multiple rendezvous and sample return missions to near-earth objects using solar sailcraft

Acta Astronautica 59 (2006) 768–776www.elsevier.com/locate/actaastro

Multiple rendezvous and sample return missions to near-Earthobjects using solar sailcraft

B. Dachwald∗, W. Seboldt, L. RichterGerman Aerospace Center, Institute of Space Simulation, 51147 Cologne, Germany

Available online 7 October 2005

Abstract

Solar sailcraft are due to their high �V -capability especially capable to perform multiple rendezvous and sample returnmissions to near-Earth objects. Even with moderate-performance solar sails of the first generation, challenging scientific missionsare feasible at relatively low cost. Within this paper, it will be shown that a 300 kg-spacecraft (including a lander and a samplereturn capsule), propelled by a (70 m)2 solar sail with an additional mass of about 110 kg (specific weight 23 g/m2), is capableto return a sample from a near-Earth asteroid to Earth within 10 years from launch. In another scenario, a solar sail of the samesize and weight is able to propel a 75 kg-spacecraft to rendezvous three near-Earth asteroids subsequently within 7.6 years fromlaunch (with about 200 days of operations at each asteroid). A larger solar sail of about (140 m)2 would even be capable totransport a spacecraft that returns samples from the three near-Earth asteroids to Earth within about 10 years from launch.© 2005 Published by Elsevier Ltd.

1. Introduction

Being propelled solely by the freely available solarradiation pressure, solar sailcraft provide a wide rangeof opportunities for low-cost missions, many of whichare—due to their large �V -requirement—difficult orimpossible for any other type of conventional space-craft. Many of those high-energy missions are of greatscientific relevance, such as missions to near-Earth ob-jects (NEOs, asteroids and short period comets) withhighly inclined or retrograde orbits.1 Such missionscan be performed with solar sails, but a demanding

∗Corresponding author.E-mail addresses: [email protected] (B. Dachwald),

[email protected] (W. Seboldt), [email protected](L. Richter).

1More than 55% of the NEO population has inclinations largerthan 10◦, more than 30% has inclinations larger than 20◦.

0094-5765/$ - see front matter © 2005 Published by Elsevier Ltd.doi:10.1016/j.actaastro.2005.07.061

sail performance (low specific weight) is required tokeep mission durations within moderate limits. Taking,however, the current state of the art in engineering ofultra-lightweight structures into account, solar sailcraftof the first generation will be of relatively moderate per-formance, if assessed w.r.t. flight duration alone, eveninferior to already state of the art electric propulsionsystems (although solar sailcraft might have an advan-tage in launch mass). Nevertheless, on the way to moreadvanced solar sailcraft, they are an indispensable firststepping stone. Near-Earth asteroids (NEAs) with amoderate inclination are a promising category of targetbodies for near-term solar sailcraft, since they can beaccessed relatively easily. Therefore, in August 2000,a dedicated mission for the exploration of NEAs withsolar sailcraft (ENEAS) was proposed by DLR in co-operation with the Westfälische Wilhelms–Universitätat Münster (Germany) as a candidate within the Ger-man small satellite program for space sciences. Using

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B. Dachwald et al. / Acta Astronautica 59 (2006) 768 –776 769

a (50 m)2 square sail with a specific weight of about30 g/m2, ENEAS was intended to rendezvous a NEA(1996FG3) with a total payload of about 75 kg (incl.spacecraft bus and 5 kg scientific payload) within lessthan 5 years [1,2]. Based on our experience gained dur-ing the successful ground deployment of a (20 m)2 so-lar sail structure [2–4], we consider a (70 m)2 solar sailwith a specific weight of about 20 g/m2 to be a realistic,however still ambitious, near-term development goal.

