Automated astronaut traverses with minimum metabolic workload: Accessing permanently shadowed regions near the lunar south pole

Ac a As onau ica 214 (2024) 324–342 A ailable online 14 Oc obe 2023 0094-5765/© 2023 The Au ho s. Published by Else ie L d on behal o IAA. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Au oma ed as onau a e ses wi h minimum me abolic wo kload: Accessing pe manen ly shadowed egions nea he luna sou h pole Eloy Pe˜ na-Asensio a , b , * , Jenni e Su he land c , d , P a eek T ipa hi e , Kashauna Mason , A hu Goodwin g , Valen in T. Bickel h , Da id A. K ing i a Depa amen de Química, Uni e si a Au ` onoma de Ba celona, Bella e a, Ca alonia, 08193, Spain b Ins i u de Ci` encies de l’Espai (ICE, CSIC), Campus UAB, C/ de Can Mag ans S/N, 08193, Ce danyola del Vall` es, Ca alonia, Spain c Ins i u Laue-Lange in, 71 A . des Ma y s, 38000, G enoble, F ance d Ins i u e o Ae onau ics and As onau ics, Technische Uni e si ¨ a Be lin, Ma chs . 12-14, 10587, Be lin, Ge many e Depa men o Ci il Enginee ing, Indian Ins i u e o Technology, Roo kee, U a akhand, 247667, India Depa men o Geology and Geophysics, Texas A&M Uni e si y, 400 Bizzell S ., College S a ion, TX, 77843, USA g Depa men o Ea h and En i onmen al Sciences, The Uni e si y o Manches e , Ox o d Rd., Manches e , M13 9PL, Uni ed Kingdom h Cen e o Space and Habi abili y, Uni e si y o Be n, Gesellscha ss . 6, 3012, Be n, Swi ze land i Luna and Plane a y Ins i u e, Uni e si ies Space Resea ch Associa ion, 3600 Bay A ea Bl d., Hous on, TX, 77058, USA ARTICLE INFO Keywo ds: A emis Pe manen ly shadowed egions Luna sou h pole As onau ABSTRACT The A emis explo a ion zone is a opog aphically complex impac -c a e ed e ain. S eep undula ing slopes pose a challenge o walking ex a ehicula ac i i ies (EVAs) an icipa ed o he A emis III and subsequen missions. Using 5 m/pixel Luna O bi e Lase Al ime e (LOLA) measu emen s o he su ace, an au oma ed Py hon pipeline was de eloped o calcula e a e se pa hs ha minimize me abolic wo kload. The ool combines a Mon e Ca lo me hod wi h a minimum-cos pa h algo i hm ha assesses cumula i e slope o e dis ances be ween a lande and s a ions, as well as be ween s a ions. To illus a e he unc ionali y o he ool, op imized pa hs o pe manen ly shadowed egions (PSRs) a e calcula ed a ound po en ial landing si es 001, nea by loca ion 001(6), and 004, all wi hin he A emis III ‘Connec ing Ridge’ candida e landing egion. We iden i ied 521 PSRs and compu ed (1) a e se pa hs o accessible PSRs wi hin 2 km o he landing si es, and (2) op imized descen s om hos c a e ims in o each PSR. Slopes a e limi ed o 15◦and p e iously iden i ied boulde s a e a oided. Su ace empe a u e, as onau body illumina ion, egoli h bea ing capaci y, and as onau - o-lande di ec iew a e simul aneously e alua ed. T a el imes a e es ima ed using Apollo 12 and 14 walking EVA da a. A o al o 20 and 19 PSRs a e accessible om si es 001 and 001(6), espec i ely, ou o which main ain slopes <10◦. Si e 004 p o ides access o 11 PSRs, albei wi h highe EVA wo kloads. F om he c a e ims, 94 % o PSRs can be accessed. All ound- ip a e ses om po en ial landing si es can be pe o med in unde 2 h wi h a cons an walk. T a e ses and descen s o PSRs a e compiled in an a las o suppo A emis mission planning. 1. In oduc ion The ini ial A emis explo a ion zone (AEZ) is a egion wi hin six deg ees la i ude o he luna sou h pole (Fig. 1). The Sun ci cumna i- ga es his egion nea he ho izon, p o iding nea -cons an illumina ion o he highes summi s [1–3]. Se e al o hese loca ions we e iden i ied as po en ial A emis landing si es [4], in pa because sola powe can be used o suppo a sus ainable p esence. As he Sun is wi hin a ew deg ees o he ho izon, he opog aphy o he impac -c a e ed e ain cas s long shadows. Some a eas a e pe manen ly shadowed egions (PSRs). As no ed decades ago [6], hese egions a e e y cold (<120 K) and may ap ola ile ma e ial like wa e ice. Such a eas could p o ide ano he esou ce o sus ained de elop- men o he luna su ace; wa e can be used o c ew consumables, adia ion shielding, and ocke p opellan . Cap u ed ola iles also o e impo an in o ma ion abou he o igin, deli e y, and e olu ion o ol- a ile subs ances in he Ea h-Moon sys em. In a s udy commissioned by NASA, he Na ional Resea ch Council (2007) [7] ecommended in- es iga ions o u u e c ewed and obo ic missions o (a) de e mine he composi ional s a e and dis ibu ion o he luna ola ile componen , (b) * Co esponding au ho . Depa amen de Química, Uni e si a Au ` onoma de Ba celona, Bella e a, Ca alonia, 08193, Spain E-mail add esses: [email p o ec ed], [email p o ec ed] (E. Pe˜ na-Asensio). Con en s lis s a ailable a ScienceDi ec Ac a As onau ica jou nal homepage: www.else ie .com/loca e/ac aas o h ps://doi.o g/10.1016/j.ac aas o.2023.10.010 Recei ed 8 May 2023; Recei ed in e ised o m 21 Augus 2023; Accep ed 10 Oc obe 2023 Ac a As onau ica 214 (2024) 324–342 325 de e mine he sou ces o luna pola ola iles, (c) unde s and he anspo , e en ion, al e a ion, and loss p ocesses expe ienced by ol- a ile ma e ials in luna PSRs, (d) unde s and he physical p ope ies o he ex emely cold pola egoli h, and (e) de e mine wha he cold pola egoli h e eals abou he ancien sola en i onmen . These a ge s a e inco po a ed in he A emis III science objec i es as a se ies o Goal 2 in es iga ions [4]. Those PSRs, and all p oposed A emis III candida e landing egions, occu wi hin a eldspa hic highland e ain ha p o ides oppo uni ies o add ess many o he NRC (2007) explo a ion science objec i es, i.e., o e alua e he bomba dmen his o y o he inne sola sys em; o sample a di e se sui e o luna c us al ocks; o s udy impac p ocesses; and o s udy egoli h p ocesses [7]. A key o mission success will be accessing p omising s a ions iden- i ied in p e-mission mapping. Owing o locally he e ogeneous slopes, la ge ele a ion changes, and low illumina ion, ex a ehicula ac i i ies (EVAs) may be challenging. Au oma ing he ini ial assessmen o a la ge numbe o po en ial a ge s can bene i he planning o hese a e ses. To il e he abundance o oppo uni ies and mo e e icien ly design ou es, we de eloped a compu a ional mapping ool o calcula ing a e se pa hs ha minimizes he me abolic wo kload on c ew. We demons a e i s u ili y by applying o he A emis III candida e landing egion ‘Connec ing Ridge’ and po en ial landing si es he ein. Po en ial landing si e 001 is along he idge be ween Shackle on and Henson c a e s [2,4]. In he icini y o si e 001, se en polygons we e iden i ied as sui able o he A emis III Human Landing Sys em’s (HLS) equi emen s o a su ace wi h a slope <8◦, ha a e a leas 100 m om s eepe slopes [5]. Among hose se en a eas, he la ges is designa ed 001(6). Si e 004 is on he im o Shackle on c a e . Si es 001, 001(6), and 004 a e used he e o de ine a egion o in e es (ROI) 18.5 ×16.2 km (~300 km 2 ) (Fig. 1). Tha ROI con ains se e al ypes o geologic a ge s [8–12] ha as- onau s can explo e o illumina e he his o y o he Moon, i s neighbo Ea h, and he inne Sola Sys em, while also e alua ing he dis ibu ion o icy esou ces [4,7]. To illus a e he applica ion o ou EVA planning ool we ocus on PSR a ge s, i s mapping PSR loca ions wi hin he egion and hen applying he ool o calcula e EVA ou es ha minimize me abolic wo kload. While we demons a e how he ool can be used o op imize as onau a e ses o PSRs, i can be applied o any o he geologic and explo a ion a ge s. 2. Geologic con ex The luna sou h pola egion is an impac -c a e ed su ace supe - imposed on he im o he Moon’s la ges impac basin, he Sou h Pole- Ai ken (SPA) basin [13]. The SPA basin- o ming e en , es ima ed a 4.25 o 4.39 Ga [14–16], gene a ed a se ies o massi s along i s ma gin, some o which ha e such high unobs uc ed ele a ions >1800 m ha hey a e exposed o sunligh up o ~85 % o he ime [1–3,17]. Al hough p i- ma ily eldspa hic highland e ain, edis ibu ed ma e ial exca a ed Fig. 1. Uppe le : pas c ewed su ace missions we e limi ed o equa o ial la i udes. Middle: P incipal c a e s wi hin he AEZ; he blue ec angle s addling Shackle on c a e delinea es he conside ed egion o in e es . Uppe igh : opog aphy o e laid on LOLA hillshade (5 m/pixel); black polygons indica e a LOLA illumina ion da a-de i ed PSR p oduc o ou pixels o mo e (60 m/pixel) [2], while inse ed polygons a e landing zones ha mee A emis III Human Landing Sys em slope equi emen s [5]. Da a c edi s: NASA/LROC/GSFC/ASU. (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he Web e sion o his a icle.) E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 326 om dep hs o 100 km du ing he impac [18] may also include con- ibu ions om he en i e c us al column o ano hosi e, oc oli e, no i e, and gabb o, plus uppe man le li hologies [19,20]. A se ies o p e-Nec a ian (e.g., Hawo h, 4.18 ±0.02 Ga; Shoemake , 4.15 ±0.02 Ga; Faus ini, 4.10 ±0.03 Ga), Nec a ian (e.g., de Ge lache, 3.9 ±0.1 Ga), and Imb ian (e.g., Sla e , 3.8 ±0.1 Ga; S e d up, 3.8 ± 0.1 Ga) age impac c a e s [21,22] u he ewo ked hose li hological componen s. Shackle on c a e was he las majo impac shaping he egion. I has an es ima ed age o 3.43+0.04 −0.05 Ga om c a e coun ing [23]. This ~21 km diame e by ~4.1 km deep ea u e exca a ed wo li hological uni s: a massi composed, in pa , o ano hosi e, o e lain by a leas one s a - i ied uni exposed on he c a e wall ha likely ep esen s successi e ejec a blanke s [11]. The A emis III ‘Connec ing Ridge’ candida e landing a ea is blan- ke ed by Shackle on impac ejec a ha may be ~150 m hick on he im [10], hinning wi h dis ance along he idge (Fig. 2). O bi al spec os- copy a a spa ial esolu ion o 1 km/pixel indica es he egion is domi- na ed by plagioclase [11], wi h he lowes FeO alues (~8–16 w %) in he AEZ ound in he a ea a ound Shackle on c a e (including si es 001 and 004) [11,24]. These FeO alues a e consis en wi h small amoun s o ma ic mine als ha a e no mally co-mingled wi h ano hosi e bu may also ep esen a con ibu ion om SPA impac mel in he egoli h co e ing he idge. Because he e ain encompassed by he AEZ is simila o, albei much olde han, he eldspa hic ma e ial o he Apollo 16 si e, we in e as onau s may a e se (and collec ) a su ace composed o ano hosi ic egoli h b eccias, agmen al b eccias, impac mel b eccias, and soils (Fig. 2), do ed wi h a la ge numbe o boulde s [8]. Obscu ed li hologies wi hin he PSR a e assumed om a s anda d model o c a e o ma ion and simula ion e o s [10,26–29]. The chemical and iso opic composi ions o c us al li hologies exposed nea he luna sou h pole (e. g., ano hosi e, no i e, oc oli e) may con ibu e o u he de eloping he luna magma ocean hypo hesis [7], and hei di e si y could help illumina e he e olu ion o he luna c us a om he Apollo si es. Impac mel s along he idge could span he ange om ha o he SPA basin o Shackle on impac e en s, p o iding an oppo uni y o be e cons ain he age o he oldes basin- o ming impac on he Moon, o es he luna ca aclysm hypo hesis, and assess he o bi ally-de e mined age o Shackle on o help calib a e luna c a e ch onology. Those c a e ing p ocesses p oduced he i egula su ace o he AEZ, including dep essions ha hos PSRs. O e geologic ime, wa e and o he ola iles anspo ed o he poles may ha e been apped in PSRs. The la ges deposi s o wa e ice could ha e been deli e ed by he oldes c a e - o ming e en s and inco po a ed wi hin hei ejec a blanke s, hen bu ied by subsequen ejec a [30,31]. Smalle PSRs accessible ia walking EVAs will ha e been p oduced by younge (<100 million yea s old) c a e ing p ocesses. Any ices wi hin hose PSRs will likely be domina ed by ola iles deli e ed by sola wind and impac ing mic ome eo i es. 3. Da a and me hods 3.1. Pa h- inde algo i hm Rou e design o EVAs has ypically been comple ed manually by geology expe s. Owing o ecen luna o bi al missions, opog aphic da a is now a ailable a high esolu ion (up o 5 m/pixel) o ele a ion Fig. 2. In e p e ed c oss-sec ion o he ‘Connec ing Ridge’ (cen e le ) and Shackle on c a e . Shackle on impac ejec a blanke s he idge. D awing upon he Apollo 16 landing si e, which also occu ed in a eldspa hic e ain, one in e s a se ies o li hologies (pic u ed) migh be ound in p oximi y o he ‘Connec ing Ridge’. Ele a ion and dis ances ex ac ed om LOLA and NAC da a. Pho og aphs cou esy o LPI Luna Sample A las and Washing on Uni e si y in S . Louis; sec ion de eloped om Re . [11]; SPA basin p o ile om Re . [25]. