FREE RETURN AND ENERGY-EFFICIENT TRAJECTORY FOR EARLY MANNED MARS MISSIONS EMPLOYING SPLIT EXPEDITION

Yon Wui Ng

Department of Aerospace Engineering, RMIT University, (03) 9329 5583, yonwui@yahoo.com

 

ABSTRACT

This paper proposes an innovative trajectory for early manned Mars missions. Characteristics of the trajectory include the free return capability, the energy-efficient launch, and the two-burn Earth escape maneuver for propellant saving purpose. The launch window identified for the proposed trajectory is in March 2012 with 150 days of TMI transit and 200 days of TEI transit. Total delta-V required for the mission is about 5.1 km/s. The major drawback for the proposed trajectory is the close Sun passage during the free return trip. However, it is believed that the radiation issue as a result of the close Sun passage can be overcome with proper radiation shielding for the spacecraft.

INTRODUCTION

Many scientists targeted Mars as the next milestone for human space exploration soon after Neil Armstrong made the first step on Moon, on July 20, 1969. Since then, a wide range of research has been conducted to render a technologically feasible and economically affordable solution for a manned Mars mission. Some previous studies are in favor of a single LEO launch expedition which is characterized primarily by a huge spacecraft that requires at least 4-6 LEO rendezvous prior to trans-Mars injection (TMI). Trajectories chosen for this category of expedition vary from the opposition-class type with Venus swing-by or the conjunction-class type with near Hohmann transfer. Conceptual configurations of spacecraft for such an expedition are shown in Figure 1a and Figure 1b.

Nevertheless, many latest Mars mission plans, such as Mars Direct [1] and the Reference Mission [2] discarded this type of strategy. This is mainly due to the inherent complexity associated with a 4-6 rendezvous plan, which is further worsened by the corresponding issues of rendezvous such as loss of cryogenic propellant due to boiloff during LEO built-up phase, stringent LEO construction station requirements, enormous operating/monitoring cost, and particularly, the sky high risk involved in the rendezvous process. Upon identifying these drawbacks, recent Mars mission plans call for a split expedition that will consecutively launch payload components like the habitat module, the ascent module, and the Earth-return vehicle separately to either the Mars surface or the Mars orbit, depending on the strategy of the mission. Figure 2 shows a mission planning flow chart for a typical split expedition. Despite the fact that this category of expedition may be more expensive than the single LEO launch expedition; it is simpler, more flexible from operational point of view, and involves lower overall mission risk than its counterpart. However, as a result of sending the cargo and crew on separate missions, most of the split expeditions suffer from a higher risk of losing crew lives. Not to mention that the crew missionís TMI stage is considerably long (range from 150 Ė 250 days), and if anything goes wrong after the TMI stage is commenced, it is not likely that any rescue mission will help to save the crew. This drawback of the split expedition leads to the study in this paper for a safer and yet energy-efficient trajectory for crew mission.

In this paper, trajectory requirements are first briefly discussed. An envisaged trajectory that would meet all of the specified requirements is then presented. Analytical methods are then used to formally validate whether or not the envisaged trajectory is available and affordable in reality. It is found that the opportunity for such a trajectory is available once every 6.405 years. However, the potential issues associated with the trajectory must be solved before the trajectory can be applied in any practical mission.

Trajectory requirements

The study in this paper is based on the trajectory requirements for MAB (Mars And Beyond) crew mission. MAB is one of the undergraduate teams in RMIT Aerospace which undertaking a Mars mission planning and design project for year 2002. In a nutshell, the MAB mission has the following features: 1) Split expedition employing chemical launch vehicles, 2) Common crew transfer module design, 3) Aerobraking using biconic aeroshell for Mars capture and Earth re-entry, 4) In-situ resources utilization (ISRU) for ascent propellant and life support systems, and 5) High energy transfer trajectory for crew mission and low energy transfer trajectory for cargo mission.

