About feasibility of SpaceX’s human exploration Mars mission scenario with Starship | Scientific Reports – Nature.com

Baseline mission scenario

The baseline scenario for the mission as intended by SpaceX is given in Fig.1, which is based on7. For our purpose we assume two uncrewed missions carrying equipment, e.g. for power generation and ISRU, will launch from Earth in 2027 and two uncrewed and two crewed Starships will travel to Mars in 202932,33, similar to the initial concept7, but with a postponed time frame. Starship will launch (1) from Earth and stay in LEO (2), while the main stage returns to Earth (3) and is reused for launching a cargo version of Starship, which subsequently refuels (5) the crewed vessel. This is repeated until sufficient propellant is on board. Starship transfers to Mars (6), where it uses aerobraking in Mars atmosphere (7) to reduce its velocity for landing (8). During the stay, ISRU technology produces propellant (9) until Starship launches again (10) into a Mars orbit (11). A transfer orbit injection burn sends Starship on its way to Earth (12), where again aerobraking is used (13) to accomplish landing (14).

The current baseline scenario for a Mars mission using SpaceX Starship. 1 Starship launches from Earth. 2 It reaches LEO, waiting for refueling. 3 the main stage returns to Earth to be equipped with a cargo version of Starship. 4 the cargo Starship launches into LEO. 5 the main stage returns to Earth, while the crewed Starship is refueled. This is repeated until the propellant is sufficient for a Mars mission. 6 Transfer to Mars. 7 Aerobraking in Mars atmosphere and 8 Landing. 9 During stay on Mars, ISRU is used for propellant generation. 10 launch from Mars 11 into a circular orbit and subsequent 12return to Earth. 13 Aerobraking is used for 14 landing on Earth. [Source: Mars and Earth images: NASA, public domain, overall image: own, with information based on7].

SpaceX does not provide information about e.g. orbit altitudes; therefore, we assume a 500km (altitude) circular orbit for (2). This way, there is sufficient time for refueling, even in case of some launch failure for the subsequent launches, without risking decay of orbit into a realm where Starship can no longer stay on orbit. Also, this is above the ISS, i.e. the risk of collision is reduced. Overall, this orbit altitude has almost no effect on e.g. v and therefore can be set arbitrarily. The altitude at Mars at arrival is not fixed, but determined by the maximum possible velocity at closest approach, which is 7.5km/s according to SpaceX7. For the return flight, an initial orbit altitude at Mars (11) is assumed to be 200km. The approach at Earth (13) occurs at 12.5km/s maximum [12, p. 38], but may not go below 500km orbit altitude to avoid collision with ISS. As a baseline, the crewed version is assumed to carry 12 persons, but it will also be reviewed for the effect of carrying 100 persons [8, p. 5].

For further calculations regarding the mass budget, the following nominal mission values are assumed, based on this given mission scenario. These assumptions are are: ToF of 180 d for flight to Mars and back to Earth, as well as 500 d of surface time. Actual times might differ in the trajectory analysis, but these are assumed as baseline. The ascent to Earth orbit is not regarded as refueling means that the actual mission from a budget point of view starts in LEO.

In the following, the mass budget of Starship as derived within this work is explained. It is based on existing information where available and extrapolated for the remaining values. The goal is to determine a plausible mass budget for the Starship system and subsequently compare it to the proposed values by SpaceX, resp. determine its fit for the mission scenario given by SpaceX.

Starship can carry a payload mass of 100 MT into LEO34. A detailed mass budget for Starship itself has not been published by SpaceX. Based on public statements, SpaceX targets at a system dry mass of 100 MT, which includes all subsystems11. Assuming a 20% system margin according to ESA standards13, this means there are 83.333 MT of mass available for actual subsystems. Of these 4.167 MT are harness, when setting that mass as 5% of the system dry mass without margin, following the same standard13. While other numbers have been published in the past, SpaceX gives the propellant mass as 1200 MT on its website31. Being the most recent number, this is taken as baseline. Of these, 2% are assumed to be residuals, i.e. not available for actual maneuvers, as stated by ESA standard13. Therefore, 1176.47 MT of propellant are available for orbit maneuvers. A summary of these values is given in Table 5 for reference.