Within this paper, it will be demonstrated that evenwith moderate-performance solar sails of the first gen-eration, challenging scientific missions, like a samplereturn mission (ENEAS-SR) or a multiple rendezvousmission (ENEAS+) to near-Earth asteroids, are feasi-ble at relatively low cost. It will be shown that, usinga (70 m)2 solar sail with a specific weight of 23 g/m2,ENEAS-SR would be able to return a sample from theC type NEA 1996FG3 to Earth within 10 years fromlaunch. The payload (the total system except the sail as-sembly) for this mission is about 300 kg, including a lan-der and a sample return capsule. With a 75 kg-payload, asolar sail of the same size and weight would also be ableto rendezvous three NEAs (2000AG6, 1989UQ, and1999AO10) subsequently within 7.6 years from launch(with about 200 days of operations at each NEA). Alarger solar sail of about (140 m)2 would even be ca-pable to transport the ENEAS-SR payload to the threeENEAS+ target bodies and sample all of them. Thesamples could be returned to Earth within about 10 yearsfrom launch.

2. Solar sailcraft

For the optical characteristics of a solar sail, differ-ent assumptions can be made, which result in differentmodels for the magnitude and the direction of the solarradiation pressure (SRP) force acting on the sail. Sim-ple models assume an ideally reflecting sail surface ormodel its non-ideal reflectivity by introducing an over-all sail efficiency factor. It is shown in [5] that thoseSRP force models should not be used except for verypreliminary mission feasibility analyses, since they mis-represent the direction of the real SRP force. Withinthis paper, a more realistic SRP force model is usedfor trajectory simulation and optimization that consid-ers the optical characteristics of the real sail film, whichis aluminum-coated on the front side2 and chromium-coated on the back side.3 Using the optical parameters

2 For high reflectivity.3 For high emissivity.

Fig. 1. SRP force on a non-perfectly reflecting solar sail.

for an Al|Cr-coated sail, it can be shown (cf. [6,7]) that,as Fig. 1 illustrates, the SRP force acting on the sail hasa component perpendicular to the sail surface

Fn = PAQn(�) cos � (1)

and a component parallel to the sail surface

Ft = PAQt (�) cos �, (2)

where

Qn(�) = 1.8272 cos � − 0.010888, (3)

Qt(�) = 0.1728 sin � (4)

and where P is the solar radiation pressure, A is the sailarea, and � is the light incidence angle. Introducing aunit vector f that is always along the total SRP force di-rection, the SRP force acting on the sail may be writtenas

FSRP =√

F 2n + F 2

t f (5)

and, by defining

Q(�) = 1

2

√Q2

n(�) + Q2t (�) cos � (6)

as

FSRP = 2PAQ(�)f , (7)

where Q(�) depends only on the light incidence angle� and the optical parameters of the sail film. The anglebetween the Sun-line and f is

� = � − arctanQt(�)

Qn(�). (8)

The orbital dynamics of solar sailcraft is in many re-spects similar to the orbital dynamics of other low-thrustspacecraft. However, as Fig. 2 shows, other low-thrustspacecraft may orient its thrust vector into any desired

770 B. Dachwald et al. / Acta Astronautica 59 (2006) 768 –776

Fig. 2. Spiralling towards and away from the Sun.

direction, whereas the thrust vector of solar sailcraft isconstrained to lie on the surface of a “bubble” that isalways directed away from the Sun. Nevertheless, bycontrolling the sail orientation relative to the Sun, solarsailcraft can lose orbital angular momentum and spi-ral inwards—towards the Sun—or gain orbital angularmomentum and spiral outwards—away from the Sun.

Now, the commonly used performance parameters forsolar sailcraft will be introduced:

The sail assembly loading

�SA = mSA

A(9)

is defined as the mass of the sail assembly (the sailfilm and the required structure for storing, deployingand tensioning the sail, index “SA”) per unit area. Thus,the sail assembly loading is the key parameter for theefficiency of the solar sail’s structural design.

The sailcraft loading

� = m

A= mSA + mPL

A= �SA + mPL

A(10)

is defined as the specific mass of the sailcraft includingthe payload (index “PL”), where the term payload standsfor the total sailcraft except the solar sail assembly (i.e.except the propulsion system).

The SRP force acting on the sail may also be ex-pressed in terms of the characteristic acceleration ac,which is defined as the SRP acceleration acting on a so-lar sail that is oriented perpendicular to the Sun-line atSun–Earth distance r0, where Peff,0

.= 1.8163 ·P(r0).=

8.288 �N/m2, and therefore

ac = Peff,0A

m= Peff,0

�= Peff,0

�SA + mPL/A. (11)

Fig. 3. Deployed (20 m)2 solar sail and CFRP boom at DLR.