The following outlines the trajectory requirements for the MAB crew mission.

  • Launch date > Jan 01, 2007 (JD 2454101.5)
  • Total delta-V, D Vtotal < 6.0 km/s
  • 180 days stay time, 300-450 days total trip time
  • Mars-entry velocity < 10 km/s, Earth re-entry velocity < 15 km/s

Apart from those essential requirements listed above, the crew mission trajectory must be designed such that a free return is available for the spacecraft, so that if what has planned for the mission goes wrong after the crew have departed for Mars, they can still take the advantage of the Mars gravity to coast back to Earth. This is an important fail-safe design feature that must be incorporated into any split expedition, especially for those which have to send the cargo mission long before the crew mission in order to utilize the in-situ resources at Mars.

Crew mission trajectory design

The envisaged trajectory for the MAB crew mission is shown in Figure 3a and Figure 3b. Note that the trajectory shown in solid line is designed for the normal operating scenario, whereas the trajectory shown in dotted line is designed for the failure scenario. The following paragraph will briefly explain the mission sequence employing such a trajectory.

After lifting off from ground station via a heavy-lift launch vehicle (HLLV) such as Energia or Saturn V, the spacecraft is parked in Earth parking orbit waiting for ground station to schedule the correct launch time. Once everything is set to go, the spacecraft will commence the first-burn maneuver so as to coast in an intermediate ellipse around Earth. When the spacecraft is costing near to the perigee of the ellipse, the second-burn maneuver is initiated and the spacecraft is brought into the final escape hyperbola heading for Mars. Note that in case of system malfunction or any sort of failure, the spacecraft will not fire the second burn. Instead, it will stay in the ellipse and wait for the corrective actions to be performed. When the spacecraft is approaching Mars, the on board crew and the ground station will perform a final systems check. If all systems are working perfectly, the on board crew will fire the RCS system (a small amount of impulse designed for maneuver purpose only, not to be related as the retro thrust of the spacecraft) so that the spacecraft escapes from the free return trajectory and is set into the Mars capture configuration. On the other hand, if any kind of system failure is detected, the spacecraft will stay in the same trajectory and wait for Mars gravity to deflect it into the free return trajectory heading for Earth.

Crew mission trajectory design

The envisaged trajectory for the MAB crew mission is shown in Figure 3a and Figure 3b. Note that the trajectory shown in solid line is designed for the normal operating scenario, whereas the trajectory shown in dotted line is designed for the failure scenario. The following paragraph will briefly explain the mission sequence employing such a trajectory.

After lifting off from ground station via a heavy-lift launch vehicle (HLLV) such as Energia or Saturn V, the spacecraft is parked in Earth parking orbit waiting for ground station to schedule the correct launch time. Once everything is set to go, the spacecraft will commence the first-burn maneuver so as to coast in an intermediate ellipse around Earth. When the spacecraft is costing near to the perigee of the ellipse, the second-burn maneuver is initiated and the spacecraft is brought into the final escape hyperbola heading for Mars. Note that in case of system malfunction or any sort of failure, the spacecraft will not fire the second burn. Instead, it will stay in the ellipse and wait for the corrective actions to be performed. When the spacecraft is approaching Mars, the on board crew and the ground station will perform a final systems check. If all systems are working perfectly, the on board crew will fire the RCS system (a small amount of impulse designed for maneuver purpose only, not to be related as the retro thrust of the spacecraft) so that the spacecraft escapes from the free return trajectory and is set into the Mars capture configuration. On the other hand, if any kind of system failure is detected, the spacecraft will stay in the same trajectory and wait for Mars gravity to deflect it into the free return trajectory heading for Earth.