In the following an estimate for the subsystems is set up, based on information given by SpaceX where possible or extrapolated from other information, mostly about Orion (see following paragraphs for details), and calculations where necessary. Subsequently, a mass budget is determined and compared to the budget in Table 5.

To minimize the radiation and risk exposure of the crew on a long duration mission to Mars, different protection measures have to be included in the spacecraft. Materials protective against cosmic and solar radiation are e.g. water, polyethylene and aluminium, whereby elements with hydrogen, such as the first two, have a particularly protective effect for both types of radiation35. The importance of crew sleeping compartments and control centre leads to the assumption of a polyethylene cover. Furthermore, it is assumed that water pipes (e.g. for water supply and waste water transport) cover as much habitable volume as possible. To minimize the necessary mass, on-board equipment and cargo, e.g. food, are used for radiation protection as well. In the event of a solar flare, similarly to Orion36, cargo and food can be used for shelter. Further it was mentioned by SpaceX too that a central solar storm shelter17 would be provided for the crew. Details were not given.

The habitable volume of the Orion capsule is 9 m3 and the total pressurized volume is 20 m337. For Starships first missions with a crew of twelve, 16% reduction for elements not scaling linearly (e.g. 4 people need one toilet, 12 need not 3 toilets) are assumed, i.e. ten times the volume of Orion for larger cabins and rooms are assumed. Thus, for the model approximately 90 m3 habitable and 200m3 total pressurized volume are assumed. The pressurized volume of ISS is 1005m3 for comparison38. With a usable diameter of the payload section of 8m [8, p. 2] and thus a base area of about 50 m2, the pressurised area is 4m high, which corresponds to about two habitable floors. The surface area of this cylinder is consequently calculated to:

$${S}_{pressurized ,volume}=2cdot pi cdot rcdot h+1cdot pi cdot {r}^{2}=left(100+1cdot 50right) {{text{m}}}^{2}=150 {{text{m}}}^{2}$$

(11)

It is assumed that the area specific mass of the polyethylene layer is 20g/cm2 (200kg/m2) with a thickness of 0.217m [39, p. 28]. The mass of this shielding is therefore 30 MT. Note only one top side is assumed to be needed to be covered, as the lower side is covered by spacecraft systems and thus is already shielded.

Woolford & Bond report on the habitable volume necessary for human spaceflight missions, which is a function of mission duration, but reaches a plateau at about six to seven months40. They provide a so-called performance limit, which is needed if the crew is supposed to conduct tasks and activities, which go beyond survival and also an optimal range. For mission durations of 3months, the optimum is about 15.5 m3, the performance limit is about 7 m340. For six months, the values are 20m3 resp. 11.3 m340. For 12 crew members, this means, the minimum volume for a 90-day mission is 84 m3, the optimal is 186m3. For 180-day missions, which is a realistic flight time at least for some missions, see Section "Trajectory analysis", the values are 135.6m3 resp. 240m3. The assumed 90 m3 of this paper thus on the lower range and from a mass budget point of view on the optimistic side. In turn, SpaceX reported previously that they expect a pressurized volume of 825 m3 for 40 cabins17. A crew size was not given, but with 40 cabins would exceed the here assumed 12 person crew, i.e. the 825 m3 are not regarded.

For micro-meteoroid protection, Starship, similar to the Columbus module of the ISS, is assumed to have a protective layer reinforced with Kevlar and Nextel, a so-called Stuffed Whipple Shield (SWS), which bursts incoming objects with three layers of protective material and thus prevents them from penetrating41.

