PRELIMINARY ANALYSIS AND DESIGN OF POWERED EARTH MARS CYCLING TRAJECTORIES

Transcription

1 AIAA/AAS Astrodynaics Specialist Conference and Exhibit 5-8 August 2002, Monterey, California AIAA PRELIMINARY ANALYSIS AND DESIGN OF POWERED EARTH MARS CYCLING TRAJECTORIES K. Joseph Chen, * Daon F. Landau, * T. Troy McConaghy, Masataka Okutsu, and Jaes M. Longuski School of Aeronautics and Astronautics, Purdue University West Lafayette, Indiana and Buzz Aldrin Starcraft Enterprises Los Angeles, California We discuss preliinary results on constructing a powered cycler fro sei-cycler trajectories. We present a powered cycler with reasonable transfer ties and low encounter velocities. In addition, we develop a etric for evaluating cycler designs in coparison to other ission-to-mars scenarios. The etric suggests that as vehicle ass (with respect to propellant ass) increases, the ost advantageous syste progresses fro a Design Reference Mission scenario to Sei-s to s, which is highly indicative of how a huan Mars transportation syste ight evolve. a f GM g I sp n V 'V P Subscripts Noenclature = seiajor axis, k = cofort factor, ( transport + cofort ) / transport = gravitational paraeter of planet with ass M, k 3 /s 2 = standard acceleration due to gravity at Earth s surface, /s 2 = specific ipulse, s = ass, t (etric tons) = nuber of rocket stages = hyperbolic excess speed, k/s = instantaneous change in velocity, k/s = ass fraction cv E f loose M p pay peri stage struc surf taxi = Vehicle = Earth = final = loose parking orbit = Mars = propellant = payload = periapsis = stage of a rocket = structure = surface of a planet = rocket used to transport ass fro the surface of a planet to the Vehicle or vice versa. transport = refers to ass that is transported fro one planet to the other 0 = initial as = aeroshell cofort = refers to ass that is used solely for safety or cofort of astronauts * Graduate Student. Graduate Student, Student Meber AIAA, Meber AAS. Professor, Associate Fellow AIAA, Meber AAS. President, Fellow AIAA. S Page 1 of 11 Introduction INCE the late 1960s, nuerous Earth-Mars circulating trajectories have been developed and proposed These concepts can be separated into two categories the cyclers and the sei-cyclers. Both types of trajectories eploy gravity assists to reshape and turn the orbits so that the spacecraft repeatedly encounters Earth and Mars. The ain difference between the two types is that the seicyclers reain in an orbit about Mars for a period of tie before returning to the Earth, while the cyclers perfor only flybys at each planet. Copyright 2002 by the author(s). Published by the, Inc., with perission.

2 One notable cycler trajectory is the Aldrin, proposed in The Aldrin can provide fast transfers to Mars (in which case it is called the Outbound ) or fast transfers back to Earth (in which case it is called the Inbound ). Two cycler vehicles, one on each cycler trajectory, would allow a visit to each planet every Earth-Mars synodic period (about 2.14 years). The transfer tie is typically less than 6 onths. At each flyby, saller vehicles dubbed Taxis rendezvous with the cycler vehicles to transport astronauts and goods to and fro each planet. The ain drawback of the Aldrin is the oderate to high Mars flyby V (ranging fro about 7 k/s to 12 k/s). These high V can ake Taxi rendezvous with the cycler vehicle very costly. The sei-cyclers were developed partly to circuvent this disadvantage of the Aldrin. Since the sei-cycler is placed in an orbit about Mars, the Taxi rendezvous is less costly. However, because of this orbit insertion, there will be a coproise on the transit ties, which are typically longer for sei-cyclers than for cyclers. In addition, there is the extra propellant cost for capture and escape fro the planet. In October of 2001, Aldrin proposed connecting several sei-cycler trajectories into a continuous full cycler. The resulting trajectory cobines the advantages of the cyclers and the sei-cyclers, while lessening the undesired features fro both. In this paper, we suarize soe of our preliinary results and findings on linking the seicyclers. Our analysis is aided by several software tools developed at Purdue University and the Jet Propulsion Laboratory (JPL). In addition, we copare cycler trajectories to other known Earth- Mars ission architectures using our evaluation etric. Methodology To design cycler and sei-cycler trajectories, we first use the Satellite Tour Design Progra (STOUR), 11 a conic trajectory propagator, to interactively construct trajectories. STOUR is a software tool that was originally developed by JPL for the Galileo ission tour design. This progra was later enhanced and extended at Purdue University. After STOUR design, we begin preliinary optiization with JPL s ballistic optiizer, the Mission Design and Analysis Software (MIDAS). 