Discuss about the 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 (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 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
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 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)
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
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
Where = velocity in correlation with atmosphere vector; = altitude vector, and = 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)
Where = 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).
Where KI = integral gain, Kp = proportional gain, KD = derivative gain, and e(t) = position error
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: https://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.
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.
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