The three layers consist of two bumper shields (BS) and the back wall (BW). Since Starship, unlike the Columbus module, will only be in space and on Mars for approximately 2.5years, the values are oriented to those of the module but have been reduced. For example, the outer layer of the SWS should consist of a 2mm thick Al 6061-T6 aluminium layer with an areal density of 0.6g/cm2 and the intermediate stuffing of two layers of Nextel 312 AF-62 with 0.2g/cm2 as well as eight layers of Kevlar 129 Style 812 with 0.4g/cm241. On the outer walls of the crewed Sect.(100 m2, see Eq.(7), the back wall should not consist of an aluminium layer, but instead of the polyethylene layer of the radiation shielding. In this way, mass can be saved. This results in 1.2g/cm2 (12kg/m2) and therefore 1.2 MT for the SWS around the crewed section of Starship. For the remaining part of Starship, 3mm thick Al 2219-T851 aluminium with 0.8g/cm2 is to be used as the back wall41. For simplification, a height of 40m is assumed without protection of the engine area, which results in an outer skin of 1005 m2 with the same base area of 50 m2 according to Eq.(7). With an areal density for this protection of 2g/cm2 (20kg/m2), it results in a mass of 20.1 MT, adding 10% margin, this leads to 22.1 MT. Figure2 shows the described structure of the SWS for Starship. The dimensions refer to the aluminium and not the polyethylene layer with a thickness of 0.217m of the crewed section, as this is considerably thicker. However, the distances between the individual layers should be identical.

Stuffed Whipple Shield for Starship with two bumper shields (BS) and one back wall (BW), after41.

Furthermore, Starship must be designed and built in such a way that its structure can carry the payload of up to 100 MT with empty tanks, because they will be almost empty by the time it arrives on Mars. To estimate the mass of the remaining structure, the simplification is made that Starship is a 50m high cylinder with a diameter of 9m and thus, similarly to Eq.(10c), a surface area of 1541 m2. Since this shape is larger than the one of Starship, additional structural elements within the fuselage are compensated for. As with the current prototypes, 3mm thick 304L stainless steel is used for Starships outer skin42, which has a density of 8000kg/m343. For the calculation of the outer skin, the areal density is needed, which is the density multiplied by the thickness of the material and thus amounts to 24kg/m2 for the stainless steel used. This results in a mass of 37 MT. With a 10% margin, e.g. for internal structure elements, the structural mass is estimated at 40.7 MT.

For the thermal protection Pica-X is used44. It has a density of 0.27g/cm3 and typically has a thickness of 6cm in a heat shield44. Assuming a cylinder of 9m diameter and 48m height17, as Starships size (not regarding the conic nature of its upper part, due to lack of measurement data for that), this yields a surface area of 1357.2 m2. Covering that with 6cm of PICA-X heat shield would mean a volume of 81.43 million cm3. With the given density, this would result in a mass for the thermal protection of 22 MT. Assuming not every part needs to be covered with the full 6cm, but on average 3cm, would result in 11MT for the heat shield.

The life-support system, accommodation and thermal control is not provided for Starship by official sources. For Orion, a mass of 1.2 MT is given as mass for these subsystems18. It is assumed that these scale with the crew size, e.g. as the amount of CO2 produced by the crew is one driver for the ECLSS and that scales with the crew size. Thus, for this calculation this leads to a mass of 3.6 MT (12-person crew, instead of 4-person crew). This is a rough estimate as certain mission parameters are different, e.g. mission duration. Since the value given in18 is an estimate as well, no further margin is added here. The Orion ECLSS is also the basis for the ECLSS system of the Lunar Gateways Habitation and Logistics Outpost (HALO) module45. Mera et al.45 state that the operation of the ECLSS for longer mission durations than 30days concern e.g. the exercise mode and removal of trace contaminants, but indicate that no substantial system change is needed for that. Indications for scaling the system to larger crews and volume are not provided in the paper, so that we remain with the conservative estimate given above.