The SRP force may then be written as

FSRP = mac

( r0

r

)2 2Q(�)

1.8163f . (12)

At DLR, a (20 m)2 solar sail was successfully deployedin December 1999 on-ground in a simulated gravity-free environment and ambient environmental conditions(Fig. 3) [2,3]. The DLR solar sail baseline design is asquare sail that consists of four carbon fiber reinforcedplastics (CFRP) booms and of four triangular sail seg-ments. The booms are made of two CFRP shells thatare bonded at the edges to form a tubular shape, so thatthey can be pressed flat and rolled up in a central de-ployment module. During deployment, they unfold au-tomatically and return to their tubular shape with highbending and buckling strength. Subsequently, the foursail segments are deployed by ropes.

3. NEA rendezvous mission (ENEAS)

ENEAS was intended to transport a scientific pay-load of 5 kg (CCD camera+IR spectrometer+magneto-meter) to a NEA within less than five years (Table 1

Table 1ENEAS

Sail area A (50 m)2

Sail assembly mass mSA 73 kgSail assembly loading �SA 29.2 g/m2

Payload mass mPL 75 kg(incl. spacecraft bus)Total sailcraft mass m 148 kgSailcraft loading � 59.2 g/m2

Characteristic acceleration ac 0.140 mm/s2

Characteristic SRP force Fc 20.7 mN


Fig. 4. ENEAS trajectory option for C3 = 0 km2/s2.

Fig. 5. ENEAS trajectory option for C3 = 4 km2/s2.

summarizes the ENEAS parameters). 1996FG3 hadbeen chosen as the target body for the ENEAS mis-sion, since it has orbital elements not too different fromthat of Earth and since it is an object of exceptionalscientific relevance. Observations [8,9] indicate that1996FG3 is a binary C type asteroid, consisting of aprimary body with a rotation period of about 3.6 h anda secondary body with an orbital period of about 16 h.Based on the typical C type albedo of 0.06, the primarybody has an estimated diameter of about 1.4 km and thesecondary body an estimated diameter of about 0.4 km.The separation of the two bodies is about 1.7 times the

diameter of the primary body. The determined averagebulk density is 1.4±0.3 g/cm3, which is highly sugges-tive of a “rubble pile” structure. ENEAS was intendedto determine the morphological properties and the com-positional properties of the 1996FG3 system via remotesensing [1]. Trajectory optimization using InTrance, anevolutionary neurocontrol-based global trajectory opti-mization method recently developed at DLR [10–12],yields an optimal transfer time of 4.18 years forC3=0 km2/s2 (Fig. 4 ) and 2.74 years for C3=4 km2/s2

(Fig. 5). Thus, it would be very beneficial, if thelauncher could provide some hyperbolic excess energyfor interplanetary injection, but this is not absolutelynecessary to accomplish the mission.

4. NEA sample return mission (ENEAS-SR)

To study the 1996FG3 system in detail, it would benecessary to place a lander on the surface of the asteroid(e.g. for mass spectrometry and/or alpha-proton spec-trometry). Some investigations (e.g. micro-structure andisotope analysis) to determine the age and the evolutionof 1996FG3 could probably only be accomplished bytaking samples of the asteroid back to Earth. Solar sail-craft are—due to their high �V -capability—supposedto be especially capable to perform such a mission.However, compared to the ENEAS rendezvous mission,the payload has to be extended considerably, includinga lander and a sample return capsule.

To derive the required minimum solar sailcraft perfor-mance for this mission, the maximal mission durationwas set to 10 years, since we consider a longer missionduration to be not acceptable.4 Trajectory optimizationusing InTrance shows that the ENEAS-SR mission to1996FG3 can be achieved even with a low characteristicacceleration of 0.10 mm/s2 in exactly 10 years, includ-ing a rendezvous trajectory of 6.7 years (Fig. 6), 117.5days of operations at the asteroid, and an Earth returntrajectory of 3.0 years (Fig. 7). The Earth return leg ismuch shorter than the outward leg, since no rendezvousis required at Earth.