12 MIDAS is a patched-conic interplanetary trajectory optiization progra that is able to iniize the total 'V by varying event ties (i.e. launch, flyby, and arrival dates). MIDAS is also capable of adding and deleting deep space aneuvers. In addition to optiizing ballistic trajectories, we can also design and optiize low-thrust versions of cyclers with our Gravity-Assist Low-Thrust Local Optiization Progra (GALLOP), which axiizes the final spacecraft ass. We ay use GALLOP to optiize trajectories fro STOUR and MIDAS, as well as candidate guesses found by other eans. Another analytical tool we currently use is the Radial Distance Plot. This plot shows the distance of the spacecraft fro the Sun with respect to tie, along with the positions of the Earth and Mars, and Earth-Mars opposition dates. Besides being a sketchpad of new cycler ideas, such plots also help us validate the repeatability of proising candidate cycler trajectories. Sei-s Several sei-cyclers have been proposed, ost notably the ones developed by Bishop et al. 7 and Aldrin et al. 10 The Aldrin et al. proposal includes two versions of sei-cyclers. In the first version (Version I), the Vehicle leaves fro an orbit about Mars, encounters the Earth twice, then returns to an orbit about Mars. The transit ties between the two planets range fro about 6 onths up to about 9 onths, and the entire sequence takes two synodic periods. The second version (Version II) is siilar to the first one, except there are three Earth flybys separating the Mars departure and arrival. The tie of flight between the first two Earth encounters is 1 year, while the tie between the second and third Earth encounters is 6 onths. Version II seicyclers have Mars flyby V that range fro about 2 k/s to 7 k/s, and Earth encounter V that range fro about 3 k/s to about 5 k/s. The entire sequence takes two synodic periods, thus at least two vehicles are needed to provide Earth-Mars and Mars- Earth transfers every synodic period Out of these three candidate sei-cyclers, we choose to patch together Version II sei-cyclers into a full cycler. The other sei-cyclers ay have erit in constructing full cyclers, but these considerations will have to be addressed in a future work. Page 2 of 11

3 Table 1: Trajectory suary of patched sei-cyclers (fro STOUR) Encounter Date (/dd/yyyy) V or V b (k/s) Altitude (k) B-plane Angle (deg) Orbit Period (days) TOF (days) M-1 11/29/ start E-2 7/25/ E-3 7/26/ Man a -1 7/29/ n/a n/a n/a n/a E-4 1/23/ M-5 9/26/ M-6 7/1/ E-7 1/22/ E-8 1/22/ Man a -2 1/25/ n/a n/a n/a n/a E-9 7/27/ M-10 4/5/ c M-11 1/8/ n/a n/a n/a 1374 a V aneuver. b V are in bold. c 200-k altitude constraint not et. Table 2: Trajectory suary of optiized low-thrust cycler a (fro GALLOP) Encounter Date (/dd/yyyy) V (k/s) Altitude (k) TOF (days) E-1 12/08/ M-2 10/26/ M-3 06/06/ b 1320 E-4 01/06/ E-5 01/21/ b 380 E-6 07/24/ M-7 06/11/ b 322 M-8 09/17/ E-9 05/17/ E-10 05/16/ E-11 11/18/ Total V = 2.55 k/s a Initial ass is 75.0 t, final ass is 69.4 t, for Isp of 3000 seconds. b At 200-k altitude constraint. trajectory Orbit of Mars Orbit of Earth Connecting Version II Sei-s Aldrin proposed that we link the Version II sei-cyclers in the following way. First the Vehicle leaves Mars for Earth, encounters the Earth three ties in 18 onths, and then returns to Mars. The transits between Mars and Earth are about 6 onths each. Upon Mars arrival, the vehicle then goes into a 3:2 resonance orbit with Mars (i.e. three vehicle revolutions during two Mars revolutions around the Sun). The tie of flight (TOF) for this resonance orbit is 45 onths, aking the total tie of flight about 76 onths, or 3 synodic periods. After the final Mars arrival at the end of the resonance orbit, the cycle repeats, and the vehicle heads for Earth again. Since the entire sequence takes three synodic periods to coplete, three Fig. 1: Radial distance vs. tie (for 2013 launch). The vertical lines indicate Earth- Mars opposition dates. vehicles are needed to guarantee that there will be a short TOF-transfer leg to each planet at every synodic opportunity. We begin connecting Version II sei-cyclers by first duplicating the published result 10 with our trajectory propagator, STOUR. At the end of the MEEEM sequence, we place the vehicle into a 3:2 resonance orbit with Mars, and then attept to return to Earth to begin the new cycle. In this way we are able to link two Version II sei-cyclers. Table 1 shows the suary of this trajectory. The result shown in Table 1 is not optiized. We use our ballistic optiizer, MIDAS to iniize total 'V. We also allow MIDAS to adjust event ties, as well as adding and deleting aneuvers to Page 3 of 11