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 327 and slope. This accu acy allows he implemen a ion o minimum-cos calcula ion algo i hms o ob ain op imized a e ses ha educe bo h dis ance a eled and he isk om high slopes. Pa icula ly in he con ex o o e ou ing design, se e al e o s ha e been made o de elop algo i hms ha ind he op imal pa h be ween wo poin s on a map. G aph heo y o e s a solu ion o ind he sho es pa h be ween nodes in a ne wo k, which, o p ac ical pu poses, is de ined as he as e pixels ha comp ise a map. We b ie ly e iew he main al e na i es and highligh he ela i e s eng hs o he adop ed Dijks a solu ion. The me hod de eloped by Re . [32] inco po a es human in e en ion o ine- une he pa h and ensu e compliance wi h mission ules, whe e small adjus men s could ha e led o imp o ed a e ses, such as a oiding iola ions o he me abolic cos cons ain and enhancing is- ibili y and sun sco e. They no e ha es ima ing a low-ene gy di ec ion o a el mode is possible h ough he use o he di ec ional heigh -heigh co ela ion unc ion [33]. Howe e , his app oach does no explici ly sea ch o he minimum-cos pa h be ween wo poin s by e alua ing all possibili ies in an e icien manne like Dijks a’s algo i hm [34]. When planning in high-dimensional and dynamic en i onmen s, s ochas ic algo i hms a e commonly used. One such app oach is andom sampling-based planne s, such as p obabilis ic oadmaps (PRMs) [35] and apidly-explo ing andom ees (RRTs) [36], which wo k by sam- pling a p obabilis ic g aph o ind a pa h o he goal [37]. de eloped a a ian o RRTs, known as RRT*, ha inds asymp o ically op imal pa hs by upda ing edge connec ions. Howe e , sampling-based planne s can gene a e poo pa hs i many subop imal o undesi able s a es a e sampled, especially when compu a ion is limi ed. RRTs build a ee s uc u e by andomly sampling poin s in he sea ch space and con- nec ing hem o he nea es poin in he ee. They a e p obabilis ically comple e, meaning a solu ion will e en ually be ound i one exis s, bu he e is no gua an ee ha i will be op imal. In con as , Dijks a’s al- go i hm is a comple e algo i hm: i is gua an eed o ind he sho es pa h be ween wo poin s i one exis s, al hough his can be compu a- ionally expensi e when applied o high-dimensional o complex en i onmen s. Using a heu is ic, he g aph pa h sea ch algo i hm A* [37–39] inds a speci ic s a loca ion o he goal in a simila way o Dijks a’s algo i hm. Howe e , A* equi es mo e memo y space, as i s o es all gene a ed nodes and depends on he quali y o he heu is ic unc ion, which can a ec i s pe o mance and op imali y. Field D* [40] is a a ian o D*, an in o med inc emen al sea ch algo i hm [41] ha uses linea in e pola ion o gene a e smoo he pa hs in non-uni o m cos en i onmen s. Field D* is inc emen al, such ha i can euse p e ious calcula ions when he en i onmen changes, whe eas Dijks a’s algo i hm has o ecompu e e e y hing om sc a ch. As we did no conside a dynamic en i onmen , no eal- ime upda ing o obs acles o changes in opog aphy, we did no implemen D* amily algo i hms. Fo simplici y, and because EVAs du ing A emis III will be limi ed o 6 ±2 h [42], we ha e conside ed a ixed empo al ligh ing condi ion o a gi en da e, as opposed o o he ene gy budge -awa e app oaches [3, 43–45]. Conside ing hese di e en app oaches and echniques, we selec ed Dijks a’s algo i hm as he p ope solu ion o compu ing a e ses ha minimize he me abolic wo kload o a speci ied illumina ion condi ion. We es ablish ou c i e ion o minimum me abolic wo kload based on he assump ion ha he a e ses will be u ilized o ound ips, wi h each EVA in ol ing isi ing a single a ge . The e o e, ou p io i y is o iden i y pa hs ha s ike a balance be ween minimizing he accumu- la ed absolu e slope and achie ing he sho es dis ance possible. By p io i izing bo h la e ains and sho e ou es, we aim o op imize e iciency while educing he physical exe ion equi ed du ing he a e ses. We de eloped a Py hon pipeline called MoonPa h ha , gi en a s a ing poin , a maximum slope, and a dis ance h eshold, au oma i- cally compu es all op imized a e ses o nea by accessible PSRs. A he same ime, i also e alua es bea ing capaci y, empe a u e, as onau sunligh incidence ( o a gi en da e), a e se walking ime, and as onau - o-lande iew oppo uni y. 3.2. P ocessing pipeline The da a p ocessing pipeline equi es a se ies o baseline da a p oduc s, which we de eloped using p ima y and seconda y Luna Reconnaissance O bi e (LRO) da a p oduc s. The opog aphy o he egion is assembled using an enhanced 5 m/pixel LOLA da a p oduc [46] de i ed om LOLA Digi al Ele a ion Coun s (LDEC), a LOLA Digi al Ele a ion Model (LDEM), and a LOLA Digi al Slope Model (LDSM). The published geoloca ion unce ain y is ~10–20 cm ho izon ally and ~2–4 cm e ically o each pixel. No e, howe e , ha ~90 % o he 5 m/pixels a e in e pola ed, i.e., do no con ain physically measu ed da a. Fo isual inspec ion o he egion and o ob ain de ailed images o he PSRs, we use a 1 m/pixel mosaic o he sou h pola egion [47] which was gene a ed om he 0.5 m/pixel Luna Reconnaissance O bi e (LRO) Na ow Angle Came a (NAC) da a [48], o ho ec i ied using a 5 m/pixel DEM and egis e ed ho izon ally o he LOLA global DEM [49]. An assemblage o NAC images downloaded and calib a ed using In e- g a ed So wa e o Image s and Spec ome e s (ISIS) was also mosaiced o c ea e base maps. The da a was geo e e enced and mosaiced using ENVI and A cGIS 10.6 so wa e [50]. To de e mine he mean bolome ic b igh ness empe a u es, ~10 yea s o nadi -poin ing Di ine Radiome e Expe imen obse a ions we e compiled [51] om 7 IR channels o e a wa eleng h ange o 7.55 μ m–400 μ m. Fo he p esen s udy, we use he Le el 4 g idded 240 m/pixel Pola Cumula i e P oduc s desc ibed in Re . [52], ocused on he sou he n summe season as indica i e o minimum PSR ex en and o mo e a o able explo a ion condi ions a high la i ude. A bea ing capaci y map wi h 5 m/pixel esolu ion was p oduced ollowing [53] and a a ia ion o Hansen’s o mula. Because an analysis o Apollo and Lunokhod da a ecommended bea ing capaci ies o >7 kNm −2 [54], calcula ed a e ses a e subsequen ly es ic ed o hose su aces. An analysis o Apollo walking EVA speeds [55] was expanded wi h a new non-linea analysis using ansc ip s o Apollo 12 (EVA 2) and Apollo 14 (EVA 2) a e ses [56]. O hese wo missions, he la e co e ed e ain mo e akin o upcoming su aces and as onau s also hauled a Modula Equipmen T anspo e (MET), analogous o he ool ca /ca ie being designed o A emis III. The loca ions o PSRs we e mapped by applying a p ocess simila o ha o [2], who use 240 m/pixel LOLA da a, albei wi h he 5 m/pixel LOLA equi alen and he simpli ica ion o no conside ing backsca e ed (seconda y o e lec ed) illumina ion. The p ocess is also compa able o ha o [1,57], hough we do no conside he leng h o ime o illumi- na ion no ay acing, espec i ely. Candida e PSRs we e gene a ed using he A cGIS ’Hillshade’ unc ion on he 5 m/pixel LDEM p oduc . The simula ed Sun was a ied a ound 360◦azimu h in 0.5◦inc emen s a a maximum ele a ion o 2◦abo e he ho izon, a sui able a e age o ou egion as deduced using NASA JPL’s Moon T ek Sun Angle and JPL Ho izons [58,59]. The esul an illumina ion map was h esholded and il e ed o a eas o ze o illumina ion. We hen applied ou il e s. Fi s , wo au oma ed me hods: (1) emo ing small noisy PSRs <3 pixels in size, and (2) emo ing small poo ly de ined PSRs wi h <3 LOLA LDEC poin s inside hem. The emaining PSRs we e manually inspec ed and (3) compa ed wi h he 1 m/pixel NAC image mosaic, emo ing candi- da es wi hin illumina ed