For thermal insulation, Multi-Layer Insulation (MLI foil) is assumed, which provides additional low radiation shielding. The MLI foil encloses the entire Starship except for the engine bay and the entire crew area. The 40m high cylinder with a surface area of 1005 m2 already mentioned is therefore used as an assumption for the volume to be enclosed, to which the floor and ceiling of the crewed area with 50 m2 each are added. The surface area to be covered is thus 1105 m2. Good insulation is to be provided by 40 layers of MLI with a surface density of 0.2g/cm2 (2kg/m2)41. The mass of the required MLI is thus 2.21MT.

For additional protection against strong solar storms, special vests are to be available on-board Starship, which should be worn when a solar flare occurs. One such vest is the AstroRad vest, which will be tested on the Artemis missions. The mass of a vest depends on the size of the person wearing it. On average, it weighs 27kg46, which corresponds to a mass of 324kg for a crew of twelve. Furthermore, the ECLSS is to be expanded to include a radiation warning system that will warn the crew when solar storms occur and they have to seek shelter. The HERA (Hybrid Electronic Radiation Assessor) radiation warning system, which is used on board the Orion capsule, will be used for this purpose36.

For communication and avionics, a similar system as for Orion is assumed, lacking further references and information. The mission profile is similar, although not identical, therefore, the system is not scaled up. For instance, an increased crew size would not necessarily lead to an increase in communication data to be sent or commands to be handled by the system. Therefore, the value for Orion is selected, i.e. 0.6 MT18. Again, as this is already an estimated value, no further margin is added.

It has to be noted that the currently intended mission profiles for Orion (lunar environment) and this analysed Mars mission, differs in solar distance, which affects the link budget of the communication system. Considering Mars distance of about 1.5AU and that of Earth of about 1 AU, this means maximum distance would be about 2.5 AU, i.e. resulting in a signal strength of about 1/6 (~1/d2). This change can be compensated by directiveness of antenna, antenna size, increase in transmitter power or accepting a reduced amount of transmitted data. Especially during transfer, where no significant scientific activities are to be assumed, this change in the link budget does not warrant a larger system. In a Mars environment, communication satellites could also be used as relays for Earth communication, allowing a similar system without further losses. More detailed information about Orions communication system is not available, but NASA press releases explain that the current Orion communication system is intended for use beyond the lunar environment47.

Solar arrays, which are stowed in the engine area during launch and landing and are deployed during the flight, are responsible for the power generation during the flight. Therefore, they must not only be deployable but also retractable. Similar to the Orion capsule, the solar arrays are supposed to have a mechanism that allows them to constantly align themselves with the sun so that they can deliver full power.

Orions four 7m long and 2m wide solar arrays, each consisting of three foldable panels, provide 11.2kW of power for a crew of four people48. Therefore, Starships solar arrays should have about ten times the power, 100kW. In addition, the radiation intensity decreases by about half during the flight to Mars. In order for the solar arrays to deliver the required power near Mars, they need to deliver at least twice as much power near Earth. With some margin for failing solar cells, for example, an output of around 250kW is required near the Earth. One solar panel that should be able to deliver this amount of power is the MegaFlex from Northrop Grumman, which is foldable and unfolds into a round panel by rotating 360. The MegaFlex is a scalable system that is currently still being tested, but its smaller versionthe UltraFlexis already being used on, for example, the Cygnus spacecraft and the InSight lander on Mars49. So, the technology is already proven and has a flight heritage. A system consisting of two MegaFlex arrays, each with a diameter of around 24m, should be able to deliver this power49,50. Together, the two arrays have a mass of about 2 MT49. To this a 5% margin is added, as the system is already developed.