4 iprove the trajectory. Due to a software liitation in MIDAS, we cannot odel three consecutive encounters with the sae planet, thus we replace the iddle three Earth flybys with two Earth flybys. However, due to the phasing of this trajectory, the neglected Earth flyby will still be present, and in fact cannot be ignored, as pointed out by Byrnes. 16 We also change the trajectory to reflect an Earth launch instead of a Mars launch. Using MIDAS, we are able to extend this trajectory to three cycles (about 17 years). Table 3 suarizes the optiized trajectory fro MIDAS. The optiized trajectory has a total 'V of k/s. The V at Earth and Mars are relatively low. We believe that siilar trajectories can be constructed for the other two vehicles required in the Version II cycler (to ensure transit opportunities at every synodic period). At this stage of our research, we consider Table 3 to be our best result and we will use it as our baseline case. To odel the ignored Earth flybys and further iprove the result, we use our low-thrust trajectory optiizer, GALLOP to construct the trajectory suarized in Table 2. GALLOP does not have the flyby liitation that MIDAS has, thus we are able to odel all of the Earth flybys. Coparing Tables 2 and 3, we see that even ignoring the Earth flybys in MIDAS, the trajectory suarized in Table 3 is still valid, as the issing Earth flybys can be achieved by backflips which will not significantly perturb the energy of the orbit. (For a discussion of the backflip orbit see Uphoff. 17 ) The 2.55 k/s of total 'V is very good by low-thrust standards, considering that an Earth-Mars-Ceres case with just one flyby and a 3- year TOF has a higher cuulative 'V of 8.69 k/s. 15 Since the I sp is 3000 seconds, the propellant ass expended by the is only 15 t in 13 years. With GALLOP, we are also able to construct siilar trajectories for the other two required vehicles. We next present a etric for evaluating trajectories under consideration for a huan transportation syste to Mars. Propellant Assessent of Baseline Basic Assuptions To assign a cost (etric) to a given, we calculate the required propellant ass. Design and developent costs are not considered as we wish to assess the cost of sustaining a transportation syste over a long period of tie. Certain assuptions and restrictions are ade to keep our estiation general enough to copare different scenarios (, Sei-, DRM-type 18 and others). The assuptions applied to our baseline analysis are as follows: trajectory. Page 4 of 11 1.) The aount of ass being transported between Earth and Mars is 15 t. This will be referred to as the transport ass. We assue the sae transport ass in either direction (i.e. Earth- Mars and Mars-Earth) to exaine an even trade scenario (though we acknowledge that uch ore ass will be transported to Mars during an early colonization phase). 2.) The Vehicle carries three ties the transport ass (45 t) on its interplanetary routes. The added ass is tered cofort ass and accounts for anything that is required for interplanetary travel, but is not actually taken fro one planet to the other (e.g. radiation shielding, structures, furniture etc.). Thus for our baseline, the cofort factor is f = 3. This cofort factor is estiated fro ass values found in Refs. 9 and 19. In our study, a range of cofort factors is considered, since we find the value of f drives the cost etric. 3.) The Vehicle carries only enough propellant to achieve all necessary 'V s until the next Taxi rendezvous. 4.) Propellant fro Mars will be ethane/oxygen. This propellant will be ade fro hydrogen sent fro Earth on a low energy (Hohann) transfer. One kilogra of this hydrogen is cobined with the carbon dioxide in the Martian atosphere to yield 16 kilogras of propellant. This estiate accounts for hydrogen boiloff losses during transfer. 5.) When a Vehicle is captured into a loose orbit about a planet, the periapsis will be 300 k above the planet s surface and the period will be one week. An orbit of this size and shape will stay well within the sphere of influence (SOI) of both Earth and Mars (SOI E 145 R E, SOI M 170 R M ), so ulti-body perturbations are assued to not significantly alter this reference orbit. Thus the parking orbit will be odeled as a two-body proble. The orientation of this loose orbit is not coputed and all 'V values are coputed at periapsis. In practice the orientation will need to be accounted for in ore refined 'V calculations. 6.) Mars Taxis are odeled as three-stage rockets that leave the surface and rendezvous with the Vehicle. One-third of the required 'V is achieved by each stage. 7.) Earth Taxis are odeled as four-stage rockets. The first three stages will each achieve one-third of the 'V necessary to leave Earth s surface and reach a loose orbit as defined in assuption 5. The final upperstage is required to rendezvous with the Vehicle on a hyperbolic