It may be noticed that two-burn Earth escape maneuver is employed in the aforementioned trajectory. The purpose of such an escape maneuver is intended for yielding an energy-efficient trajectory. This mode of escape has been intensively studied in [3] and [4]. Furthermore, the study in [4] shows that the two-burn escape mode results in propellant saving compared to the conventional single-burn maneuver, regardless of the number of launch vehicle stages and propulsion system variations. What is more, the propellant saving is progressively increased for higher launch energies. This implies that the envisaged trajectory, which requires high launch energy, will have an approximately 10-20 percent of propellant saving with the incorporation of two-burn Earth escape maneuver (Figure 5). It is worthwhile to mention here that increasing the number of burn maneuvers for more than two-burn yields insignificant increase of propellant saving and hence it is not recommended for the envisaged trajectory (Figure 6) [4].

The second feature of the envisaged trajectory is the incorporation of the free return capability. Free return capability is an important safety element which must be built-in to any kind of crew mission trajectory. Without the incorporation of the free return capability in Apollo mission trajectory, the crew of Apollo 13 would not have been able to safely return to Earth. Keep in mind that the mission to Mars discussed here involves a total trip time of approximately 350-450 days compared to that of 2-3 days for Apollo mission. The increase of total trip time clearly indicates that free return capability is of even more importance for a mission to Mars, since the likelihood of system failures is dramatically increased with total trip time.

Analysis methods

Having specified the envisaged trajectory, analytical methods were carried out in order to validate whether or not such a trajectory could be designed in practice. Since the two-burn Earth escape maneuver does not involve any transfer trajectory, it can generally be performed as required without being constrained by launch date. This implies that the opportunity for the envisaged trajectory is merely a question of whether or not a launch date can be identified such that it yields a reasonably low energy requirement, and at the same time, also allows for Mars swing-by to get back to Earth in the failure scenario. Hence, the search for such an opportunity was separated into two main tasks: 1) Search for launch opportunity for direct heliocentric transfer based on different total trip time, 2) Using the launch opportunities identified in 1) to check if Mars swing-by is possible.

Procedures for searching the direct heliocentric transfer launch opportunities

A Patched conic method was employed. Iteration was carried out in order to stimulate the total change of velocity (D Vtotal) required for the direct heliocentric transfer from 2007 to 2015 (approximately one Earth-Mars ephemeris cycle) based on different inputs of total trip time. Assumptions for the iteration include:

  • Earth and Mars were in the same heliocentric plane during trans-Mars and trans-Earth injections; hence the total change of velocity calculated did not include the change of velocity required for plane change.
  • The parking orbit at both planets was 200 km.
  • The stay time was 180 days.
  • The effect of perturbation forces on the spacecraft was neglected.
  • Aerobraking with biconic aeroshell was employed; hence no retro thrust was required during Mars capture and Earth re-entry.

In each of the iteration, the distance of Earth at departure and the distance of Mars at arrival were calculated using the planetary data and equations obtained from [5]. Knowing the distances upon departure and arrival allows formulation of Lambertís problem. This classical problem was then solved to find the change of velocity (D VTMI) required during trans-Mars injection (TMI). Similar procedures were performed for the trans-Earth injection (TEI) so as to find the change in velocity (D VTEI) required. With both D VTMI and D VTEI calculated, D Vtotal is simply given by:

The data of D Vtotal was collected to plot the variation in D Vtotal with launch date for different total trip times (Figure 7a to Figure 7c). These plots allow the search for Mars swing-by opportunities based on launch date that yields energy-efficient transfer.

Procedures for searching the Mars swing-by opportunities

Once the launch opportunities were identified, the search for Mars swing-by opportunities could be easily done by using the FLYBY program developed by Science Software. The program is available for download at [6]. The FLYBY program is designed for searching the gravity-assist interplanetary trajectories between any three planets of our solar system. The inputs required by the program include: 1) Launch date, 2) Launch, flyby, and arrival planets, 3) Flyby altitude, and 3) Iteration requirements such as the number of search intervals and the error tolerance rate. A typical input file for searching the Mars swing-by opportunities is attached in Appendix 1. The output of the program contains a list of useful information for the optimum trajectory found within the allowable search intervals.