As with Orion, lithium-ion batteries are to be used to store surplus energy. They have a high energy density and can power Starship in the absence of sunlight and as a back-up51. SpaceX could use batteries from Tesla here. It is assumed that the batteries have to provide power over a time span of 6h in case of a power loss which results with a power of 100kW in a required battery size of 600 kWh. The 6h are assumed as no public figure provides information about duration of assumed emergencies. For redundancy there should be second a battery pack with the same size. With the use of the 100-kWh battery from Tesla, which has a mass of 625kg52, and a factor of 1.2 for aging and recharging this results in a mass of 9 MT for the batteries in total. Here as well, a 5% margin is assumed.

The assumed total mass of the EPS, including the solar arrays and a margin of 10% for additional components (e.g. cables), is approximately 12 MT.

The propulsion system is based on 6 Raptor engines, each with a mass of 2 MT10. It is also using a cryogenic propellant tank, which has to house 1200 MT of propellant31. Super Heavy, i.e. the main stage for Starships ascent from Earth, has a tank for 3600MT of propellant with a mass of 80 MT10. As there are no further details on the tank system, it must be assumed that the masses given already include the systems for cryogenic propellant storage. Assuming SpaceX will use the same technology for the tank in Starship, the following estimate is made.

The tank mass ({m}_{T}) can be expressed as:

$${m}_{T}={S}_{T}cdot {d}_{T}cdot {rho }_{T}$$

(12)

where ({S}_{T}) is the tanks surface, ({d}_{T}) the tanks wall thickness and ({rho }_{T}) the material density. It is assumed that the material and thus density of both tanks (Super Heavy and Starship) are identical. Furthermore, it is assumed that the inside pressure and loads (e.g. during launch) to be withheld are similar as well, i.e. the wall thickness is also assumed to be identical for both tank types. Therefore, for our calculations is true, that:

$${m}_{T} sim {S}_{T}$$

(13)

Assuming a spherical tank and using formulas for sphere volume ((=4/3 cdot pi cdot {r}^{3})) and surface ((=4 cdot pi cdot {r}^{2})), one can write for the relations between the two:

$$frac{S}{V}=frac{3}{r}$$

(14)

$$S=frac{3}{r}cdot V$$

(15)

$$V=frac{Scdot r}{3}$$

(16)

Considering the propellant mass of 1/3 in comparison to Super Heavy, the Volume of the tanks is regarded as:

$${V}_{S}=frac{1}{3}cdot {V}_{SH}$$

(17)

where the index S denominates Starship and SH Super Heavy. From this relation one can derive that:

$$r_{S}^{3} = frac{1}{3} cdot r_{SH}^{3} Rightarrow r_{S} = sqrt[3]{1/3} cdot r_{SH}$$

(18)

Using Eqs.(14) and (15), this leads to:

$$S_{S} = frac{1}{{sqrt[3]{1/3} cdot r_{SH} }} V_{1} = frac{{S_{1} }}{{3 sqrt[3]{1/3}}} = 0.231 cdot S_{1}$$

(19)

With Eq.(12) follows:

$${m}_{T,S}=0.231cdot {m}_{T,SH}=18.49 {text{MT}}$$

(20)

Using the ESA margin for to be modified components, i.e. 10%13, this leads to a tank mass for Starship of 20.3MT. The Helium tanks for the cold gas reaction thrusters10 are assumed as 5 MT, this is an estimate as a suitable reference is not available. For the reaction control system (RCS) it is assumed, that 50 RCS thrusters are used for Starship, since the smaller Space Shuttle had 4453. There should be two pairs of five thrusters in the front and rear on each side of the flaps, five thrusters in the front in flight direction and five thrusters in the rear against flight direction (aligned like the main thrusters). As a rough estimate for the mass of a thruster, the 220 N RCS thruster of the Orion capsule is used, which has a mass of approximately 2kg54. This results in a mass of approximately 100kg for Starships RCS thrusters. With the 10% margin this results in 5.5 MT for the helium tanks and 0.11 MT for the thrusters respectively. As the raptor engines are mostly developed, only a 5% margin is assumed13. This subsystem also requires piping, which is included in the numbers for harness (see Table 5).

