ASEN 5050 Space flight Dynamics

FALL 2000

Ben Mottinger

Aerobraking as a method for orbit energy reduction is presented in addition to further analysis to optimize the technique for certain parameters. Fundamental equations and methodology are introduced as used by the Mars Global Surveyor mission. Key parameters are investigated to improve aerobraking design, while keeping vehicle mass to a minimum. Of these parameters, dynamic pressure and material selection were found to influence aerobraking performance the most.

Abstract *

Table of Contents *

Introduction *

Methodology *

Aerobraking Analysis: Improving Aerobraking at Mars *

Conclusion *

References *

Appendix A—Additional Comparison of Earth-Mars Aerobraking *

Aerobraking is a means of energy reduction, used generally to circularize a highly elliptical orbit by taking advantage of atmospheric drag to reduce the orbital energy, thus saving expensive fuel otherwise needed for the task (Fig. 1). Aerobraking was first introduced in the Magellan mission to Venus in 1993. With the successful application on Magellan, aerobraking was employed on Mars Global Surveyor (MGS) starting in 1997.

Aerobraking is an economical method for orbit capture because the fuel required to circularize an orbit is much less than a conventional planetary capture. The savings in launch mass are substantial; MGS saved about $200 million on the launch. A similar mission, Mars Observer, used a conventional capture with a launch cost five times that of MGS. The spacecraft payload masses only differed by 81kg, but Mars Observer’s total mass was 2572kg, while MGS was 1060kg. [1] This great savings prompted further use of aerobraking, as Mars Climate Orbiter planned to do.

Aerobraking is initiated after an orbit insertion burn to place the spacecraft in a highly elliptical orbit. In the case of MGS, the initial orbital period after Mars Orbit Insertion (MOI) was about 48 hours, which was eventually reduced to 2 hours. [2] For aerobraking to work efficiently, some small propulsive maneuvers at apoapsis are required to adjust the periapsis altitude. Atmospheric density limits are placed on the mission depending on the spacecraft’s maximum dynamic pressure and temperature capability. Thus, the periapsis altitude must be raised if the density increases beyond an allowable level.

Since the atmospheric density is the most variable parameter in Mars navigation, the aerobraking plan must be continually modified to account for fluctuations in the density. Dust storms, which cause the atmosphere to swell, effectively making the density higher at the same altitude can raise the density to a dangerous level. These rises in density can damage the spacecraft by exposing the solar panels to an environment beyond their design limit. Once a major shift in density is measured, the periapsis altitude must be raised to prevent damage. Aerobraking is not necessarily suspended since the density at the higher altitude may still be within the planned density corridor.

As a preliminary estimate for mission planning purposes and open-loop navigation software, acceleration due to atmospheric drag, the density, and orbit period reduction are formulated as follows.

The exponential density model

(1)

and the acceleration due to atmospheric drag

(2)

were used in the MGS navigation software where r_o and h_o are the base density and altitude respectively, H is the density scale height, v_r is the spacecraft’s velocity relative to the atmosphere, C_d is the coefficient of drag, A is the effective cross sectional area, and m is the spacecraft mass after the insertion burn (MOI). [3]

An estimate of the change per orbit of the period is:

(3)

where r_p is the density at periapsis passage, a is the semi-major axis, e is the eccentricity, and m is the gravitational parameter of Mars (m = 42,828.3 km³/s²). [3]

Although estimates of the aerobraking phase may be made for mission design purposes, in practice, the mission timeline will change based on unpredictability of atmospheric density on Mars. This section will present both a general approach to incorporating aerobraking into mission design and the methodology used by JPL on MGS.

The MGS spacecraft was launched on November 7, 1996 aboard a Delta II launch vehicle with a 1250 m/s deficit in mission D V, normally used for orbit circularization. The goal of the MGS mission was to conduct a global mapping of Mars of the atmosphere, gravitational and magnetic fields, and the planet surface. The final mapping orbit was required for the return of quality science data. Thus, aerobraking was a mission-critical event for MGS.

Before aerobraking could begin, the spacecraft was slowed from an initial hyperbolic trajectory to an elliptic orbit around Mars (Fig. 2). The transition from a hyperbolic orbit to a highly elliptic orbit is required to begin aerobraking.

Once an elliptic orbit is established, the first aerobraking phase, walk-in, begins (Fig. 3). During the walk-in phase, the spacecraft first encounters the atmosphere. When periapsis is lowered to the point that the dynamic pressure values are near the limits of the mission design, the main phase begins. The majority of orbit period reduction occurs during this phase and continues until the spacecraft’s orbit lifetime is two days. The orbit lifetime in this case is defined to be the time it takes the apoapsis altitude to decay to 300km. After the main phase, the aerobraking walk-out phase begins. The purpose of the walk-out phase is to increase the periapsis altitude until the final mapping orbit is obtained.

