Interplanetary Exploration: Application of the Solar Sail and Falcon Heavy

Gregory Matloff’s contributions to interstellar studies need scant introduction, given their significance to solar-and beamed sail development for decades, and their visibility through books like The Starflight Handbook (1989) and Deep Space Probes (2005). A quick check of the bibliography online will demonstrate just how active Greg continues to be in analyzing the human future in space, as well as his newfound interest in the nature of consciousness (Star Light, Star Bright, 2016). The paper that follows grows out of Greg’s presentation at the 2016 iteration of the Tennessee Valley Interstellar Workshop, where he discussed ways to advance deep space exploration using near term technologies like Falcon Heavy, in conjunction with the solar sail capabilities he has so long championed. Read on for an examination of human factors beyond lunar orbit and a description of a useful near-term mission that could reach an object much closer than Mars relying on both chemical and sail capabilities. Dr. Matloff is a professor of physics at New York City College of Technology, CUNY.

ABSTRACT

The possibility of applying the Space-X Falcon-Heavy booster to human exploration of the inner solar system is discussed. A human-rated Dragon command module and an inflatable habitat module would house and support the 2-4 person crew during a ~1 year interplanetary venture. To minimize effects of galactic cosmic rays, older astronauts should conduct the mission during Solar Maximum. Crew life support is discussed as is application of a ~1-km square solar photon sail. The sail would be applied to rendezvous with the destination Near Earth Object (NEO) and to accelerate the spacecraft on its return to Earth. An on-line NASA trajectory browser has been used to examine optimized trajectories and destinations during 2025-2026. A suitable destination with well established solar-orbital parameters is Asteroid 2009 HC. Because the NASA Space Launch System (SLS) has a greater throw mass than the Falcon-Heavy, the primary propulsion for NEO rendezvous and Earth return would likely be a chemical rocket. The sail would be used in this case as an abort mechanism and a back-up for the primary propulsion system. In either scenario, a single Falcon-Heavy or SLS launch would be adequate.

Keywords: NEO Exploration, Falcon-Heavy, Dragon, BEAM, GCR, ECLSS, SLS

Introduction

The United States is currently developing two separate approaches to launching inner solar system exploration by human crews beginning in around 2020: the NASA Space Launch System (SLS) and the commercial Space-X Falcon Heavy [1,2]. The advantage of the SLS is its greater throw-weight on interplanetary trajectories. A disadvantage of SLS is the cost permission and constraints imposed by the current state of the US federal government. Although Falcon-Heavy has less launch capacity than the SLS, this booster is a composite of three existing and mass produced Falcon-9 boosters. These have an excellent reliability record to date on NASA-sponsored resupply missions to the International Space Station (ISS) and commercial launches. Experiments indicate that the Falcon 9 first stage may eventually be recovered and reused, which promises to greatly reduce the cost of space missions to low Earth orbit (LEO) and beyond.

This paper concentrates upon interplanetary ventures using a single Falcon-Heavy launcher and a small crew (2-4 people). As well as a Dragon V2 capsule appropriately modified for interplanetary application (3), an inflatable Bigelow space habitat similar to the one to be launched to the ISS [4} in the near future will be used for crews habitability. Life support for the crew on their 1-2 year interplanetary venture will utilize recycling of oxygen and water. Food recycling by biological means will likely not be ready by 2020.

After the spacecraft is launched towards Mars, a state-of-the-art solar photon sail with a dimension of ~0.7 km will be unfurled. This will allow, as will be demonstrated, non-rocket accelerations of 1-2 km/s per month in the solar system region between Earth and Mars.

A recent comprehensive study of in-space radiation effects reveals that galactic cosmic radiation beyond LEO is reduced by a factor of ~5 above LEO, if missions are conducted during solar maximum. During solar flares and coronal plasma discharges, the crew could be protected by aligning the Dragon’s heat shield between the crew quarters and the Sun.

Human landings on Mars will not be possible using a single Dragon launch. But a host of Near Earth Objects of asteroidal and cometary origin and possibly the Martian satellites Deimos and Phobos will be open to human explorers.

But any human expedition beyond the Moon will likely require cruise durations of months to years. Solar and galactic cosmic radiation will certainly be a limiting issue. The possibilities and effectiveness of using the capsule and habitat mass for self shielding is discussed in the next section.