To support a crew of 12 astronauts on their long duration trip to mars, different crew and consumable elements need to be considered. The final crew and payload mass depend highly on the number of astronauts and the time of flight. Therefore, an overview of required masses per astronaut and per astronaut-day is established and shown in Table 6.

As no detailed information on crew and consumable masses are provided by SpaceX, the mass values for the listed elements are selected based on literature research18,55,56,57. The compared values often contain a large scale of deviations depending on the given assumptions. The selected values in Table 6 are assumed to be suitable to establish a first mass model of the described mars mission scenario but may be subject to change. The improvement of life support technologies towards a closed loop system is an important step in realizing long term interplanetary missions. As SpaceX has not yet published any detailed information about the type and quality of recovery systems, that will be used on their mission to mars, a best-case rate of 100% recovery for gases, fluids and solids is assumed to establish a reference mass.

The total consumable mass per person per day mconsumables can be calculated using the given recovery factor krec from Table 6 in formula (21).

$${m}_{consumables}={(1-k}_{rec, oxygen})*{m}_{oxygen}+{(1-k}_{rec,food})*{m}_{food}+(1-{k}_{rec,pot,water})*{m}_{pot.water}+{(1-k}_{rec hyg.water})*{m}_{hyg,water}+{(1-k}_{rec,hyg.items})*{m}_{hyg.items}+(1-{k}_{rec,clothing})*{m}_{clothing}$$

(21)

A recovery rate of 100% means, that in theory the systems are able to use an initial payload mass required for 12 astronauts for one day and completely recover it. Therefore, the system is by calculation able to supply the crew without any additional storage or resupply for the entire mission duration. The consumable mass mconsumables per person per day turns to zero.

The calculation of the crew and consumable mass on a mission with a closed loop ECLSS System can be derived using Eqs.(21) and (22) and are given in Table 7.

$${m}_{c&c,IB/OB}=left(1+{k}_{safety}right)*({n}_{astronaut}*{m}_{astronaut}+{m}_{science}+{m}_{consumables,initial}*{n}_{astronauts}+{n}_{astronaut}*TOF*{m}_{consumables})$$

(22)

$${m}_{c&c,surface}=left(1+{k}_{safety}right)*({m}_{consumables,initial}*{n}_{astronauts}+{n}_{astronaut}*TOF*{m}_{consumables})$$

(23)

While the astronaut masses and the mass of the scientific payload are relevant for the transfer trips, they can be neglected during the surface stay. Here, only the plain consumable masses are relevant to examine the necessary resupply capacities. In the given equations ksafety represents the safety factor, nastronauts represents the number of astronauts, mastronaut represents the mass assumed per astronaut (200kg according to Table 6), mscience represents the mass of the scientific payload (100kg according to Table 6), TOF represents the Time of Flight in days and mconsumables represents the mass of consumables required per person per day. As mconsumables turns to zero for a recovery rate of 100% the total required consumable mass is not dependent on the ToF anymore.

With the bottom up estimates as formulated in the previous sections a mass budget summary can be formulated. This is shown in Table 8. The total on orbit mass adds to 1510.5 MT, of which 1200 MT are propellant and 100 MT payload and the 12person crew and their consumables for an ToF of 180 d. This is assuming that 100% of consumables can be recovered by the ECLSS of Starship for the flight. Overall, the total mass on orbit is exceeding the proposed mass summary by SpaceX by more than 100 MT. This is summarized in Table 9 and input for the trajectory calculations in the following section.