Looking at Eq. (11), one can see that the solar sail-craft performance depends on three design parameters,the sail assembly loading �SA, the payload mass mPL,and the side length s (or area A = s2) of the solarsail, defining a three-dimensional solar sailcraft designspace. Fig. 8 shows the required sail size for different

4 Looking at the Rosetta-mission, about 10 years seem to bethe scarcely acceptable maximum duration for a mission with anexceptional scientific return.


Fig. 6. ENEAS-SR outward trajectory option.

Fig. 7. ENEAS-SR return trajectory option.

sail assembly loadings and payload masses, to obtaina characteristic acceleration of 0.10 mm/s2. Based onour experiences with the ground-based solar sail tech-nology demonstration, a maximum sail size of (70 m)2

with a sail assembly mass of 111 kg (�SA = 22.7 g/m2,sail film+booms+deployment module) is considered asa realistic—however still challenging—baseline for theENEAS-SR mission [13]. This yields a payload mass of295 kg. The realization of a spacecraft within the spec-ified mass budget, including a lander of about 150 kgand a sample return capsule of about 50 kg, appears to

Fig. 8. The side length s of the solar sail that is required to achievea characteristic acceleration of 0.10 mm/s2 as a function of �SAand mPL.

Table 2ENEAS-SR

Sail area A (70 m)2





be feasible but requires further investigation. Table 2summarizes the ENEAS-SR parameters.

Since for solar sailcraft of moderate performance itis difficult and time consuming to gain orbital energy inthe Earth’s gravitational field, the launcher inserts theENEAS-SR sailcraft directly into an interplanetary tra-jectory. After injection and deployment, the sail is ori-ented to follow the pre-calculated attitude profile thatleads to an optimal interplanetary transfer trajectory.During the transfer, the ENEAS-SR sailcraft runs al-most autonomously, so that ground monitoring is carriedout on a weekly basis only [2]. At the end of the trans-fer trajectory, the solar sailcraft makes a rendezvouswith 1996FG3 within its gravitational sphere of influ-ence (Hill-sphere) of between 70 and 150 km radius (at1996FG3’s perihelion and aphelion, respectively).

Even in the near field of the asteroid, the SRP accel-eration of between 0.05 and 0.21 mm/s2 (at aphelionand perihelion, respectively) is larger than the aster-oid’s gravitational acceleration (0.01–0.00005 mm/s2


Fig. 9. Hovering at the asteroid.

in a distance ranging from 5 to 50 km), so that the sail-craft is able to hover on artificial equilibrium surfacesin the hemisphere that is opposite to the Sun (Fig. 9).Those quasi-stationary hovering positions are unstablebut can be stabilized using a feedback control loop [14].Hovering near the asteroid, the (likely complex) grav-itational field is studied, so that a coarse gravitationalfield model can be determined. Thereafter, the landerwith the integrated Earth return capsule is separatedfrom the solar sail to go into closer orbit around theasteroid. While measuring the asteroid’s gravitationalfield with increasing accuracy, the orbit of the lander iscontinuously lowered until a safe landing trajectory canbe computed (some or all of those extensive computa-tions may be performed on Earth) and landing can beperformed.

For acquiring asteroid samples, an evolution of the“Mole” subsurface soil sampler (PLUTO—PlanetaryUnderground Tool) developed for the Beagle 2 Marslander of ESA’s 2003 Mars Express mission [15] is fore-seen (Fig. 10). This device, a slender cylinder of about30 cm in length with a pointed tip, achieves penetra-tion into soil-like materials with an internal hammer-ing mechanism driven by a single motor/gear actuator.With each shock, the medium surrounding the Mole ispartially displaced and compressed to allow an addi-tional forward motion of up to a few millimeters pershock, while a tether connecting the Mole to the landeris trailed behind for power supply of the mechanism,data transmission from internal Mole sensors, and to re-tract the device to the lander. Soil penetration depths ofseveral meters are feasible and have been demonstratedin ground testing prior to the Beagle 2 application ofthe system on Mars. Since the upper meters of even