Falcon-Heavy Interplanetary Throw Mass and Cosmic Ray Shielding

According to Ref. 2, a Falcon-Heavy is capable of projecting 13,200 kg on a trans-Mars trajectory. From Ref. 3, the dry mass of a Dragon V2 capsule is 4200 kg and the endurance of this spacecraft is about 2 years in space. The mass of the BEAM inflatable module is 1360 kg [4].

From Ref. 3, the Dragon’s configuration can be approximated by a cone with a diameter of about 3.7 m and a height of about 6.1 m. From Ref. 4, the BEAM inflatable habitat can be approximated by a cylinder with a diameter of about 3.2 m and a length of about 4 m. Assuming that the base of the Dragon abuts one of the circular end caps of the BEAM, it is easy to demonstrate that the surface area of the spacecraft is about 100 m2. Assuming that all of the Falcon’s throw mass can be used for self-shielding against cosmic rays during an interplanetary venture, the approximate shielding areal mass thickness is 130 kg/m2 or 13 g/cm2.

There are two major sources of cosmic radiation beyond the Earth’s magnetosphere. These are eruptions of solar energetic particles (SEPs), which are most common during solar maximum and galactic cosmic rays (GCR), which are alway present. We first consider the effects of a 13 g/cm2 shield on SEPs.

Shielding From SEPs

A recent paper by an international team summarizes the latest results on cosmic ray shielding above LEO [5}. Figure 6 of that reference compares the Effective Dose Equivalent predicted to be incurred by an astronaut from four SEP events: a 20-year event, a 10-year event, a worst-case modeled event and a Carrington-event estimate. This data is plotted against aluminum shield thickness and compared with currently recommended European Space Agency (ESA) career dose limits. In all cases presented, a 13 g/cm2 aluminum shield is adequate.

Figure 7 of Ref. 5 presents similar information and compares predicted doses from the above SEP events with the 30-day and annual ESA limit. Once again, a 13 g/cm2 aluminum shield seems to be adequate, although the Carrington-event predicted dose rate is very close to the 30-day limit.

Therefore, SEPs do not seem to pose an insurmountable health risk to crews venturing beyond LEO with an equivalent a 13 g/cm2 aluminum shield. Additional shielding could be affected by orienting the Drago heat shield between crew and Sun during a major SEP event.

Shielding from GCRs

Galactic cosmic rays, on the other hand, pose a larger risk to the crew’s health. Since at least 1979, it was known that energetic galactic cosmic rays more massive than helium nuclei (high-Z GCR) are potentially dangerous to human health and very difficult to shield against [6]. Figure 1 of Ref. 5 reveals that during solar maximum, the modeled flux of galactic hydrogen and helium nuclei are reduced by a factor of 5-10 when compared with fluxes of the same ions during solar minimum. But the fluxes of galactic lithium and iron nuclei are apparently independent of the solar activity cycle.

Cucinotta and Durante estimate that during an interplanetary transfer, the high-Z GCR dose might be 1-2 mSv per day or 0.4-0.8 Sv per year [7]. From Tables 1 and 2 of McKenna et al, the NASA one-year dose limits for 40-year old female and male astronauts are respectively 0.7 and 0.88 Sv. For older astronauts, the limits are higher. Dose limits for men are higher than dose limits for women.

During a 1-year interplanetary voyage, the dose limits for 40-year old astronauts may be exceeded. Exposures beyond these recommended limits may result in a 3% increased risk of fatal cancers.

Health effects on interplanetary astronauts from high-Z galactic cosmic rays is an ongoing field of research. Mewaldt et al. also conclude that interplanetary voyagers will experience a higher galactic dose during solar minimum than during solar maximum. According to their study, a thin aluminum shield of about 3 g/cm2 may reduce solar minimum dose rates to the NASA LEO career limit of 50 cSv for a 1-year interplanetary round trip [8].

It should also be mentioned that it is not always possible to predict future GCR doses in interplanetary space from data obtained during previous solar cycles. Schwadron et al have noted that unusually high levels of GCRs were measured during a prolonged solar minimum in 2009 [9].