5 8.) The upperstage of each Taxi will ride along with the Vehicle as a eans of transporting ass fro the Vehicle to the planet during an encounter. The booster stages will fall back towards the planet. Thus, there is no accuulation of Taxi aterial fro one planet to the other. 9.) A portion or installent of the Vehicle is launched at each Earth-to-Mars leg. This is to account for aintenance or renovation of the Vehicles over an extended period of tie. We assue that the Vehicle is copletely renewed every five synodic periods. 10.) Vehicles are odeled as single-stage rockets. 11.) The I sp assued for Earth Taxis is 450 seconds (LOX, H 2 ), while the I sp of Mars Taxis is 380 seconds (CH 4, O 2 ). Vehicles will use ethane propellant with an I sp of 380 seconds as well. 12.) The structure factor, Pstruc = struc / ( struc + p ) is 10% for Taxis and Vehicles. 13.) Taxis and Vehicles will aerobrake whenever needed at a planet. Fifteen percent of the payload ass will be used for aeroshells, i.e. Pas = as / transport = 15%. Vehicles on full cyclic trajectories do not decelerate at a planet; therefore, they do not require aeroshells. 14.) Both Earth and Mars are assued to be nonrotating spheres. Thus, no rotational velocity is added to taxi launches. 15.) The gravitational sources are odeled as a point asses. Equations The following fundaental equations allow us to estiate the aount of propellant that is required to sustain a transportation syste between Earth and Mars. We find the change in velocity required by the Taxis to rendezvous with the Vehicle and the change in velocity required by the Vehicles to enter or leave a loose orbit about a planet fro the following: 9 taxi 2 GM r surf E cv ¹ (1) where E cv is the specific energy of the Vehicle at rendezvous and is given by E cv ½V 2 (hyperbola ), E cv GM 2a loose (ellipse) (2) 9 loose 2GM r peri V 2 GM 2 r peri 1 a loose ¹ (3) Velocity losses such as drag, steering, gravity, etc. are neglected. The rocket equation is used to deterine ass fractions for a single stage P stage exp V ngi ' sp ¹ (4) Fro Eq. 4, expressions for the initial ass and propellant ass are derived: 0 0 f ª ««stage 1 struc n º struc» stage (5) (6) The payload ass on a Vehicle includes the transport ass, the aeroshell(s), the cofort ass, and any propellant required for future aneuvers. The Taxi payload is the transport ass plus an aeroshell and propellant to refuel the Vehicle. The propellant cost estiate is the sae if a separate Taxi is used to refuel the Vehicle or if only one Taxi is used per rendezvous. Whenever propellant is a payload, the structure required to contain it (fro Pstruc) is included. Equation 6 deonstrates that the propellant ass is directly proportional to the payload ass. Using this property we ay express the required propellant in ters of transport ass, then siply ultiply this propellant ass fraction by the transport ass to calculate the value in ass units. For exaple, the propellant required by a Vehicle to perfor a aneuver is (7) where Pp-cv is found using Eqs. 4, 5, and 6. Since this propellant reaches the Vehicle via a Taxi, the total Taxi propellant is ª º struc p transport 1 as «1f p cv 1» p taxi «1 struc¹» ¼ 1 (8) We note that Pstruc / (1-Pstruc) = struc / p. Thus the propellant ass required by both Vehicles and Taxis is directly proportional to the transport ass.» ¼ p p 0 11 struc pay p transport f 1 as p cv Page 5 of 11

6 Baseline and Sei- Propellant Estiation Propellant costs for the Version II and the Version II Sei- are calculated using the above assuptions. The results are suarized in Tables 3 and 4, respectively. The Cost per Synodic Period of each estiate incorporates all of the vehicles necessary to coplete a transfer fro Earth to Mars and another transfer fro Mars to Earth every synodic period (e.g. three vehicles for the Version II and two vehicles for the Version II Sei-). The other two vehicles required for the Version II are assued to perfor siilarly to the one presented in Table 3 to give an estiate for the entire syste. The resulting costs of the two systes are rearkably siilar, yet the patched is slightly ore efficient than the Sei-. Launching a payload fro Earth requires ore propellant than launching fro Mars due to the relatively strong gravity field (copare, for exaple, E-1 and M-3 in Table 3). However, the Mars-launch propellant cost is ore than doubled to account for the transportation of hydrogen (fro Earth to Mars) for ethane production (on Mars), and becoes a considerable factor. For exaple, approxiately 230 t of propellant ust be expended at Earth to launch enough hydrogen to create the t of ethane/oxygen required at M-3, thus the M-3 propellant cost is ore than doubled to about 420 t (where the extra ass is accounted for in the total propellant value). In general, the idcourse corrections