Several key parameters determine the level of aerobraking for a mission. The upper limit of an aerobraking dynamic pressure corridor is constrained by the material properties of the spacecraft. Thermal limitations of the vehicle will generally drive this corridor. The density is related to the dynamic pressure as in Equation 1, with the dynamic pressure defined as r v_r²/2, so the lower the periapsis altitude, the higher the velocity, and greater dynamic pressure. Since altitude is generally correlated to density and velocity, and the periapsis altitude is nearly constant throughout the aerobraking phase, the "density corridor" is often examined as a parameter. Once a thermal analysis of the spacecraft determines the maximum safe environment, a dynamic pressure corridor may be chosen based on the density and velocity. The critical density determined for MGS was 143kg/km³ (given a periapsis altitude), which was driven by the solar panel qualification. [4]

Another key parameter in aerobraking is the effective cross sectional area of the spacecraft. From Equation 3, we can see that the period reduction is proportional to the cross sectional area. MGS attached additional "braking flaps" to the ends of the solar panels to increase the drag, making the effective cross sectional area 17.02 m² (Fig. 4).

Another parameter that affects aerobraking is the mass of the spacecraft. From Newton’s simple F = ma equation, we can see that acceleration is inversely proportional to the mass of the vehicle, so a less massive vehicle will require less force to slow down. Obviously, a spacecraft’s mass is not driven by aerobraking requirements, but rather launch costs, so mass is not a flexible parameter when designing an aerobraking phase. However, varying the cross sectional area and/or material of the spacecraft to improve aerobraking performance will likely increase the mass of the vehicle. Thus, mass of the vehicle is only indirectly affected by aerobraking design.

Finally, aerobraking depends on the body around which it is orbiting. The atmosphere of the planet greatly affects aerobraking performance. A relatively thin atmosphere like Mars requires a low periapsis altitude (higher velocity) to obtain the necessary dynamic pressure. The velocity, however, also depends on the mass of the planet from the gravitational parameter in the Vis Viva equation. (See Appendix A for further analysis)

Aerobraking at Mars on MGS was successful despite a mechanical failure of one of the solar array hinges. The mission timeline was adjusted significantly to account for the decreased aerobraking performance due to the broken hinge, but eventually MGS was placed in a circular orbit around Mars to conduct its science mapping. MGS demonstrated that an aerobraking capture can substantially reduce launch costs by decreasing orbit energy through drag instead of propulsive maneuvers.

A trade study of different aerobraking parameters is performed to find a combination of cross sectional area and dynamic pressure that minimizes the spacecraft mass. This configuration will allow the vehicle to reduce orbital energy quickly with a minimal mass. Of course the argument can be made, that no special modification should be made to enhance aerobraking performance, since the job can be accomplished over a longer time with the current materials. However, a mission requirement may arise sometime for a spacecraft to obtain a circular orbit within a given time frame. An example may be a rendezvous with Mars to conduct measurements during a seasonal phenomenon. Since the period of Earth-Mars phasing is about every two years, the launch window is constrained, so the aerobraking phase may have to be shortened by months to meet the science phasing goal. With proper modifications, an aerobraking scheme may still be implemented so that launch costs are kept to a minimum.

The main limitation of aerobraking performance is the material properties used for the braking surfaces. The temperature increases rapidly due to friction at the extremely high orbital velocities when the density increases at lower altitudes. Normally, ablative materials are used for reentry to withstand these extreme thermal environments, however, these heat shields are very massive, and aerobraking performance on this level is not required. On Mars Polar Lander, the heat shield and aeroshell assembly alone had a mass of about 140kg, which is over twice the mass of all the propellant needed for cruise and descent. [7] Thus, protective heat shields to this extreme are not efficient for aerobraking applications.

To save mass, solar arrays take on the function of drag flaps in addition to providing power during the aerobraking phase. Solar arrays, however, are extremely fragile and a mission-critical spacecraft component that must not be compromised to achieve higher aerobraking performance. To truly optimize a spacecraft for aerobraking maneuvers, additional thermal protective composites must be added to the leading edges of aerobraking surfaces.

Carbon-carbon composites can operate at temperatures up to 3000^oC and increase in strength with temperature. [8] Other applications of this composite include the leading edges of the space shuttle and brake discs of racing cars, where temperatures can soar. Even if a thin layer of C-C composite is affixed to the backside of the solar panels and the rest of the surfaces normal to the aerobraking direction, much higher dynamic pressures could be achieved with a small increase in spacecraft mass.

As mentioned before, dynamic pressure varies with the square of velocity, so as the periapsis altitude is lowered, aerobraking performance increases as a result of the increased velocity and density. Since MGS suffered a failure of one of the hinges of its solar array assembly, a comparison of the dynamic pressure corridor of which MGS actually experienced with the planned corridor is made. The planned pressure demonstrates the increased performance of a higher dynamic pressure (Fig. 5). Over 110 orbits, the total orbit time for the actual MGS mission was 102 Earth days, while the planned aerobraking would have reduced the orbital period by 8 hours more in the same number of orbits and in only 66 Earth days.