Crew Life Support on Interplanetary Ventures

We next consider the mass requirements to maintain a small crew (2-4 people) during a 1-2 year interplanetary expedition. According to the wikipedia entry on space-life-support systems and in substantial concurrence with one classic reference [10], daily average human metabolic requirements can be summarized:

oxygen: 0.84 kg

food: 0.62 kg

water: 3.52 kg.

If partial recycling were not built in to the mission, a two-person crew could not be supported in the proposed spacecraft for missions of one year or longer. Projections from International Space Station technology indicate that a near-term goal for water recycling is 85% and the oxygen recovery rate can be raised to 75% [11,12]. Applying these values for an interplanetary mission applying near-term recycling technology, the daily consumable requirement per astronaut is 0.21 kg oxygen, 0.62 kg food, and 0.53 kg of water. Each crew member consumes about 1.4 kg per day of these resources or about 500 kg per year. A 4-person crew therefore requires about 2,000 kg of these resources for a 360-day duration interplanetary voyage.

It is next necessary to estimate the mass of the Environmental Control and Life Support System (ECLSS) equipment, not including consumables, necessary to support the mission. In Table 4.3 of his monograph, Rapp estimates the mass of the water-recovery system for a 180-day transit to Mars at 1.4 metric tons or 1,400 kg and the mass of the oxygen recovery system at 0.5 metric tons or 500 kg for a 6-person crew [13]. We are here considering a smaller crew and the 180-day return voyage as well as the 180-day flight to the interplanetary destination. Since we have no idea regarding ECLSS reliability on a deep-space mission, we will assume here that the required mass of ECLSS equipment is 3,000 kg. Including the 2,000 kg requirement for oxygen, food and water, the total ECLSS mass is about 5,000 kg.

Application of a Near-Term Solar Photon Sail

From the above discussion, the mass of the Dragon is estimated at 4,200 kg and the BEAM habitat mass is 1,360 kg. Since the Falcon-Heavy can project 13,200 kg towards Mars and our ECLSS mass projection is 5,000 kg, the remaining mass amounts to 2,640 kg. If 640 kg is required for scientific equipment, 2,000 kg remains to be allowed. We will therefore assume that the sail mass is 2,000 kg.

As an example of a large solar-photon sail that could be constructed in the not very distant future, we consider a 90% reflective (REF) opaque 1-km2 sail with an areal mass density of 2 g/m2. The sail mass is 2,000 kg and the areal mass density of the spacecraft (σ eff ) is 0.0132 kg/m2.

The lightness factor (β) of a solar-photon sail is the ratio of solar radiation-pressure acceleration on the sail to solar gravitational acceleration. It can be calculated by modifying Eq. (4.19) of Ref.14 for a solar constant of 1,366 W/m2:

Substituting in Eq. (1) for sail reflectivity and spacecraft areal mass density, we find that β = 0.11.

Since the Earth is in a near-circular solar orbit at a distance of 1 Astronomical Unit (1 AU = 1.5 X 1011 m) and the Earth’s solar-orbital velocity is about 30 km/s, the Sun’s gravitational acceleration on the spacecraft at a distance of 1 AU is about 0.006 m/s2. The solar radiation-pressure acceleration on the sail is therefore about 6.6 X 10-4 m/s2, if the sail is normal to the Sun at a distance of 1 AU from the Sun. Such a sail configuration can result in a daily velocity increment of about 57 m/s. Every month, the sail can alter the spacecraft velocity by about 1.6 km/s, if it is oriented normal to the Sun at a solar distance of 1 AU. At the orbit of Mars (1.52 AU), this sail oriented normal to the Sun can alter the spacecraft’s solar velocity each month by about 0.69 km/s.

The effectiveness of this configuration for non-landing missions to Mars can be evaluated using Table 4.2 of Ref. 15. The duration of a Hohmann minimum-energy Earth-Mars trajectory is given in that table as 259 days. Although application of the sail can shorten this a bit on the Mars-bound trajectory, sail or some other form of propulsion must be used to accomplish Mars rendezvous. Aerocapture with a deployed sail of this size will be difficult or impossible. Table 4.2 of Ref. 15 also presents Earth-Mars transit times for spacecraft flying a logarithmic spiral trajectory at a sail pitch angle relative to the Sun of about 35 degrees, as a function of lightness factor. For β = 0.1, the time required for a return journey on such a trajectory is about 431 days. To accomplish logarithmic-spiral Earth-return trips from Mars approximating the Hohmann-trajectory duration with the spacecraft configuration considered here would require a substantial increase in sail area without an increase in spacecraft mass. More advanced sails, smaller crews, or less massive ECLSS would be required.