Results and discussion

Despite many energy-efficient launch windows being found for different total trip times, not many of them yield reasonable free return to Earth. The most favorable launch window is in March 2012. The optimum solution found is a launch at March 14, 2012 (JD 2456000.5) with 150 days of TMI transit and 200 days of TEI transit (Figure 4 and Figure 7b). With the employment of Earth and Mars aerobraking systems, together with a 15 percent of propellant saving assumed for the two-burn Earth escape maneuver, this trajectory requires a D Vtotal around 4.6 km/s for the TMI and the TEI in the normal operating scenario. In the failure scenario, the spacecraft will flyby Mars at a perigee altitude of 500 km before starting the 202 days of free return to Earth. The FLYBY program output for this solution is attached in Appendix 2.

 

As shown in Figure 4, the optimum solution found requires the spacecraft to fly at approximately 0.5AU when it is near the perihelion of the free return orbit. This result is certainly undesirable because during close Sun passage, the crew will be exposed to high level of radiation from solar flares. However, it is believed that the solution remains the best one in the range searched and under the requirements specified. Not to mention that the radiation issue can be overcome with proper radiation shielding for the spacecraft. The primary reason for lack of possible solutions is because the trajectory requirements, especially the free return characteristic, require that Earth and Mars aligned at a specific heliocentric position. Based on the Earth-Mars ephemeris cycles stated in [7], the opportunity for such a trajectory only occurs once every 6.405 years.

 

The output in Appendix 2 shows that the inertial velocity of the spacecraft when it is approaching Mars is higher than the velocity of Mars. In a physical sense, this implies that the spacecraft has to catch up Mars, rather than waiting for Mars to capture it as in a conventional interplanetary capture scenario. The implications of this difference in the failure scenario are that the inertial velocity of the spacecraft increases from 29.85 km/s during the outbound leg to 30.6 km/s during the inbound (free return) leg; and therefore the inbound transit, though significantly longer than the outbound transit, requires only 52 extra days. However, in a normal operating scenario, the need for catching up to Mars imposes a light penalty on Mars-entry velocity. This is because in a normal operating scenario, the RCS system of the spacecraft has to be fired up as to speed up the spacecraft while correcting the spacecraft to the right Mars-entry flight path angle. In view of the Mars-approach hyperbolic velocity in Appendix 2, together with the RCS firing requirement (assumed 0.3 km/s max), one can estimate that the Mars-entry velocity of the spacecraft will be around 8.3 km/s. Using the Sutton-Graves equation obtained from [7], the convective aeroheating rate at 100 km during Mars-entry can be estimated as:

Although this aeroheating rate is still in the reasonable range for employing Mars aerobraking system, it is hoped that future analysis could find out ways to reduce it in order to minimize the risk involved in the crew Mars-entry phase.

As mentioned previously, the crew mission requires D Vtotal about 4.6 km/s for the TMI and TEI transits. By adding 0.3 km/s of D V for mid-course correction and 0.2 km/s of D V for plane change, the D Vtotal becomes 5.1 km/s. Clearly, this propulsion requirement is not too much higher than the propulsion requirement for either Venus swing-by or near Hohmann transfer trajectory. Still, this propulsion requirement may be a problem for split expedition employing a direct launch to Mars. This is because based on the MAB weight estimation, the total payload weight for the crew mission is about 30 tons; there are not many existing launch vehicles that can meet such payload and propulsion requirements. Recommended launch vehicles for such a mission are Energia and Saturn V. It is believed that with some small-scale development, both of them will be really for the mission in no time.