required by the patched are significantly less than the transport ass with the notable exception of DSM (Deep Space Maneuver) 5, while the Sei- 'V costs are greater than the transport ass. The large trajectory correction (DSM5) sees to balance out the large Sei- Mars encounter costs, resulting in siilar costs per synodic period. Propellant Cost Analysis We see that in the specific case of the Version II Sei- and patched, neither syste provides a significant advantage in propellant cost; however, it is inforative to see how different transportation systes copare in general. We now investigate the role that V, the cofort factor, and the agnitude of trajectory-correction aneuvers have on the relative cost of cycling systes. Moreover, we extend our analysis to other types of transportation systes. In addition to s and Sei-s, we exaine a NASA DRM-type 18 ission (our version is only concerned with whether the cofort ass is launched or placed in a parking orbit, not the specifics of the DRM), a syste that incorporates parking orbits at both Earth and Mars (tered Double Park), and a syste with Mars flybys and a parking orbit at Earth (Reverse Sei-). All of these systes follow the previously entioned set of assuptions (regarding Taxis, loose orbits, etc.) and are distinguished by the role of the transport vehicle at a planetary encounter. Since the DRM type of ission launches a new cofort ass each ission, it does not need to aerobrake at the Earth return encounter. Table 5 provides a suary of each syste. While no actual trajectories will be presented for the Double Park and Reverse Sei- class issions, we expect that the Double Park trajectories will have uch freedo in ters of Earth-Mars phasing because no gravity assists are required (as in NASA s DRM), while Reverse Sei-s will have phasing restrictions siilar to those of full cyclic trajectories since Mars is a poor gravity-assist body. Our analysis provides a preliinary estiate of the propellant advantages and disadvantages of these systes. To exaine the effects of the cofort factor and V, f is varied fro one to five and V is varied fro 3 to 10 k/s. A cofort factor of one has no aenities and ay not lead to a successful ission, while a cofort factor of five ay be considered soewhat extravagant. The lowest energy (Hohann) transfer has a V of below 3 k/s at Earth or Mars and is thus the lower V bound. The transport ass and V at Earth and Mars are assued to be equal. It is also assued that the only transportation syste that will require significant id-course trajectory corrections is the. These corrections are odeled as a single 'V with a agnitude of 300 /s. The cost of a given syste is calculated on a per synodic period basis, where a shipent of ass fro Earth to Mars and a separate shipent fro Mars to Earth will occur each synodic period. This propellant cost is noralized by transport, since the propellant ass is directly proportional to transport ass. The regions where a particular transportation syste is cheaper than the other four are presented in the f-v plane in Fig. 2, where the regions are separated by a solid line. All five transportation systes are evaluated to generate Fig. 2, however only s and Sei- s provide the cheapest ethod of transporting a given ass fro Earth to Mars and vice-versa. Page 6 of 11

7 Moreover, we note that as the cofort ass and V increase, full cyclic systes are always the best perforer. This arises because the cost of accelerating the Vehicle out of Mars gravity well increases as the Vehicle ass (dependent on f) increases and the 'V (dependent on V ) increases. The propellant cost ( p / transport ) at the noinal point (f = 3 and V = 5 k/s) are provided in Table 6. The ain cost driver in these systes is the aount of ass that ust be accelerated. Since the transport ass ust be launched fro the surface of a planet for each syste, the cofort ass leads to the largest variation in cost aong these systes. Full cyclic systes only require the transport ass to be accelerated to reach another planet, while the sei-cycling systes have the additional cost of accelerating the cofort ass at one of the planets. The Double Park syste ust accelerate the cofort ass at both planets, and finally, the DRM class ission ust accelerate the cofort ass fro Earth s surface in addition to the propellant required to accelerate the cofort ass out of a loose Mars orbit. Consequently the relative rank of these systes is directly affected by how uch the cofort ass ust be accelerated out of a gravity well. The data in Tables 3 and 4 correspond to the point in Fig. 2 where f equals three and V is around 4.5 k/s, which is clearly ost efficient for a full. However, in Tables 3 and 4, the and the Sei- have very siilar propellant costs per synodic period (1,154 t vs. 1,177 t, respectively). The