Application of Falcon/Dragon/BEAM for NEO Exploration

So the configuration presented here is marginal at best for Mars-vicinity missions such as exploration of the natural Martian satellites Phobos and Deimos. Instead, it might see more immediate application to near Earth objects (NEOs) orbiting the Sun close to the Earth’s solar orbit.

A suitable target NEO for such an expedition would be in a near-circular, low-inclination orbit approximately 1-AU from Earth. If the mission is timed appropriately, the Hohmann trajectory duration should be considerably less than the time required to reach Mars and the Falcon-Heavy payload should be greater than that estimated for a Mars mission. One NEO class of potential targets is Earth’s quasi-satellites in “corkscrew orbits” [16].

The principal use of the sail on the out-bound trajectory leg would be deceleration for rendezvous with the NEO. The sail would be used to accelerate the spacecraft for Earth rendezvous on the return trajectory leg. Although the Sail and BEAM inflatable habitat could be maneuvered into Earth orbit for possible reuse, the Dragon would return crew and payload (including NEO samples) to Earth in a ballistic reentry.

It is possible to investigate mission possibilities with the aid of the NASA on-line Trajectory Browser (trajbrowser.arc.nasa.gov). After accessing this site on May 23 and 25, 2015, we specified a mission to a NEO with a well established orbit during the next solar-max (2025-2026) to reduce crew exposure to GCRs. Two mission types were considered: a round-trip with a maximum duration of 360 days and a one-way, rendezvous mission with a maximum duration of 180 days. For the one-way rendezvous mission, the maximum delta-V for departure from a 200-km low-Earth orbit was 4 km/s. For the round-trip. the maximum delta-V was 5 km/s.

The results of this exercise are presented in Table 1 [following the references]. The destination NEO determined by the Trajectory Browser software is Asteroid 2009 HC. Browser output is summarized in Table 1. This table also includes physical data on this NEO from the NASA Jet Propulsion Laboratory NEO data base (ssd.jpl.nasa.gov).

It is assumed that the pre-rendezvous propulsion requirements will be met by the Falcon upper stage, since this configuration is capable of reaching Mars, a more distant destination. Since the post-injection delta-V is small and the sail’s characteristic acceleration at 1 AU is greater than 1 km/s, the sail can be used to match velocity with the destination NEO without significantly increasing pre-rendezvous mission duration.

Note from Table 1 that the difference between post-injection delta-V for one-way rendezvous and round-trip missions is less than 1 km/s. So it is safe to assume that use of the sail to power Earth-return maneuvers does not significantly increase mission duration.

Another way to consider use of the sail on the Earth-bound trajectory is to estimate time required for the sail to be used for orbital inclination adjustment or “cranking”. From Eq. (5-74 of McInnes’s monograph [15]), a sail operating at the optimal cone angle can change its inclination by

∆ i = 88.2 β degrees/orbit. (2)

According to McInnes, Equation (2) is independent of solar-orbit radius. Inclination correction for Earth-return will add a few months to the duration of the round-trip mission.

Conclusions: Use of the Sail with the NASA Space Launch System on NEO-Visit Missions

From the work presented here, it seems that round-trip visits to selected Near Earth Objects with durations not much greater than one year can be accomplished using a single Falcon-Heavy launch and a combination of a Dragon spacecraft, an inflatable habitability module, state of the art partially closed environmental system and a state of the art square solar photon sail with a 1-2 km dimension.

To reduce the Galactic Cosmic Radiation risk to the 3-4 person crew, it is advisable to conduct lengthy voyages above Low Earth Orbit during periods near the maximum of the solar activity cycle and to position the Dragon heat shield facing the Sun to shield against solar flare events. It may also be advisable to select older astronauts to crew such interplanetary ventures.