egions, o (4) emo ed i , when plo ing a- e ses, local sun epheme is o PSRs indica ed illumina ion in hei cen e s (as we gene a e he PSRs wi h a ixed Sun ele a ion alue, which could e u n inco ec esul s whe e his ele a ion inc eases). Addi- ionally, we also mapped PSRs up o 5◦sola ele a ion as his limi is mo e endu ing in e ms o po en ial accumula ion o apped ola iles, wi h possibili y o g ea e olumes, o pe haps di e en cha ac e is ics. On geological imescales, he axial il o he Moon — and hence sola E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 328 illumina ion a he poles — may ha e shi ed signi ican ly a e he Cassini S a e T ansi ion 2.5 Ga [60–62]. The 5 m/pixel LDEM used in ou s udy p esen s inhe en limi a ions, wi h app oxima ely 90 % o i s as e pixels being in e pola ed, lacking o iginal opog aphic heigh measu emen s [46]. To mi iga e he impac o hese limi a ions on he gene a ed PSRs, we assessed he pe cen age a ea o he LDEC as e wi hin each PSR con aining non-in e pola ed ele a ion da a poin s, ensu ing a minimum co e age o 5 % o all PSRs. PSRs wi h less han 5 % co e age o ewe han 3 LDEC ele a ion da a poin s we e au oma ically excluded om he analysis. Addi ionally, we manually emo ed PSRs ha con lic ed wi h he NAC image y, speci ically a ge ing hose si ua ed in illumina ed a eas. We used Dijks a’s algo i hm, as jus i ied, o p oduce a sho es -pa h ee om he s a ing poin (landing si e o c a e im) o he endpoin (PSR edge o cen e ), allowing bo h la e al and diagonal mo emen s be ween adjacen pixels [63,64]. The 5 m/pixel LDSM da a is employed as a cos map, using cumula i e slope as he op imiza ion me ic. The ‘bes ’ a e se is chosen by e alua ing he lowes cumula i e slope esul . The algo i hm in insically conside s dis ance and heigh . By u ilizing he LDSM as e as a cos map, he algo i hm ewa ds sho e pa hs wi h lowe slopes, as longe dis ances wi h lowe slopes o sho e dis ances wi h highe slopes would esul in a wo se cumula i e slope. Heigh is conside ed in he slope (as he cumula i e slope is assessed), he e o e a g ea e ele a ion change o e a se dis ance implies a highe slope (wo sening he cumula i e slope esul ). Gi en ha he g aph is ep esen ed as an adjacency ma ix, i.e., a egula and gapless s uc u e, he algo i hm e ec i ely balances he ade-o be ween dis ance and ele a ion change, esul ing in a e ses ha minimize he cumula i e slope and, consequen ly, he me abolic wo kload. Addi ionally, we included in o ou s udy he loca ions o isola ed boulde s iden i ied by Re . [8] in he icini y o si es 001 and 004. These ea u es we e manually mapped using high- esolu ion NAC images a app oxima ely 0.5–2 m esolu ion. The au ho s s a ed ha hey we e able o iden i y objec s ha spanned a leas 3 pixels, sugges ing a minimum size o 3 m o he mapped boulde s. Howe e , no speci ic in o ma ion ega ding he size o each boulde was collec ed. Addi- ionally [11], iden i ied wi hin ou ROI some o he la ges boulde s, which measu ed up o 30 m in diame e . Conside ing ha hese a e expec ed o be less common, we adop ed a ep esen a i e size o 5 m o each boulde . By imposing a size o a pixel (i.e., 5 ×5 m) o he boulde s in ou analysis, we e ec i ely cons ain he po en ial a e ses o a oid hese geological ea u es. This es ic ion is based on he unde s anding ha a e sing o e o a ound boulde s can pose challenges o as onau mobili y and may impede he e iciency o ex a ehicula ac i i ies. We adop h esholds o (1) encoun e ed slopes being <15◦, which is conse a i e because 20◦is conside ed a pe missible limi , and (2) he a hes dis ance o any a e se poin o he luna lande being no mo e han 2 km [65]. To ob ain a mo e na u al pa h close o how an as o- nau would walk, we smoo hed he slope map unde 5◦ou side c a e s, meaning slopes <5◦a e ea ed as he same alue. Fo he in e io o c a e s, we did no apply any smoo hing. Slopes g ea e han 15◦a e no o bidden bu highly penalized, as some a e ses mus pass h ough a ew high slope pixels. Fi s , we calcula ed he op imal pa h om he landing si e o each o he e ices ou lining he edge o he PSR. In his way, we ob ain he sho es a e se ea u ing he lowes cumula i e slope o he edge o a PSR. We hen calcula ed he op imal pa h om his edge poin o he PSR cen e . In addi ion, we de e mined he bes descen om any poin on he c a e im o he hos ed PSR ega dless o he landing si e o all PSRs in he ROI. This uses he same unc ion desc ibed abo e wi h an addi- ional s ep, as he op imal ini ial poin o lowes -cos descen is no known be o ehand. We pe o med a Mon e Ca lo simula ion by gene - a ing equally spaced (20 m) andom poin s on he pe ime e o he c a e o compu e he op imized descen om each poin . Subsequen ly, all cumula i e slope esul s ( o e e y im s a ing poin o e e y PSR edge) a e compa ed o ob ain he bes descen . Fig. 3 illus a es he op imized descen compu a ion p ocess. No e ha no all s a ing poin s ha e a iable pa h ( unca ed lines). Fig. 3. Illus a ion o he Mon e Ca lo echnique applied o compu e he op imal descen om he im o he cen e o he PSR. The mesh 3D model is a 5 m/pixel slope map o e lying a 5 m/pixel LOLA DEM. Randomly gene a ed s a ing poin s a e shown as la ge do s on he c a e edge. Colo ed a e ses a e used only o dis inguish di e en pa hs. The la ge mesh has 5x e ical exagge a ion. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 329 Fig. 4. Le : An illus a ed example o he coas line pa adox, whe e he dis ance be ween wo poin s dec eases wi h inc easing pixel size. Blue and g een lines show wo di e en sample s ep sizes used o smoo hing, wi h aliasing-like beha io o he poo ly op imized s ep size. Righ : Augmen ed Dickey-Fulle es applied o he polynomial i de ia ion o he dis ance as a unc ion o he pixel s ep. (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he Web e sion o his a icle.) Fig. 5. Top-le : Ele a ion map (5 m/pixel) o he ROI wi h 20 m con ou s, wi h po en ial landing si es 001 and 004 (black c osses) bo h loca ed in a eas o high ele a ion. Top- igh : Slope map gene a ed om 5 m/pixel LDEM, wi h po en ial landing si es 001 and 004 bo h loca ed on a eas o low slope. Bo om-le : NAC image y was mosaiced using maximum illumina ion o pixels. Black a eas co ela e wi h a eas o poo illumina ion and/o pe manen shadow. Bo om- igh : Bea ing capaci y map gene a ed using LDSM da a. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 330 Fo he as onau body sunligh incidence calcula ion ( o which we will hence o h e e o as as onau illumina ion, ha is, he body a ea pe cen age ha is illumina ed by di ec sunligh ), we chose as a case s udy he mon h o maximum sola ele a ion (o subsola la i ude) o 2025 a landing si e 001, i.e., he mos a o able mon h in e ms o gene al e ain illumina ion condi ions. Decembe is he mon h o 2025 when he Sun eaches i s highes ele a ion (2.1◦on he 16 h, o he ROI. In con as , on 31 Decembe he Sun ele a ion is 0.8◦, ep esen ing he wo s illumina ion condi ion o he mos illumina ed mon h o 2025). The posi ion o he Sun is que ied o JPL Ho izons epheme ides [66]. We selec hese wo days o e alua e he ull ange o a e se illumina ion p ope ies. We es ima ed when he analyzed illumina ion condi ions will be epea ed up o 2029, meaning he ob ained esul s a e also applicable o speci ic days in subsequen yea s. Illumina ion condi ions on Decembe 16, 2025 will occu again on No embe 6, 2026, Oc obe 26, 2027, and Oc obe 14, 2028, while he Sun posi ion on Decembe 31, 2025 will be he same on Oc obe 23, 2026, Oc obe 12, 2027, and Sep embe 1, 2028. Gi en ha low sola illumina ion angles cas long shadows, his ype o calcula ion becomes signi ican o assess empe a u e a ia ions an as onau may be exposed o. To p ope ly compu e he pe cen age o an as onau ’s body ha would be illumina ed, we de eloped a bespoke ay acing code. Using epheme is om JPL Ho izons, we de e mined he local Sun posi ion o e e y pixel and ay aced om each pixel o he Sun. Sunligh is p ojec ed on o he luna su ace o e alua e i he ele a ion o he e ain is highe han he ay. I he line o sigh is in e sec ed by opog aphy, he ay is blocked, and he pixel does no ecei e di ec sunligh om his di ec ion. We epea ed he p ocess a 20 cm in e als up o a modeled as onau heigh o 2 m o calcula e he pe cen age o he as onau ’s body in sunligh . Analogous o he as onau illumina ion calcula ion, we ay- aced he di ec iew o he Space X A emis III HLS window (40 m high [67]) om he a e ses. Fo each s ep we checked he pe cen age o an as onau ’s body (again, om 0 m o 2 m, in 20 cm in e als) in isual con ac wi h he lande . This ea u e could be o conside able assis ance o guide as onau s du ing hei EVAs in absence o geoloca ion sys ems, bo h o sel -guiding and o ecei e di ec ions om he HLS. Howe e , i would be impossible o main ain eye con ac i he Sun is di ec ly behind he lande . We also add ess his Sun iew o ien a ion- ela ed p oblem by compu ing he angula dis ance be ween he as onau - o-lande line o sigh and he Sun posi ion. In his way, 0◦means ha he line o sigh coincides head-on wi h he Sun and 180◦indica es he Sun is di ec ly behind he iew. Rega ding dis ance compu a ion, we emphasize a p oblem de i ed om he so-called coas line pa adox. The calcula ed a e se o each PSR does no ha e a well-de ined leng h, as dis ance calcula ions depend on he pixel size o he map, beha ing in his way as a ac al dimension issue [68]: he la ge he pixel size is on a map, he smalle he compu ed dis ance will be (Fig. 4 le ). In addi ion, as he minimum-cos pa h al- go i hm is es ic ed o la e al and diagonal mo ion be ween adjacen pixels, his mo ion will di e om pe o med as onau pa hs which a e expec ed o be mo e di ec and hus sho e . Smoo hing is needed o accoun o es ic i e pixel mo ions and o emo e noisy a ia ions inhe en in he slope map ha o e es ima e he expec ed pa h leng h. We smoo h by sampling a e se pixels a an op imized s ep-spacing, which mus comp omise be ween small spacing (including noisy pa h mo ions) and la ge sample spacing (missing impo an pa h Fig. 6. Tempe a u e maps o he ROI gene a ed using Le el 4 g idded 240 m/pixel Pola Cumula i e P oduc s om Di ine , co e ing he luna sou he n summe du ing a 10-yea pe iod. Po en ial landing si es 001 and 004 a e labeled. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 331 in o ma ion). We sea ched o he la ges pixel s ep be o e signi ican a e se ea u es a e o e looked, which p oduces no able a ia ions in he dis ance wi h small changes. We es ima ed his sampling in e al o smoo hing o gene a e he minimum ealis ic dis ance by inc easing he pixel size s ep un il a non-s a iona y s a e is eached. An augmen ed Dickey-Fulle es [69] allows he s a iona y end o he pa h o be analyzed wi h a con idence le el o 99 %, e alua ing he de ia ion o a polynomial i wi h a leas R 2 =0.8 (Fig. 4 igh ). A s aigh -line a- e se will always esul in he same compu ed dis ance ega dless o he pixel size, whils a meande ing pa h will a y d as ically a some pixel-smoo hing s eps based on he cu e shapes. 4. Da a p oduc s and esul s 4.1. Base maps Fig. 5 displays he base maps de i ed om LOLA da a elabo a ed in Sec ion 3: 5 m/pixel ele a ion wi h 20 m con ou s, 5 m/pixel slope de i ed om LDEM, NAC mosaic, and bea ing capaci y gene a ed using LDSM. Bea ing capaci y a ies om ~0 o 13.2 kN/m 2 , in ag eemen wi h maps gene a ed o he Shackle on-Hansen idge egion encom- passing po en ial landing si es 001 and 004 [5]. F om 240 m/pixel summe Di ine da a (de ined as whe e he sub- sola la i ude is in he Sou he n hemisphe e a noon local ime), we gene a ed a e age, minimum, and maximum empe a u e maps, as well as local ime maps o e alua e bo h he lowes PSR empe a u e and highes empe a u e encoun e ed du ing a a e se. O e a 6-h EVA, o ins ance, only 12 luna minu es elapse (no malizing a luna day o 29.53 Ea h days o 24 h), so sola posi ion ela i e o a ixed poin is assumed cons an o e he du a ion o a a e se. Whe eas seasonali y has li le in luence on su ace empe a u es a low o mid-la i udes, he in e play o illumina ion g azing angles in pola egions wi h opog aphy exe s a signi ican in luence on su ace empe a u e wi h he posi ion o he subsola la i ude (Fig. 6). 4.2. Apollo a e se speed By compa ing maps o aced a e ses o ansc ip s om Apollo 12 and 14 (bo h EVA 2) missions, way poin s we e gene a ed ha link disc e e imes wi h spa ial posi ions o a gi en as onau (Figs. 7 and 8). Only way poin s sepa a ed by >25 m we e used o ensu e a e se speed calcula ions encompass pe iods ha we e p edominan ly walking, a he han hose in ol ing geological ac i i ies a s a ions o sho bu s s o speed be ween poin s o in e es . Apollo 12 (EVA 2) had egula s ops, and a e ages con ain he ime o geological obse a ions and pho og aphs. Apollo 14 (EVA 2) was cha ac e ized by 12 s a ions o da a collec ion sepa a ed by long walks. Da a collec ed on as onau walking speed p o ide ope a ional imes included in a e se models calcula ed o his ROI. T a e se coo dina es and way poin s summa ies o bo h Apollo EVAs can be ound in he supplemen a y ma e ial (SP-A). The Apollo 12 EVA 2 a e se las ed app oxima ely 2 h and 45 min, o which only ~30 min we e spen walking [56]. The as onau s co e ed almos 1.6 km, eaching a dis ance o ~400 m om he lande , including a 100 m segmen a 14◦inclina ion. The EVA eco e ed ~18 kg o geological samples, including co es (~60 cm deep), and