The orbital period reduction is estimated using Equation 3 and plotted along side the actual MGS orbital telemetry to demonstrate the accuracy of this model (Fig. 5). Over the 110 orbits plotted here, the average difference in period was 0.83 hours, which is good enough for rough estimates.

To understand the effect of varying the effective cross sectional area of the vehicle during aerobraking, different areas are plotted showing the period reduction as a function of the number of orbits starting from an initial orbital period of 45 hours and eccentricity of 0.88 (Fig. 6). The largest area, 68m², which is four times the effective area of MGS, circularized the orbit of the vehicle in about 32 orbits, which is a factor of over 5 times less than with an area of 17m². Such a large surface area for arrays is not likely for a planetary mission because of the increased mass and difficulty of stowing and deploying the larger array structure.

A more reasonable parameter to vary is the dynamic pressure. The planned dynamic pressure corridor for MGS averaged 0.65N/m² so this parameter is increased by factors of 1.5 and 2 to obtain dynamic pressures of 0.975N/m² and 1.30N/m², respectively (Fig. 7). The number of orbits to circularize an initial 45 hours orbital period at Mars is cut in half (exactly) by the linear dependence of density and delta P in Equation 3 (assuming the same periapsis altitude). The time to circularize the orbit is not linear, however, since the period reduction depends on the square of the semi-major axis (Table 1). This is why the largest reductions in period occur early in the highly eccentric orbit. As the orbit is circularized, period reduction slows considerably.

An analysis of optimizing aerobraking for mass of the spacecraft and time to circularize an orbit indicates that the most reasonable approach is to increase the dynamic pressure corridor. A higher dynamic pressure mandates the use of highly temperature-resistant materials such as carbon-carbon composites to protect the spacecraft from the extreme thermal environment created by atmospheric drag. The tradeoff for the additional mass of protective thermal material for increased aerobraking performance may be required for a mission that must circularize its orbit in a fast time, while also saving on launch costs. This is a reasonable constraint in the "faster, better cheaper," paradigm of today’s spacecraft.

Aerobraking was examined for Mars Global Surveyor while introducing the fundamental parameters and equations used in an aerobraking model. The two most important parameters were found to be dynamic pressure and mass of the planet in aerobraking performance. MGS proved the aerobraking concept despite the hinge failure that increased the time in the circularization phase. The MGS mission also demonstrated that accurate navigation during aerobraking depends on small adjustments in the apoapsis altitude to account for variations in atmospheric density. These small propulsive maneuvers were also necessary to keep the spacecraft within the density corridor limitations imposed.

Aerobraking is indeed an exciting new technique to reduce orbital energy by natural means. Missions such as Mars Climate Orbiter and Genesis planned or are planning to use aerobraking at Mars as a viable and cost-efficient alternative to propulsive deceleration. Advances in the method are sure to take place since its practice is less than a decade old. We can only hope that future missions will not attempt such an aggressive aerobraking scheme as was attempted by Mars Climate Orbiter.

[1] Goodall, Kirk, "An Explanation of How Aerobraking Works," JPL-NASA, http://mars.jpl.nasa.gov/mgs/confirm/aerobexp.html

[2] Johnson, M.D., Esposito P.B., Alwar, V. et al, "Mars Global Surveyor: Aerobraking at Mars," Jet Propulsion Laboratory, AAS 98-112, 1998.

[3] Esposito, P.B. Alwar, V. Demcak, E. et al, "Mars Global Surveyor: Navigation and Aerobraking at Mars, Jet Propulsion Laboratory, AAS 98-384, 1998.

[4] Mars Global Surveyor Mission Plan, Final Version, Rev B. MGS 542-405, 1996.

[5] Shevell, Richard S., "Fundamentals of Flight," Prentice Hall, Englewood Cliffs, NJ, 1989.

[6] Vallado, David A., "Fundamentals of Astrodynamics and Applications," McGraw-Hill, New York, 1997.

[7] NASA-JPL, "Mars Polar Lander,": http://marslander.jpl.nasa.gov/lander/bus.html

[8] Askeland, Donald R., "The Science and Engineering of Materials," PWS Publishing Company, Boston, 1994.

Appendix A—Additional Comparison of Earth-Mars Aerobraking

To demonstrate the dependence on the planet’s mass in aerobraking, a comparison of orbit circularization at Earth and Mars is shown (Fig. 8). This model assumes that for a given density, the dynamic pressure will be equivalent at Earth and at Mars. Of course, this is far from accurate, but the point of this chart is to only compare the planet’s mass given the simple relationship in Equation 3. Pertinent parameters used in the calculation are given in the figure. By only considering the change is mass of the planet, a huge reduction in time to circularize is seen. If the dynamic pressure were taken into account, this reduction would be even greater.

A comparison of aerobraking on Earth and Mars reveals that for the same eccentricity and density, the relative velocity at periapsis at Earth is much higher, so the dynamic pressure is also much greater (Table 1). At this dynamic pressure, thermal limitations of the spacecraft materials would be an issue.

Since the dynamic pressure varies as the velocity squared, aerobraking is more effective on Earth compared to Mars for the same eccentricity and atmospheric density.