reason the of Table 3 is only slightly better than the Sei- in Table 4 (rather than significantly better as predicted by Fig 2.) is that this particular expends a 'V of k/s (which corresponds to k/s per synodic period for the three required Vehicles). In Fig. 2, we assue a trajectorycorrection-aneuver budget of only 300 /s. Incidentally, the Aldrin 5 uses about 0.54 k/s of 'V per synodic period, which is a relatively sall aneuver, but this cycler has high V (i.e. 7 to 12 k/s at Mars). Fro Fig. 2, we know that an Aldrin is ore efficient than an Aldrin Sei- would be (for values of f even slightly greater than one) due to its high V. Since the propellant required to launch soething fro Earth s surface is generally the largest cost, the potential for significant savings exists if less ass is required to leave the surface of Earth. While transport ass launches are required to sustain a transportation syste, not all of the propellant used in Earth s vicinity is required to originate at Earth. For exaple, fuel produced at Mars (ethane/oxygen) ay be transported to Earth orbit via a low energy transfer and used in the upper stages of Vehicles to escape Earth s gravity. This syste would require a separate refueling Taxi to leave Mars with enough tie to reach Earth before a transport ass launch so that there will be propellant to leave Earth s vicinity. The propellant properties of this syste are presented in Fig. 3 and Table 7. Fro Table 7 we note that all of the systes have a discernable decrease in cost, but the Reverse Sei-, Double Park and DRM-type systes gain ore savings than s and Sei-s fro using Mars propellant. This savings is the result of launching the propellant required to leave a loose Earth orbit fro Mars instead of Earth, thereby bypassing the stronger gravity field. In this case, sei-cycling systes (including the Reverse Sei-) becoe the ost econoical ethod as the Vehicle ass decreases. However for cofort factors above 2, full cyclic systes are consistently the best alternative. While priarily using Mars-based propellant can result in significant savings, it is not guaranteed that we will be able to produce propellant on Mars. In this case, all of the propellant will need to coe fro Earth. To be as efficient as possible only propellant required at Mars surface will be launched there (i.e. propellant used by a Vehicle will be carried fro Earth) and an H 2 /LOX ix will be used (where 15% of the propellant is assued to boil off before it is used). The results are presented in Fig. 4 and Table 8. As expected, the propellant cost of this scenario is significantly greater than the other cases as uch ore propellant ust be launched fro Earth s surface and transported to Mars. The cost of launching transport ass fro the surface of Mars becoes ore significant, causing the cost savings of sending ass to a Martian parking orbit versus sending ass to a hyperbolic trajectory to be agnified. The result is a larger Sei- region in Fig. 4. However, as the cofort ass or V increases, the cost of accelerating the Vehicle out of a parking orbit becoes so large that the syste again becoes the ost efficient transportation syste. Nuclear propulsion is eerging as a viable, extreely efficient alternative. The specific ipulse that nuclear engines could achieve is in the upper hundreds of seconds (we use 900 s). However, all of the nuclear propellant ust coe fro Earth. We exaine the effects of using nuclear propulsion for the Vehicles; the results are given in Fig. 5 and Table 9. Page 7 of 11

8 Table 3: Baseline propellant cost a (fro MIDAS) Encounter Date (/dd/yyyy) V or V (k/s) Prop. Mass (t b ) TOF (Days) Altitude (k) E-1 1/23/ M-2 9/26/ aerobrake DSM 1 7/9/ M-3 7/1/ DSM 2 11/8/ E-4 1/22/ aerobrake DSM 3 5/7/ E-5 7/27/ , E-5 DV 7/27/ DSM 4 11/22/ M-6 4/18/ aerobrake M-6 DV 4/18/ DSM 5 3/7/ DSM 6 1/30/ M-7 10/20/ DSM 7 3/4/ E-8 6/22/ aerobrake DSM 8 8/25/ E-9 12/20/ M-10 8/8/ aerobrake M-11 5/13/ DSM 9 8/19/ E-12 11/23/ aerobrake 194 Total V =4.889 k/s Total Propellant = 3,460 t c Cost per Synodic Period = 1,154 t a Close passes of the Earth are expected between E-4 and E-5, and E-8 and E-9, but are not odeled here. b Metric tons (t). c Cost includes t of fuel to send hydrogen to Mars. Table 4: Version II Sei- propellant cost Vehicle 1 Encounter Date V V (k/s) S/C Propellant (t a ) Taxi Prop. (t) TOF (days) M1 2/21/ E2 9/24/ aerobrake 235 E3 9/25/ b 1 year E4 3/26/ ½ year M5 10/12/ aerobrake aerobrake 203 Vehicle 2 S/C Propellant Encounter Date V V (k/s) (t) Taxi Prop. (t) TOF (days) M1 4/25/ E2 11/26/ aerobrake 190 E3 11/26/ b 1 year E4 5/27/ ½ year M5 12/16/ aerobrake aerobrake 217 Total Cost = 2,353 t c Cost per Synodic Period = 1,177 t a Metric tons (t). No Taxi rendezvous occurs on this flyby. c Accounts for t of fuel to send hydrogen to Mars. Table 5: Suary of Earth Mars transportation systes Syste Earth Encounter Mars Encounter Flyby Flyby Sei- Flyby Parking Orbit Reverse Sei- Parking Orbit Flyby Double Park Parking Orbit Parking Orbit DRM Type Launch/Aerobrake Parking Orbit Page 8 of 11