Fig. 10. PLUTO system: qualification model (left side) and concep-tual drawing of asteroid sampling operations (right side).

small asteroids are generally believed to be composedof a regolith produced from billions of years of impactevents (including a continual flux of micrometeorites,cf. e.g. [16]), a soil sampling system—as opposed toa rock sampler—is a valid assumption for ENEAS-SR.The Mole’s operating principle is attractive because

1. acquisition of samples from below the immediatesurface is possible,

2. the overall system including a tether mechanism andsupporting elements weights less than 900 g, and

3. no reactive forces have to be accepted by the landerbecause of the tether-linking of the two elements.

However, for the self-penetration to occur, recoilfrom the forward hammering must be reacted by thesurrounding soil through friction along the Mole’souter surface. In a nearly weightless environment ason 1996FG3, skin friction between the Mole and thesoil is negligible due to its dependency on gravita-tional acceleration. Therefore, a modification to theMole design is foreseen such that during each shock,flukes that greatly increase friction with the soil to re-act shock recoil are deployed passively. Operationally,the Mole system offers the possibility to obtain severalsubsurface samples from different depths, either frommultiple Mole deployments if only one sample is takenat a time (as for PLUTO on Beagle 2) or from a single


deployment if a design with multiple sample chambersis used. The size of a given sample is in any case sev-eral tens of cubic-millimeters, which is fully sufficientfor analysis, even for rather crude in situ instrumentsas presently used in Mars landing missions.

The options presently considered for the Mole releaseare: ejection from the lander shortly before surface con-tact and/or release after landing and impression into thesurface. In both cases, due to the negligible gravity, theresulting reactive force on the lander must be controlledby the on-board chemical propulsion system. The lan-der would release the Mole from its holster-like guid-ing tube which is accommodated vertically between thelander underside and the surface. After sampling, thetether mechanism reels the Mole back into the holsterand the sample chamber is detached to be transferredinto the Earth return capsule.

After all sampling operations are finished, the lan-der brings the samples back to the hovering sailcraft.In this mission phase, the sailcraft is waiting edge-on(so that no SRP force is acting on the sail) at theL2 Lagrange point to assist the rendezvous betweenthe lander and the solar sail. Since 1996FG3 is abinary system, it would be interesting to land and ex-tract samples from both bodies, to investigate the originand the collisional evolution of the 1996FG3 system.Since the gravitational acceleration is very low nearthe asteroid and the required �V for the lander lessthan 10 m/s, a cold gas system with a propellant massof less than 4 kg is sufficient to perform all landeroperations.

After rendezvous with the hovering sailcraft, the re-docked ENEAS-SR solar sailcraft returns the sample toEarth. Finally, some hours before the arrival at Earth,the lander with the return capsule is separated from thesail, the capsule is spun-up to maintain the required en-try attitude, and injected into an Earth reentry trajec-tory, where it is decelerated by atmospheric friction andbreaking parachutes. The return trajectory is much fasterthan the transfer trajectory to 1996FG3 since no ren-dezvous is required at Earth. Thus, the sailcraft may ar-rive with a relatively large hyperbolic excess velocity ofabout 5.5 km/s. The gravitational acceleration of Earthadds another 11.2 km/s, so that the Earth entry veloc-ity may reach about

√5.52 + 11.22 km/s = 12.5 km/s.

This is slightly less than the entry velocity of NASA’sStardust capsule, which has the highest entry velocityof any Earth-returning mission up to date (12.9 km/s)[17,18].

To assess the capability of solar sail propulsion forthe ENEAS-SR mission, comparative mission analy-ses have been performed for two SEP systems, using

NASA’s NSTAR ion thruster and using a cluster ofthree NSTAR thrusters, respectively [10]. With a sin-gle thruster, the mission could be performed within atotal mission duration of 3.5 years. About 180 kg ofxenon would be required as propellant. The launch masswould, however, be 50% larger than for the solar sailoption, requiring eventually a more expensive launch.Using a cluster of three thrusters, the total mission du-ration would be further reduced to 1.9 years (this wouldnot only require a larger thrust but also about 20%more propellant). In this case, the launch mass wouldbe about twice that of the solar sail option. There-fore, if only the flight duration is considered, the so-lar sail option is clearly outperformed by the SEP op-tion, whereas, if only the launch costs are considered,the solar sail might be the favorable option. Thus, ifthe longer arising ground operation costs are lower thanthe savings in launch costs, and if the mission durationplays a subordinate role with respect to cost, the so-lar sail might be the better propulsion option for thismission.