ocks om enched (~20 cm) ma e ial [71]. Fo his EVA, we calcula ed an a e age speed o 0.56 ±0.39 ms −1 o 2.02 ±1.40 kmh −1 (mean±1 σ , No =25), and a median speed o 0.42 ms −1 o 1.51 kmh −1 . The Apollo 14 EVA 2 a e se las ed ~4.5 h, du ing which ime he as onau s co e ed ~2.9 km, eaching a dis ance ~1.4 km om he lande . App oxima ely 22 kg o geological samples we e eco e ed, including co e (~60 cm deep) and enched (~30 cm) ma e ial [71]. Due o challenges walking o e he ugged e ain, he c ew ell behind schedule; no ably, he MET p o ed di icul o anspo and o po ions o he EVA he c ew eso ed o ca ying a he han pulling i [56]. A summa y able o his EVA om Biomedical Resul s o Apollo [55] in- cludes a e se speed be ween s a ions, a e aging 0.81 ±0.38 ms −1 o 2.92 ±1.37 kmh −1 (mean±1 σ , No =13). Because a linea dis ance is used, his is an unde es ima e. We calcula e a mean speed o 0.84 ± 0.48 ms −1 o 3.02 ±1.73 kmh −1 (mean±1 σ , No =35) and a median o 0.62 ms −1 o 2.23 kmh −1 . Plo ing speed agains slope (in he di ec ion o he a e se) in- dica es a weak posi i e co ela ion o noisy da a poin s (y = −0.01x+0.75; R 2 =0.03; uni s in ms −1 ), po en ially sugges ing dec easing speed wi h a highe slope. Because Apollo 14 in ol ed he cumbe some MET, his end ep esen s a e se speed wi h a MET al e na ed be ween wo as onau s, whe e he posi ion o only one o he pai was acked. We ake o wa d an a e age o he h ee calcula ions, e u ning a mean speed o 0.74 ms −1 o 2.66 kmh −1 . 4.3. Mapped PSRs and boulde s 521 PSRs we e mapped wi hin he ~300 km 2 ROI encompassing he im o Shackle on c a e and he Shackle on-Henson idge, inco po- a ing hose analyzed by Re . [72] de i ed om he 60 m p oduc by Re . [2]. The mean PSR a ea is 11,975 m 2 , wi h a signi ican ly skewed dis ibu ion (median =1075 m 2 , s anda d de ia ion =100,859 m 2 ) owa ds smalle sizes. PSRs ange om 75 m 2 o 2,144,700 m 2 , o be- ween ~10 m and ~1600 m in diame e . The PSRs wi hin he ROI ha e an a e age LDEC co e age o 11.22 ±2.68 % (mean±1 σ , No =521), wi h a median o 10.8 %. Geoloca ion unce ain y o he 5 m/pixel DEM is ~10–20 cm ho izon ally and ~2–4 cm e ically o each pixel [17, Fig. 7. Top: Apollo 12 EVA 2, wi h ie poin s (block do s) c ea ed by linking imes acknowledged in o icial ansc ip s wi h geological obse a ions and p ocedu es comple ed on he su ace. Bo om: Repea ed o Apollo 14 EVA 2. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 332 Fig. 8. Combined a e se me ics om Apollo 12 EVA 2 (blue) and Apollo 14 EVA 2 ( ed and yellow) de i ed om Luna Su ace Jou nal ansc ip s and Biomedical Resul s o Apollo (1975) [70]. (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he Web e sion o his a icle.) Fig. 9. Le : Dis ibu ion o PSRs wi hin he ROI, o e laid on NAC 1 m/pixel image y. Ci cles deno e c a e s wi h po en ial o hos a eas o pe manen shadow. Righ : PSR edge dis ibu ion wi hin he ROI, o e laid on a slope map gene a ed om 5 m/pixel LDEM wi h ele a ion con ou lines. Diamonds ep esen boulde s. The 2 km adius pe ime e is depic ed. Da a c edi s: NASA/LROC/GSFC/ASU. Table 1 Table showing he numbe o a e ses o PSRs wi h slopes below 5, 10, and 15◦. PSRs accessible ROI <15◦slope 490 (94 %) <10◦slope 351 (67 %) <5◦slope 74 (14 %) Table 2 Table showing he numbe o a e ses o PSRs wi hin 2 km adially o po en ial landing si es 001 and 004 and loca ion 001(6) wi h slopes below 10◦and 15◦. 001 001(6) 004 # o PSRs 22 20 10 <15◦slope 20 19 10 <10◦slope 4 4 0 E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 339 Fig. A2. Example o he ables associa ed wi h each a e se wi h gene al alues calcula ed, and he 2 m/pixel NAC image and a de ailed 2D map o he hos c a e . E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 340 Fig. A3. Example o he ables associa ed wi h each PSR op imal descen wi h gene al alues calcula ed, and a de ailed 2D and 3D image o he hos c a e . Appendix B. Supplemen a y da a Supplemen a y da a o his a icle can be ound online a h ps://doi.o g/10.1016/j.ac aas o.2023.10.010. Re e ences [1] D.B.J. Bussey, J.A. McGo e n, P.D. Spudis, C.D. Neish, H. Noda, Y. Ishiha a, S. A. Sø ensen, Illumina ion condi ions o he sou h pole o he Moon de i ed using Kaguya opog aphy, Ica us 208 (2010) 558–564, h ps://doi.o g/10.1016/j. ica us.2010.03.028. [2] E. Maza ico, G.A. Neumann, D.E. Smi h, M.T. Zube , M.H. To ence, Illumina ion condi ions o he luna pola egions using LOLA opog aphy, Ica us 211 (2011) 1066–1081, h ps://doi.o g/10.1016/j.ica us.2010.10.030. [3] E.J. Speye e , S.J. Law ence, J.D. S opa , P. Gl¨ ase , M.S. Robinson, B.L. Jolli , Op imized a e se planning o u u e pola p ospec o s based on luna opog aphy, Ica us 273 (2016) 337–345, h ps://doi.o g/10.1016/j. ica us.2016.03.011. [4] NASA, The A emis III Science De ini ion Team Repo , 2020. h ps://www.nasa. go /si es/de aul / iles/a oms/ iles/a emis-iii-science-de ini ion- epo -1204 2020c.pd . (Accessed 26 July 2022). [5] D.A. K ing, V.T. Bickel, A.L. Fagan, L. Gaddis, H. Hiesinge , J.M. Hu ado, T. Huning, L. M, C.A. Loope , G.R. Osinski, S.M. Tikoo, C.H. an de Boge , Assessing landing and EVA op ions in he icini y o po en ial A emis landing si e 001, in: NASA Explo , Sci. Fo um, Boulde , 2022. h ps://dl.ai able.com/.a ach men s/83b4edad0 398cd4489452d64ebdab18/e50 092b/K ingE Al_NESF2022 _Si e001LandingAndEVAOp ions_ inal.pd ? s=1658976045&use Id=us lVLEMF3U1302KF&cs=2172c1 4355b4c0a. [6] K. Wa son, B.C. Mu ay, H. B own, The beha io o ola iles on he luna su ace, J. Geophys. Res. 66 (1961) 3033–3045, h ps://doi.o g/10.1029/ jz066i009p03033. [7] N.R. Council, The Scien i ic Con ex o Explo a ion o he Moon, The Na ional Academies P ess, Washing on, DC, 2007, h ps://doi.o g/10.17226/11954. [8] S.J. Boazman, J. Shah, Ha ish, A.J. Gaw onska, S.H. Halim, A.V. Sa yakuma , C. M. Gilmou , V.T. Bickel, N. Ba e , D.A. K ing, The dis ibu ion and accessibili y o geologic a ge s nea he luna sou h Pole and candida e A emis landing si es, Plane . Sci. J. 3 (2022) 275, h ps://doi.o g/10.3847/PSJ/ACA590. [9] H. Be nha d , M.S. Robinson, A.K. Boyd, Geomo phic map and science a ge iden i ica ion on he Shackle on-de Ge lache idge, Ica us 379 (2022), 114963, h ps://doi.o g/10.1016/J.ICARUS.2022.114963. [10] S.H. Halim, N. Ba e , S.J. Boazman, A.J. Gaw onska, C.M. Gilmou , Ha ish, K. McCanaan, A.V. Sa yakuma , J. Shah, D.A. K ing, Nume ical modeling o he o ma ion o Shackle on c a e a he luna sou h pole, Ica us 354 (2021), h ps:// doi.o g/10.1016/j.ica us.2020.113992. [11] A.J. Gaw onska, N. Ba e , S.J. Boazman, C.M. Gilmou , S.H. Halim, Ha ish, K. McCanaan, A.V. Sa yakuma , J. Shah, H.M. Meye , D.A. K ing, Geologic con ex and po en ial EVA a ge s a he luna sou h pole, Ad . Sp. Res. 66 (2020) 1247–1264, h ps://doi.o g/10.1016/j.as .2020.05.035. [12] D.A. K ing, Luna Sou h Pole geology: p epa ing o a se en h luna landing, in: NASA Explo . Sci. Fo um 2019, 2019. [13] P.J. Adams, E. S ua -Alexande , Geologic map o he cen al a side o he Moon, Shee I-1047. 