9 Fig. 2: Optial transportation syste regions. Table 6: Noralized a Propellant cost of noinal systes Syste Sei- Reverse Sei- Double Park DRM Type Cost a Propellant cost noralized by transport ass. Fig. 3: Optial systes with Martian propellant transported to Earth. Table 7: Noralized propellant cost for Martian propellant syste (f = 3, V = 5 k/s) Syste Sei- Reverse Sei- Double Park DRM Type Cost Fig. 4: Optial systes using Earth propellant only. Table 8: Noralized propellant cost for Earth propellant syste (f = 3, V = 5 k/s) Syste Sei- Reverse Sei- Double Park DRM Type Cost Fig. 5: Optial transportation systes using nuclear propulsion. Table 9: Noralized propellant cost with nuclear propulsion (f = 3, V = 5 k/s) Syste Sei- Reverse Sei- Double Park DRM Type Cost Page 9 of 11

10 Table 10: Noralized propellant cost for nonaerobraking systes (f = 3, V = 5 k/s) Syste Sei- Reverse Sei- Double Park DRM Type Cost The ain benefit of nuclear propulsion is a significant drop in cost to accelerate a large aount of ass fro a loose orbit around Earth. The savings is saller at Mars because the propellant ust be shipped there. Because the propellant is different than the previous scenarios the structure factor Pstruc ay change (but in this study we keep it at 10%), and the cofort factor (f) should be increased soewhat to account for the added ass of a nuclear engine. Because nuclear engines are assued to be ore assive than purely cheical engine, they are not used for the or Sei- Taxi upper stages at Earth. (The idea of a Taxi is to bring the transport ass to an interplanetary vehicle using the sallest payload possible.) If nuclear engines are used on these upper stages then systes will be the cheapest alternative for a larger range of cofort factors as V increases (i.e. the top curve in Fig. 5 would continue to slope down instead of turning up towards the right side of the figure). We again see the trend of systes incorporating parking orbits becoing ore efficient as cofort ass decreases leading to lighter Vehicles. Next we exaine the effects if aerobraking is deeed an infeasible way of decelerating the Vehicles. The transport ass is still assued to aerobrake as a way of landing the transport ass on a planet s surface, however. Refueling of the Vehicles will occur evenly as specified in assuption 3. The noinal point values are presented in Table 10. Due to the added cost of decelerating vehicles using cheical propulsion, a full cyclic syste will be the optial choice for any cofort factor and V above 3 k/s. The syste clearly has the lowest cost as the other systes increase draatically in cost to decelerate the cofort ass. The propellant costs of this scenario depend not only on the nuber of aneuvers involving the cofort ass, but also the aount of propellant that is essentially added cargo during a aneuver. For exaple, the propellant required by a Sei- to enter a Mars loose orbit ust be accelerated fro Earth s vicinity while the only thing to leave Earth using a Reverse Sei- is the transport ass. This causes a significant discrepancy due to Earth s relatively large gravitational field. The propellant savings of Page 10 of 11 aerobraking is seen to outweigh the coplexity of decelerating a assive object using an aeroshell. Suary of Transportation Syste Trades and Conclusions A general rule for any transportation schee is to accelerate the sallest aount of ass possible. Consequently, full cyclic systes consistently provide the cheapest ethod of sustaining a transportation syste between Earth and Mars because the least aount of ass ust work against a gravitational field. More specifically, the cofort ass (regardless of its chosen value) is never accelerated out of a planet s gravity well, which tends to provide s with a significant advantage. However, s are not always the best alternative. Systes incorporating parking orbits becoe ore efficient as the added cofort ass and/or approach velocity at planetary encounters decrease, i.e. as less ass is accelerated. Moreover as the idcourse corrections to sustain a full cyclic trajectory increase, Cycling systes becoe a less attractive alternative. The relative effect of this added cost is dependent on the scenario, but a cycling syste will still require the least propellant for large cofort factors or large V. There are several factors besides propellant cost to consider when exaining the best ethod of transporting ass between Earth and Mars. For exaple, s often provide the cheapest alternative, but are also the ost coplicated in ters of rendezvous (hyperbolic