Generally, aerobraking maneuver is where the spacecraft applies drag of the
atmosphere’s upper layer to decrease its velocity so as to reach the anticipated orbit. This
duration of aerobraking can take up to several months or even years and it is characterized by
numerous atmosphere passages (Dunham & Davis, 1999). Reduction of subsequent apogee
happens as the spacecraft passes from one passage of the atmosphere to another. When it reaches
the last apogee altitude, the vehicle gets subjected to a new impulse, which removes the
spacecraft from the transfer orbit and delivers it to the target orbit. For the thermal loads of the
spacecraft to be controlled appropriately, the trajectory of the spacecraft must be modelled
(Lyons & Beerer, 1999). Once the trajectory control model is developed, it becomes easy to
control the spacecraft simply by changing inputs of the model.
References
Assadian, N., & Pourtakdoust, S. (2010). Multiobjective genetic optimization of Earth–Moon trajectories
in the restricted four-body problem.
Advances in Space Research, 398-409.
Daniel. (2018, February 1).
Aerobraking Down, Down. Retrieved from European Space Agency:
http://blogs.esa.int/rocketscience/2018/02/01/aerobraking-down-down/
dos Santo, W., Rocco, E., & Carrara, V. (2014). Trajectory Control During an Aeroassisted Maneuver
Between Coplanar Circular Orbits.
Journal of Aerospace Technology and Management, 159-168.
dos Santos, W., Kuga, H., & Rocco, E. (2013). Application of the Kalman Filter to Estimate the State of an
Aerobraking Maneuver.
Mathematical Problems in Engineering, 1-8.
Dunham, D., & Davis, S. (1999). Optimization of a multiple lunar-swingby trajectory sequence.
Journal of
Astronautical Sciences, 275-288.

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Jah, M., Lisao II, M., Born, G., & Axelrad, P. (2006). Mars Aerobraking Spacecraft State Estimation By
Procesing Inertial Measurement Unit Data.
SpaceOps 206 Conference (pp. 1-24). Rome:
American Institute of Aeronautics and Astronautics, Inc.
Jiang, Z., & Rui, Z. (2015). Particle swarm optimization applied to hypersonic reentry trajectories.
Chinese Journal of Aeronautics, 822-831.
Kaelberer, M., Kopman, S., Brain, D., Perin, C., & Valentine, T. (2017, January 17).
MGS Aerobraking.
Retrieved from NASA: https://mgs-mager.gsfc.nasa.gov/overview/aerobraking.html
Kuga, H., Rao, K., & Carrara, V. (2008).
Introduction to Orbital Mecahnics. Sao Jose dos Campos: National
Institute for Space Research.
Kumar, M., & Tewari, A. (2005). Trajectory and Attitude Simulation for Aerocapture and Aerobraking.
Journal of Spacecraft and Rockets, 684-693.
Lyons, D., & Beerer, J. (1999). Mars Global Surveyor: Aerobraking Mission Overview.
Journal of
Spacecraft and Rockets, 307-313.
Prince, J., Powell, R., & Murri, D. (2011).
Autonomous Aerobraking: A Design, Development and
Feasibility Study. Washington, D.C.: National Aeronautics and Space Administration.
Rahimi, A., Kumar, K., & Alighanbari, H. (2013). Particle Swarm Optimization Applied to Spacecraft
Reentry Trajectory.
Journal of Guidance, Control, and Dynamics, 307-310.
Spencer, D., & Tolson, R. (2007). Aerobraking Cost and Risk Decisions.
Journal of Spacecraft and Rockets,
1285-1293.
Szondy, S. (2018, February 26).
European Mars Orbiter Completes 11-Month Aerobraking Maneuver.
Retrieved from New Atlas: https://newatlas.com/esa-mars-tgo-aerobraking-maneuver/53531/
Zhang, W., Han, B., & Zhang, C. (2010). Spacecraft aerodynamics and trajectory simulation during
aerobraking.
Applied Mathematics and Mechanics, 1063-1072.