1:5 000 000 (1978), h ps://doi.o g/10.2307/634119. [14] I. Ga ick-Be hell, K. Miljko i´ c, H. Hiesinge , C.H. an de Boge , M. Laneu ille, D. L. Shus e , D.G. Ko ycansky, T oc oli e 76535: a sample o he Moon’s Sou h Pole- Ai ken basin? Ica us 338 (2020), 113430 h ps://doi.o g/10.1016/J. ICARUS.2019.113430. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 341 [15] H. Hiesinge , C.H. Van De Boge , J.H. Pascke , L. Funcke, L. Giacomini, L. R. Os ach, M.S. Robinson, How old a e young luna c a e s? J. Geophys. Res. Plane s. 117 (2012) h ps://doi.o g/10.1029/2011JE003935, 0–10. [16] A. Mo bidelli, S. Ma chi, W.F. Bo ke, D.A. K ing, A saw oo h-like imeline o he i s billion yea s o luna bomba dmen , Ea h Plane Sci. Le . 355 (356) (2012) 144–151, h ps://doi.o g/10.1016/j.epsl.2012.07.037. [17] P. Gl¨ ase , F. Schol en, D. De Rosa, R. Ma co Figue a, J. Obe s , E. Maza ico, G. A. Neumann, M.S. Robinson, Illumina ion condi ions a he luna sou h pole using high esolu ion digi al e ain models om lola, Ica us 243 (2014) 78–90, h ps:// doi.o g/10.1016/j.ica us.2014.08.013. [18] R.W.K. Po e , G.S. Collins, W.S. Kie e , P.J. McGo e n, D.A. K ing, Cons aining he size o he Sou h Pole-Ai ken basin impac , Ica us 220 (2012) 730–743, h ps:// doi.o g/10.1016/j.ica us.2012.05.032. [19] D.J. Law ence, A ale o wo poles: owa d unde s anding he p esence, dis ibu ion, and o igin o ola iles a he pola egions o he Moon and Me cu y, J. Geophys. Res. Plane s. 122 (2017) 21–52, h ps://doi.o g/10.1002/ 2016JE005167. [20] M. Lemelin, P.G. Lucey, A. Camon, Composi ional maps o he luna pola egions de i ed om he kaguya spec al p o ile and he luna o bi e lase al ime e da a, Plane . Sci. J. 3 (2022) 63, h ps://doi.o g/10.3847/psj/ac532c. [21] A.N. Deu sch, J.W. Head, G.A. Neumann, Analyzing he ages o sou h pola c a e s on he Moon: implica ions o he sou ces and e olu ion o su ace wa e ice, Ica us 336 (2020), h ps://doi.o g/10.1016/j.ica us.2019.113455. [22] A.R. Tye, C.I. Fasse , J.W. Head, E. Maza ico, A.T. Basile sky, G.A. Neumann, D. E. Smi h, M.T. Zube , The age o luna sou h ci cumpola c a e s Hawo h, Shoemake , Faus ini, and Shackle on: implica ions o egional geology, su ace p ocesses, and ola ile seques a ion, Ica us 255 (2015) 70–77, h ps://doi.o g/ 10.1016/j.ica us.2015.03.016. [23] D.A. K ing, G.Y. K ame , D.B.J. Bussey, D.M. Hu ley, A.M. S ickle, C.H. an de Boge , P ominen olcanic sou ce o ola iles in he sou h pola egion o he Moon, Ad . Sp. Res. 68 (2021) 4691–4701, h ps://doi.o g/10.1016/J. ASR.2021.09.008. [24] K. Donaldson Hanna, M. Wya , C. Pie e s, L. Cheek, P. Isaacson, D. Paige, B. G eenhagen, Di ine and Moon mine alogy mappe in eg a ed obse a ions o plagioclase- ich egions on he Moon, in: Annu. Luna Plane . Sci. Con ., 42nd, 2011. [25] P.B. James, D.E. Smi h, P.K. By ne, J.D. Kendall, H.J. Melosh, M.T. Zube , Deep s uc u e o he luna sou h Pole-ai ken basin, Geophys. Res. Le . 46 (2019) 5100–5106, h ps://doi.o g/10.1029/2019GL082252. [26] P.D. Spudis, B. Bussey, J. Plescia, J.-L. Josse , S. Beau i e, Geology o Shackle on c a e and he sou h pole o he Moon, Geophys. Res. Le . 35 (2008), L14201, h ps://doi.o g/10.1029/2008GL034468. [27] M. Hi abayashi, B.A. Howl, C.I. Fasse , J.M. Sode blom, D.A. Min on, H.J. Melosh, The ole o b eccia lenses in egoli h gene a ion om he o ma ion o small, simple c a e s: applica ion o he Apollo 15 landing si e, J. Geophys. Res. Plane s. 123 (2018) 527–543, h ps://doi.o g/10.1002/2017JE005377. [28] J.W. Head, L. Wilson, Gene a ion, ascen and e up ion o magma on he Moon: new insigh s in o sou ce dep hs, magma supply, in usions and e usi e/explosi e e up ions (Pa 2: p edic ed emplacemen p ocesses and obse a ions), Ica us 283 (2017) 176–223, h ps://doi.o g/10.1016/j.ica us.2016.05.031. [29] H. L , Q. He, X. Chen, P. Han, Nume ical simula ion o impac c a e o ma ion and dis ibu ion o high-p essu e polymo phs, Ac a As onau . 203 (2023) 169–186, h ps://doi.o g/10.1016/j.ac aas o.2022.11.048. [30] K.M. Cannon, A.N. Deu sch, J.W. Head, D.T. B i , S a ig aphy o ice and ejec a deposi s a he luna Poles, Geophys. Res. Le . 47 (2020), h ps://doi.o g/ 10.1029/2020GL088920. [31] C.J.T. Udo icic, K.R. F izzell, G.R.L. Kodika a, M. Kopp, K.M. Luchsinge , A. Made a, M.L. Meie , T.G. Paladino, R.V. Pa e son, F.B. W oblewski, D.A. K ing, Bu ied ice deposi s in luna pola cold aps we e dis up ed by ballis ic sedimen a ion, J. Geophys. Res. Plane s (2023), e2022JE007567, h ps://doi.o g/ 10.1029/2022JE007567. [32] C.E. Ca , D.J. Newman, K.V. Hodges, Geologic a e se planning o plane a y EVA, SAE Tech. Pap. (2003), h ps://doi.o g/10.4271/2003-01-2416. [33] P.S. Dodds, D.H. Ro hman, Scaling, uni e sali y, and geomo phology, Annu. Re . Ea h Plane Sci. 28 (2000) 571–610, h ps://doi.o g/10.1146/annu e . ea h.28.1.571. [34] E.W. Dijks a, A no e on wo p oblems in connexion wi h g aphs, Nume . Ma h. 1 (1959) 269–271, h ps://doi.o g/10.1007/BF01386390. [35] L.E. Ka aki, P. ˇ S es ka, J.C. La ombe, M.H. O e ma s, P obabilis ic oadmaps o pa h planning in high-dimensional con igu a ion spaces, IEEE T ans. Robo . Au om. 12 (1996) 566–580, h ps://doi.o g/10.1109/70.508439. [36] S. LaValle, Rapidly-explo ing Random T ees: A New Tool o Pa h Planning, 1998. [37] S. Ka aman, M.R. Wal e , A. Pe ez, E. F azzoli, S. Telle , Any ime mo ion planning using he RRT, P oc. - IEEE In . Con . Robo . Au om. (2011) 1478–1483, h ps:// doi.o g/10.1109/ICRA.2011.5980479. [38] S. Koenig, M. Likhache , A. Inc emen al, Ad . Neu al In . P ocess. Sys . 14 (2002) 1539-1546. h ps://p oceedings.neu ips.cc/pape /2001/hash/a591024321c5e2b dbd23ed35 0574dde-Abs ac .h ml. (Accessed 3 Ap il 2023). [39] S. Koenig, M. Likhache , A. Inc emen al, *. InAd ances in Neu al In o ma ion P ocessing Sys ems, 2002. [40] D. Fe guson, A. S en z, Field D*: an In e pola ion-Based Pa h Planne and Replanne , ol. 28, Sp inge T ac s Ad . Robo ., 2007, h ps://doi.o g/10.1007/ 978-3-540-48113-3_22. [41] A. S en z, Op imal and e icien pa h planning o unknown and dynamic en i onmen s, In . J. Robo Au om. 10 (1995) 89–100. h ps://ieeexplo e.ieee. o g/abs ac /documen /351061/?casa_ oken=0uSlmzeHsdwAAAAA: pzA7K7h g8T w uoh8aXohb_KYblyX0l_ P U5y2uGQ U-udzhocaPJUD3iHZ4Ri9Oxw-43DkQ. (Accessed 3 Ma ch 2023). [42] NASA, Human Landing Sys em Concep o Ope a ions, 2019. [43] C. Cunningham, J. Ama o, H.L. Jones, W.L. Whi ake , Accele a ing ene gy-awa e spa io empo al pa h planning o he luna poles, in: P oc. - IEEE In . Con . Robo . Au om., 2017, pp. 4399–4406, h ps://doi.o g/10.1109/ICRA.2017.7989508. [44] P.A. Plonski, P. Tokeka , V. Isle , Ene gy-e icien pa h planning o sola -powe ed mobile obo s, J. F. Robo . 