encounters) and require the ost precision in encounter dates. Other, ore expensive, alternatives such as the Double Park or DRM scenarios achieve all ass transfers near a planet in a parking orbit, and if a transport launch is not possible on a given day, then these systes will not be affected by delays as severely as a would. Moreover, odification of the tie of flight (TOF) for s often requires a significant change in the trajectory requireents ('V, V, etc.), whereas a balance between TOF and V is ore easily attained for other, less restrictive, systes. Finally, all of the previously discussed transfer costs are to sustain a previously established transportation syste. The design and developent costs are not considered, but are iportant to initiate a huan presence on Mars. Our systes are better iagined as part of the evolution of huankind s first efforts to sustain a presence on Mars. For exaple, a DRM type ission ay be the best alternative for the first few issions to Mars, but the propellant costs can be significantly reduced if the cofort ass is put into orbit around Earth after the

11 return trip, i.e. if it evolves into a Double Park syste. Fro there, sei-cyclic and full cyclic trajectories are established by adding planetary flybys and less propellant ust be produced. The result suggests a safe, cofortable, and cost effective ethod for the routine exploration and developent of Mars. Acknowledgeents This work has been sponsored in part by the Jet Propulsion Laboratory, California Institute of Technology under Contract Nuber (G. T. Rosalia, Contract Manager and Dennis V. Byrnes, Technical Manager). We are grateful to Neville I. Marzwell for his support. References 1. Hollister, W. M, Castles in Space, Astronautica Acta, Vol. 14, 1969, pp Rall, C. S. and Hollister, W. M, Free-Fall Periodic Orbits Connecting Earth and Mars, AIAA Paper No 71-92, AIAA 9 th Aerospace Sciences Meeting, New York, NY, Jan , Friedlander, A. L., Niehoff, J. C., Byrnes, D. V., and Longuski, J. M., Circulating Transportation Orbits Between Earth and Mars, AIAA Paper , AIAA/AAS Astrodynaics Conference, Williasburg, VA, Aug , Aldrin, B., Cyclic Trajectory Concepts, SAIC presentation to the Interplanetary Rapid Transit Study Meeting, Jet Propulsion Laboratory, Oct. 28, Byrnes, D. V., Longuski, J. M., and Aldrin, B., Orbit Between Earth and Mars, Journal of Spacecraft and Rockets, Vol. 30, No. 3, May-June 1993, pp Hoffan, S. J., Friedlander, A. L., and Nock, K. T., Transportation Node Perforance Coparison for a Sustained Manned Mars Base, AIAA Paper , AIAA/AAS Astrodynaics Conference, Williasburg, VA, Aug , Bishop, R. H., Byrnes, D. V., Newan, D. J., Carr, C. E., and Aldrin, B., Earth-Mars Transportation Opportunities: Proising Options for Interplanetary Transportation, AAS Paper , The Richard H. Battin Astrodynaics Conference, College Station, TX, Mar , Nock, K. T, Cyclical Visits to Mars via Astronaut Hotels, Phase I Final Report, NASA Institute for Advanced Concepts, Universities Space Research Association Research Grant , Nov. 30, Nock, K. T., and Friedlander, A. L., Eleents of a Mars Transportation Syste, Acta Astronautica, Vol. 15, No. 6/7, pp , Aldrin, B., Byrnes, D., Jones, R., and Davis, H., Evolutionary Space Transportation Plan for Mars Cycling Concepts, AIAA Paper , Albuquerque, NM, Aug Rinderle, E. A., Galileo User s Guide, Mission Design Systes, Satellite Tour Analysis and Design Subsyste, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, JPL D-263, July Sauer, Jr., C. G., MIDAS: Mission Design and Analysis Software for the Optiization of Ballistic Interplanetary Trajectories, The Journal of the Astronautical Sciences, Vol. 37, No. 3, July-Sept. 1989, pp Petropoulos, A. E., A Shape-Based Approach to Autoated, Low-Thrust, Gravity-Assist Trajectory Design, Ph.D. Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette, May Sis, J. A. and Flanagan, S. N, Preliinary Design of Low-Thrust Interplanetary Missions, AAS Paper , AAS/AIAA Astrodynaics Specialist Conference, Girdwood, AK, Aug , McConaghy, T. T., Debban, T. J., Petropoulos, A. E., and Longuski, J. M., An Approach to Design and Optiization of Low-Thrust Trajectories with Gravity Assists, AAS Paper , AAS/AIAA Astrodynaics Specialists Conference, Quebec City, QC, Canada, July 30- Aug. 2, Byrnes, D., personal counication, Oct.-Nov Uphoff, C., The Art and Science of Lunar Gravity Assist, AAS Paper , AAS/GSFC International Syposiu, Greenbelt, MD, Apr Hoffan, S. J. and Kaplan, D. I., eds., Huan Exploration of Mars: The Reference Mission of the NASA Mars Exploration Study Tea, NASA SP 6107, Aldrin, B., Byrnes, D., Jones, R., and Davis, H., Thangavelu, M., Evolutionary Space Transportation Plan for Mars Cycling Concepts, ShareSpace Foundation Final Report, NASA/JPL Contract No , Oct Page 11 of 11