The usable propellant mass is 1176.47 MT (see Section "Starship system mass") and the specific impulse is 378s11. The ratio of launch mass ({m}_{0}) (the sum of propellant mass, system mass and payload mass) to dry mass ({m}_{d}) (the launch mass minus the propellant available for orbit maneuvers) is:

$$frac{{m}_{0}}{{m}_{d}}=frac{1200+204.2+6.3+100}{left(1200-1176.47right)+204.2+6.3+100}=4.516$$

(24)

The maximum attainable v with one fully fueled Starship thus follows, using the rocket equation27, to:

$${Delta v}_{max}={I}_{mathit{sp}}cdot {g}_{0}cdot {text{ln}}left(frac{{m}_{0}}{{m}_{d}}right)=mathrm{5,588} {text{m}}/{text{s}}$$

(25)

Any trajectory requiring more v than that cannot be flown by Starship during its Mars mission with the baseline Starship design as given in Section "Starship system mass". Without the 2% of propellant left as residuals in the tanks, the mass ratio would actually be 4.865 and ({Delta v}_{max}) would become 5864m/s. Imperfect propellant use leads to losses of more than 275m/s in v.

Due to the varying alignment of the two planets, the needed v is changing over the course of a 15-year cycle. In general, a transfer becomes feasible every 22months, an event that is called launch opportunity. Such launch opportunities stay open for 45 to 160days in the case of Starship. Each launch opportunity was examined with respect to three performance parameters:

The local minimum v for which a transfer becomes possible with a maximum time of flight of 180days and a payload mass of 100 MT

The local minimum time of flight for which a transfer becomes possible without exceeding the maximum obtainable v value of 5588m/s and a payload mass of 100 MT

The maximum payload mass that can be brought to the Martian surface according to Eq.(6)

The first analyzed launch opportunity is the one in late 2028 and early 2029, hence the one chosen by SpaceX to have their first manned flight to Mars. We also analyzed the 2033 and 2035 launch opportunities as they show a good performance of the selected three parameters. The results for each launch opportunity are displayed using porkchop plots which show the value of ({Delta v}_{Eto M}) for a given tuple of departure date and time of flight. Figure3 shows the porkchop plot for a transfer from Earth to Mars in 2028 and 2029.

Porkchop plot for an Earth-Mars-transfer in 2028 and 2029. The blue dashed line indicates the minimum ToF trajectory, the red dashed line indicates the minimum v (and hence maximum payload mass) trajectory. Darker areas indicate lower v values, bright areas indicate higher v values and white areas indicate impractical trajectories.

For that launch opportunity, the minimum v value is 5435m/s, corresponding with a maximum payload mass that can be brought to Mars of 114.4MT. This performance can be achieved with a transfer on 13.01.2029. The minimum possible time of flight in this launch opportunity is 177 d, possible with a transfer on 27.01.2029. In Fig.4, the porkchop plot for a transfer in 2033 is displayed.

Porkchop plot for an Earth-Mars-transfer in 2033. The blue dashed line indicates the minimum ToF trajectory, the red dashed line indicates the minimum v (and hence maximum payload mass) trajectory. Darker areas indicate lower v values, bright areas indicate higher v values and white areas indicate impractical trajectories.

For that launch opportunity, the minimum v value is 4820m/s (11.3% compared to 2029), corresponding with a maximum payload mass that can be brought to Mars of 178.7 MT (+56.2% compared to 2029). Both values are the global minimum/maximum values in the observed time frame. The minimum possible time of flight in this launch opportunity is 122 d.

In Fig.5, the porkchop plot for a transfer in 2035 is displayed. For that launch opportunity, the minimum is v 4896m/s, corresponding with a maximum payload mass that can be brought to Mars of 170.2MT. The minimum possible time of flight in this launch opportunity is 112 d (36.7% compared to 2029).

Porkchop plot for an Earth-Mars-transfer in 2035. The blue dashed line indicates the minimum ToF trajectory, the red dashed line indicates the minimum v (and hence maximum payload mass) trajectory. Darker areas indicate lower v value, bright areas indicate higher v values and white areas indicate impractical trajectories.