5. Multiple NEA rendezvous and sample returnmissions (ENEAS+, ENEAS+SR)

For ENEAS-SR, a (70 m)2 solar sail with a mass of111 kg was presumed to accomplish a characteristic ac-celeration of 0.10 mm/s2 with a 295 kg payload. Withinthis section, it is investigated, whether—using the samesolar sail—a multiple NEA rendezvous mission can beperformed with the small ENEAS payload of 75 kg.Thismultiple NEA rendezvous mission is termed ENEAS+.Table 3 summarizes the ENEAS+ parameters.

For the given solar sail and the given payload,the characteristic acceleration of the ENEAS+ solarsailcraft is 0.218 mm/s2. To compare the solar sailoption with the SEP option, the target objects of theHera-mission, a proposed multiple NEA sample returnmission5 that employs a spacecraft with a cluster ofthree NSTAR thrusters to return samples from threedifferent NEAs to Earth within a mission duration ofabout 4.8 years (676 kg dry mass; 1102 kg total mass)have been adopted [19]. InTrance has been used to cal-culate the transfer times between the targets for variouslaunch dates to find the optimal target sequence. Thebest found sequence is illustrated in Figs. 11–13.

The optional trajectory from 1999AO10 to Earth,shown in Fig. 14 is not part of the actual ENEAS+

5 Mission proposal to NASA under the lead of the Arkansas-Oklahoma Center for Space and Planetary Science.


Table 3ENEAS+Sail area A (70 m)2





Fig. 11. ENEAS + trajectory option for Earth-2000AG6-leg.

Fig. 12. ENEAS trajectory option for 2000AG6-1989UQ-leg.

Fig. 13. ENEAS + trajectory option for 1989UQ-1999AO10-leg.

Fig. 14. ENEAS+SR trajectory option for 1999AO10-Earth-leg.

mission. Nevertheless, the trajectories are valid forany solar sailcraft that accomplishes a characteristicacceleration of 0.218 mm/s2. Using a larger solar sail(s = 139 m), this mission might be also performed withthe ENEAS-SR payload. With such a solar sailcraft,all three visited NEAs could be sampled, and the sam-ples could be returned to Earth within 10.1 years (thismission might be termed ENEAS+SR). Regarding thequestion, whether solar sail propulsion or SEP is supe-rior for such a mission, the same conclusions as in theprevious section can be drawn.


6. Summary and conclusions

It was shown that even with moderate-performancesolar sails of the first generation, challenging scientificmissions, like a sample return mission or a multiplerendezvous mission to near-Earth asteroids, are feasibleat relatively low cost. It was shown that a (70 m)2 solarsail with a specific weight of about 23 g/m2 is ableto transport a 300 kg-spacecraft (incl. a lander and asample return capsule) to a NEA and to return a sampleto Earth within 10 years. With the same solar sail, atriple NEA rendezvous mission with a 75 kg-payload isfeasible within 7.6 years, spending about 200 days ateach asteroid.

The obtained results demonstrate that near-term so-lar sailcraft are outperformed by the SEP option, ifonly the flight duration is considered, whereas, if onlythe launch costs are considered, the solar sail mightbe the favorable option. Thus, if the longer arisingground operation costs are lower than the savings inlaunch costs, and if the mission duration plays a sub-ordinate role with respect to cost, the solar sail mightbe the better propulsion option for the missions con-sidered within this paper. Nevertheless, on the way tomore advanced solar sailcraft, as they are required forhigh-�V missions, the development of solar sails withmoderate performance is an indispensable first steppingstone.

References

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http://www.uark.edu/misc/hera

multiple rendezvous and sample return missions to near-earth objects using solar sailcraft

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