If the NASA Space Launch System is available to conduct human visits to suitable NEOs, the sail could serve at least two functions. Because the SLS has 2-3X the throw mass of the Falcon-Heavy, the sail could be accommodated as a pre-rendezvous abort option or as a back-up to the SLS propulsion module for Earth-return maneuvers.

It should also be mentioned that with either launch alternative, the sail and inflatable could be steered into high-Earth orbit for reuse after the Dragon or Orion is directed on its Earth reentry path.

References

1. “NASA Fact Sheet: NASA Space Launch System”, www.nasa.gov/pdf/ 664158main_sls_fs_master.pdf

2. “Falcon Heavy”, www.spacex.com/falcon-heavy

3. “Dragon V2), en.wikipedia.org/wiki/Dragon_V2

4. “The Bigelow Expandable Activity Module (BEAM),” bigelowaerospace.com/beam

5. S. McKenna-Lawlor, A. Bhardwaj, F. Ferrari, N. Kuznetsov, A. K. Lal, Y. Li, A. Nagamatsu, R. Nymmik, M. Panasyuk, V. Petrov, G. Reitz, L. Pinsky, M. Shukor, A. K. Singhvi, U. Strube, L. Tomi, and L. Townsend, “Recommendations to Mitigate Against Human Health Risks Due to Energetic Particle Irradiation Beyond Low Earth Orbit/BLEO”, Acta Astronautica, 109, 182-193 (2015).

6. E. Bock, F. Lambrou Jr., and M. Simon, “Effect of Environmental Parameters on Habitat Structural Weight and Cost”, Chap. II-1 in Space Resources and Space Settlements, NASA SP-428, J. Billingham and W. Gilbreath eds., NASA Ames Research Center, Moffett Field, CA (1979).

7. F. A. Cucinotta and M. Durante, “Cancer Risk from Exposure to Galactic Cosmic Rays: Implications for Space Exploration by Human Beings,” Lancet Oncology, 7, 431-435 (2006).

8. R. A. Mewaldt, A. J. Davis, W. R. Binns, G. A. de Nolfo, J. S. George, M. H. Israel, R. A. Leske, E. C. Stone, M. E. Wiedenbeck and T. T. von Rosenvinge, “The Cosmic Ray Radiation Dose in Interplanetary Space—Present Day and Worst-Case Evaluations”, Proceedings of the 29th International Cosmic Ray Conference, Pune, India, August 3-10, 2005, B. Sripathi Acharya, S. Gupta, P. Jagadeesan, A. Jain, S. Karthikeyan, S. Morris and S. Tonwar eds., ( Tata Institute for Fundamental Research, Mumbai, India, 2005), pp. 433-436.

9. N. A. Schwadron, A. J. Boyd, K. Kozarev, M. Golightly, H. Spence, L. W. Townsend and M. Owens, “Galactic Cosmic Ray Radiation Hazard in the Unusual Solar Minimum Between Solar Cycles 23 and 24”, Space Weather, 8, DOI: 10.1029/2010SW000567, (2010).

10. M. R. Sharpe, Living in Space: The Astronaut and His Environment, Doubleday, Garden City, NY (1969).

11. R. Carrasquillo, “ISS Environmental Control and Life Support System (ECLSS) Future Development for Exploration”, presented at 2nd Annual ISS Research and Development Conference (July 16-18, 2013).

12. M. Gannon, “NASA Wants Ideas to Recycle Precious Oxygen on Deep-Space Voyages”, www.space.com/25518-nasa-oxygen-recycling-space-tech.html (space.com, April 16, 2004).

13. D. Rapp, Human Missions to Mars: Enabling Technologies for Exploring the Red Planet, Springer-Praxis, Chichester, UK (2008).

14. G. L. Matloff, Deep-Space Probes: To The Outer Solar System and Beyond, 2nd ed., Springer-Praxis, Chichester, UK (2005).

15. C. R. McInnes, Solar Sailing: Technology, Dynamics, and Mission Applications, Springer-Praxis, Chichester, UK (1999).

16. P. Wajer, “Dynamical Evolution of Earth’s Quasi-Satellites 2004 GU9 and 2006 FV35”, Icarus, 209, 488-493 (2010).

Table 1. Details for a NEO Visit in 2025-2026