Since the results of the previous analysis indicate that the system mass of Starship is likely to exceed 100 MT, it is evident that this is a limiting factor on the performance of the system. The system mass influences the left-hand side of Eq.(6) and therefore the capacity of the system. As a result, the maximum payload mass decreases for higher system masses and the minimum time of flight increases. In order to model the v required for landing correctly, the structural mass in excess of 100MT is modeled as additional payload mass. This allows to calculate the maximum payload mass in the same way as in the previous section. Since our analysis showed that the system mass of Starship could exceed the 100 MT as proposed by SpaceX, the following sensitivity analysis examines the advantages of a reduced system mass in terms of mission analysis. We analyzed a transfer in 2033. In Table 10, the v capacities for a system mass of 175 MT and 150 MT, respectively, are displayed.

In Table 11, the performance of Starship for the reduced system masses is shown. The performance is measured based on the maximum payload mass and the minimum time of flight. Also, the improvement of the two parameters when compared to our baseline scenario is displayed.

It is shown that a reduction of the system mass has only a small influence on the minimum time of flight, but a big impact on the maximum payload mass. These results show the large potential of Starship when reducing the system mass and explain the aims of SpaceX in terms of mission analysis.

According to the presented model in Section "Starship mass budget", return flights from Mars to Earth have been analyzed. The launch opportunities for the return flights were chosen to open 500days after the landing on Mars, according to the mission plans presented.

in previous sections. Under the assumption that no payload apart from the astronauts and consumables is returned to Earth, the maximum v for the return flight is 6651m/s. It has been shown that the ascent to LMO alone consumes 4782m/s, which are 72% of the v budget, including margins. Another 6% are used for the TCM, while the landing requires around 2% of the budget. This leaves only 1330m/s, or 20%, of the maximum v available for the two remaining maneuvers. In order to set the boundary conditions for the return flight, a maximum time of flight must be chosen. Due to the alignment of the two planets, flight times over 300 d result in a vast increase of required v. Therefore, we selected 300 d as the maximum allowable time of flight for the return. Before further evaluating the return flight in this configuration, an excursion is needed: If Starship would have a system mass of 100 MT, as proposed by SpaceX, the maximum v would be 8711m/s. In this configuration, the global minimum v for return would be 7771m/s.

Upon comparison of these two numbers, it becomes evident that a return from Mars to Earth is beyond the capacity of Starship in the presented configuration, since the global minimum for only 100 MT of system mass is already exceeding the actual maximum v available by more than 1100m/s.

Section "Trajectory analysis" gives an overview of the required propellant masses for different mass- and trajectory options. The results show, that Starship requires the maximum available amount of 1200 MT of propellant on the outbound as well as the inbound trip for the realization of a realistic mission scenario. Following this analysis, it becomes visible, that realizing the described mission to mars with the Starship vehicle is only possible by refilling the spacecraft during the mission.

With a mixture ratio of O/F=3.6:112 940 MT of liquid oxygen and 260 MT of liquid methane need to be resupplied as propellant for the inbound trip. In addition, following the calculation in Section "Crew and consumables", the mission requires the resupply of consumable items to support the crew during the surface stay and the inbound trip. The individual as well as total masses can be derived using Eqs.(25) and (26).

$${m}_{item, resupply}={m}_{item}*{n}_{astronauts}*ToF$$

(26)

$${m}_{consumables,resupply}=sum {m}_{item,resupply}$$

(27)

Thus, for a mission with a surface stay of 500days and an inbound trip of 180days, 1,263,158 MT of consumable items need to be resupplied for one Starship with a crew of 12 astronauts. In this analysis it is assumed, that two crewed Starship vehicles will return to Earth while the cargo vehicles remain on Mars.

If the amount of 2,526,316kg is to be resupplied via cargo missions, 26 Starship cargo vehicles with the currently planned payload capacity of 100 MT are required. A reasonable alternative is the production of selected items via ISRU technologies. A detailed overview of the required resupply masses is presented in Table 12.

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About feasibility of SpaceX's human exploration Mars mission scenario with Starship | Scientific Reports - Nature.com