Conclusions and recommendations

A direct heliocentric transfer trajectory involving two-burn Earth maneuver and free return characteristic has been studied herein. Analysis results show that this trajectory is available in reality, and the opportunity is once every 6.405 years. Benefits of such a trajectory include: 1) Propellant saving from the two-burn Earth escape maneuver, 2) Fast transit with reasonably low propulsion requirement, and 3) Better salvage capability due to the free return characteristic. The potential issues identified for the trajectory include: 1) Possibly high radiation shielding requirement as a result of close Sun passage in the free return trajectory, 2) Difficulty in finding an existing launch vehicle to meet the mission requirements.

Recommended for further study are: 1) Utilization of POST [8] and SWISTO [9] for better interplanetary trajectory simulation, especially for the atmospheric passage at Mars and the re-entry passage at Earth, 2) Incorporation of the Venus swing-by in the free return trajectory so as to avoid close Sun passage, 3) Incorporation of two-burn maneuver during Mars escape in order to gain further propellant saving for the crew mission.

Acknowledgements

The author would like to extend a special thank to Dr. Chris Blanksby for his guidance in the preparation process of this paper. Without his support this paper would not have been completed in such a short period of time. Thanks are also due to Mr. Lachlan Thompson, who clarified some of my doubts about the results found.

References

[1] Mars Direct Home Page: http://www.nw.net/mars/.

[2] Hoffman, S. J. and Kaplan, D. I., Eds., Human Exploration of Mars: The Reference Mission of the NASA Mars Exploration Team, NASA SP-6107, July 1997.

[3] Johnson, Paul G. and Rom, Frank E.: Perigee Propulsion for Orbital Launch of Nuclear Rockets, NASA TR R-140, 1962.

[4] Willis, Edward A., Jr.: Two-Burn Escape Maneuvers with an Intermediate Coasting Ellipse, NASA TN D-5011, 1969.

[5] Souders, S. W.: Relative Geometries of the Earth, Sun, and Mars from the Year 1973 to the Year 2000, NASA SP-3053, 1970.

[6] SEDS Archives Web site: http://www.seds.org/pub/software/pc/sat/.

[7] Braun, R. D.; Powell R. W.; and Hartung L. C.: Effect of Interplanetary Trajectory Options on a Manned Mars Aerobrake Configuration, NASA TP-3019, 1990.

[8] Bauer, G. L.; Cornick, D. E.; and Stevenson, R.: Capabilities and Applications of the Program To Optimize Simulated Trajectories (POST), NASA CR-2770, 1997.

[9] Mead, Charles W.; and Jones, Max F.: Optimization of "Ephemeridal" Parameters for Minimum Propellant Requirements on Multiplanet Roundtrip Swingby-Stopover Missions, TM 54/30-189, LMSC/HREC A791436 (Contract NAS8-20082), Lockheed Missiles & Space Co., May 1968.

 

FIGURE 1A: Conceptual all-propulsive vehicle configuration [7]

FIGURE 1B: Conceptual aerobraking vehicle configuration [7]

 

(click here for full size image)

FIGURE 2: MAB mission planning flow chart

 

FIGURE 3A: Two-burn Earth escape maneuver

 

FIGURE 3B: The envisaged trajectory

 

 

FIGURE 4: A solution for the envisaged trajectory (normal operating TEI trajectory not shown)

 

FIGURE 5: Effect of launch energy parameter for one- and two-stage vehicles [4]

 

FIGURE 6: Optimization of initial acceleration for single-stage vehicles [4]

 

FIGURE 7a: Effects of launch date on total delta-V (D Vtotal) required (TEI transit: 150 days)

 

FIGURE 7b: Effects of launch date on total delta-V (D Vtotal) required (TEI transit: 200 days)

 

FIGURE 7c: Effects of launch date on total delta-V (D Vtotal) required (TEI transit: 250 days)

 

Appendix 1: typical FLYBY program input file

&INPUTS

IP = 3, 4, 3

LDATE = 3,12, 2012, 0, 0, 0

DDAYS1 = 150.0D0

DDAYS2 = 200.0D0

NPT1 = 2

NPT2 = 2

PALTMIN = 500.0D0

TOL = 1.0D-12

&END