30 (2013) 583–601, h ps://doi.o g/10.1002/ ob.21459. [45] J. Schlu z, E. Messe schmid, In eg a ing ad anced mobili y in o luna su ace explo a ion, Ac a As onau . (2012) 15–24, h ps://doi.o g/10.1016/j. ac aas o.2012.01.005. [46] M.K. Ba ke , E. Maza ico, G.A. Neumann, D.E. Smi h, M.T. Zube , J.W. Head, Imp o ed LOLA ele a ion maps o sou h pole landing si es: e o es ima es and hei impac on illumina ion condi ions, Plane . Space Sci. 203 (2021), h ps://doi. o g/10.1016/j.pss.2020.105119. [47] B. Day, E. Law, NASA’S Moon T ek: ex ending capabili ies o luna mapping and modeling, in: COSPAR Sci. Assem, 2018, pp. 11–18. B3.1. [48] M.S. Robinson, S.M. B ylow, M. Tschimmel, D. Humm, S.J. Law ence, P.C. Thomas, B.W. Dene i, E. Bowman-Cisne os, J. Ze , M.A. Ra ine, M.A. Caplinge , F. T. Ghaemi, J.A. Scha ne , M.C. Malin, P. Mahan i, A. Ba els, J. Ande son, T. N. T an, E.M. Eliason, A.S. McEwen, E. Tu le, B.L. Jolli , H. Hiesinge , Luna econnaissance o bi e came a (LROC) ins umen o e iew, Space Sci. Re . 150 (2010) 81–124, h ps://doi.o g/10.1007/s11214-010-9634-2. [49] R.V. Wagne , E.J. Speye e , M.S. Robinson, LROC eam, new mosaicked da a p oduc s om he LROC eam, 46 h Luna Plane , Sci. Con . 46 (2015) 1473. [50] ESRI, ENVI EX use ’s guide, Es i (2009) 275. [51] D.A. Paige, M.C. Foo e, B.T. G eenhagen, J.T. Scho ield, S. Calcu , A.R. Vasa ada, D.J. P es on, F.W. Taylo , C.C. Allen, K.J. Snook, B.M. Jakosky, B.C. Mu ay, L. A. Sode blom, B. Jau, S. Lo ing, J. Bulha owski, N.E. Bowles, I.R. Thomas, M. T. Sulli an, C. A is, E.M. De Jong, W. Ha o d, D.J. McCleese, The luna econnaissance o bi e di ine luna adiome e expe imen , Space Sci. Re . 150 (2010) 125–160, h ps://doi.o g/10.1007/s11214-009-9529-2. [52] J.P. Williams, B.T. G eenhagen, D.A. Paige, N. Scho gho e , E. Se on-Nash, P. O. Hayne, P.G. Lucey, M.A. Siegle , K.M. Aye, Seasonal pola empe a u es on he Moon, J. Geophys. Res. Plane s. 124 (2019) 2505–2521, h ps://doi.o g/10.1029/ 2019JE006028. [53] V.T. Bickel, D.A. K ing, Luna sou h pole boulde s and boulde acks: implica ions o c ew and o e a e ses, Ica us 348 (2020), 113850, h ps://doi.o g/10.1016/ J.ICARUS.2020.113850. [54] W.D. Ca ie III, G.R. Olhoe , W. Mendell, Physical p ope ies o he luna su ace, in: Luna Sou ceb., 1991, pp. 522–530. [55] J.M. Waligo a, D.J. Ho igan, Me abolism and hea dissipa ion du ing Apollo EVA pe iods, in: Biomed. Resul s Apollo, 1975, pp. 115–128. NASA SP-368), h ps ://books.google.co.in/books?hl=en&l =&id=oyFsAAAAMAAJ&oi= nd&pg=PA 115&dq=Me abolism+and+hea +dissipa ion+du ing+Apollo+EVA+pe iods&o s =XxTnab_4yo&sig=b 8TEM4kVU0LoHc5IYSu0uJpszk. (Accessed 27 Ma ch 2023). [56] M. Jones, K. Glo e , Apollo Luna Su ace Jou nal, NASA Websi e, 2013. h ps://www.hq.nasa.go /alsj/main.h ml. (Accessed 2 Augus 2022). [57] H. Noda, H. A aki, S. Goossens, Y. Ishiha a, K. Ma sumo o, S. Tazawa, N. Kawano, S. Sasaki, Illumina ion condi ions a he luna pola egions by KAGUYA(SELENE) lase al ime e , Geophys. Res. Le . 35 (2008), h ps://doi.o g/10.1029/ 2008GL035692. [58] NASA JPL Sola Sys em Dynamics G oup, Ho izons Sys em, JPL Websi e, 2017. h ps://ssd.jpl.nasa.go /ho izons/app.h ml#/. (Accessed 2 Augus 2022). [59] S. B yan , Luna pole illumina ion and communica ions s a is ics compu ed om GSSR ele a ion da a, in: SpaceOps 2010 Con , 2010, h ps://doi.o g/10.2514/ 6.2010-1913. [60] M.A. Siegle , B.G. Bills, D.A. Paige, E ec s o o bi al e olu ion on luna ice s abili y, J. Geophys. Res. Plane s. 116 (2011), h ps://doi.o g/10.1029/ 2010JE003652. [61] E.M.A. Chen, F. Nimmo, Tidal dissipa ion in he luna magma ocean and i s e ec on he ea ly e olu ion o he Ea h-Moon sys em, Ica us 275 (2016) 132–142, h ps://doi.o g/10.1016/j.ica us.2016.04.012. [62] W.R. Wa d, Pas o ien a ion o he Luna spin axis, Science 189 (1975) 377–379, h ps://doi.o g/10.1126/science.189.4200.377. [63] J.J. Ma quez, Human-Au oma ion Collabo a ion: Decision Suppo o Luna and Plane a y Explo a ion, 2007. [64] J. No heim, J. Ho man, D. Newman, T.E. Cohen, D.S. Lees, M.C. Deans, D.S.S. Lim, A chi ec u e o a su ace explo a ion a e se analysis and na iga ional ool, IEEE Ae osp. Con . P oc. (2018) 1–11, h ps://doi.o g/10.1109/AERO.2018.8396510, 2018-Ma ch. [65] NASA, Explo a ion EVA Sys em Concep o Ope a ions, 2020. h ps://n s.nasa. go /ci a ions/20205008200. (Accessed 27 Ma ch 2023). [66] J.D. Gio gini, S a us o he JPL ho izons epheme is sys em, IAU Gen. Assem. 29 (2015), 2256293. h ps://ui.adsabs.ha a d.edu/abs/2015IAUGA..2256293G. [67] L. Hawkins, NASA’s ini ial A emis human landing sys em, in: 73 d In . As onau . Cong . No. IAC-22, B3, ol. 1, 2022, X71658, 9, h ps://n s.nasa. go /api/ci a ions/20220012342/downloads/22 9 18 Hawkins HLS IAC inal.pd . (Accessed 3 May 2023). [68] T. Vicsek, H. Gould, F ac al g ow h phenomena, Compu . Phys. 3 (1989) 108, h ps://doi.o g/10.1063/1.4822864. [69] D.A. Dickey, W.A. Fulle , Dis ibu ion o he es ima o s o au o eg essi e ime se ies wi h a uni oo , J. Am. S a . Assoc. 74 (1979) 427, h ps://doi.o g/10.2307/ 2286348. E. Pe˜ na-Asensio e al. Ac a As onau ica 214 (2024) 324–342 342 [70] R. Johns on, Biomedical Resul s o Apollo, Scien i ic and Technical In o ma ion O ice, Na ional Ae onau ics and Space Adminis a ion, 1975. [71] D.A. K ing, N. Ba e , S. Boazman, A. Gaw onska, C. Gilmou , S. Halim, K. McCanaan, A. V Sa yakuma , J. Shah, A emis III EVA oppo uni ies along a idge ex ending om Shackle on c a e owa ds de Ge lache c a e , Sci. De in. Team A emis. (2020) 2042. h ps://hdl.handle.ne /20.500.11753/1709. [72] V.T. Bickel, B. Moseley, E. Haube , M. Shi ley, J.-P. Williams, D.A. K ing, C yogeomo phic cha ac e iza ion o shadowed egions in he A emis explo a ion zone, Geophys. Res. Le . 49 (16) (2022), h ps://doi.o g/10.1029/ 2022GL099530. [73] C.I. Fasse , B.J. Thomson, C a e deg ada ion on he luna ma ia: opog aphic di usion and he a e o e osion on he Moon, J. Geophys. Res. Plane s. 119 (2014) 2255–2271, h ps://doi.o g/10.1002/2014JE004698. [74] P. Ramachand an, G. Va oquaux, Maya i: 3D isualiza ion o scien i ic da a, Compu . Sci. Eng. 13 (2011) 40–51, h ps://doi.o g/10.1109/MCSE.2011.35. [75] J.D. Hun e , Ma plo lib: a 2D g aphics en i onmen , Compu . Sci. Eng. 9 (2007) 90–95, h ps://doi.o g/10.1109/MCSE.2007.55. [76] B. Ho mann, T. Schlo man, L. Cox, J. Some s, Human he mal analysis o a e se and geology asks du ing simula ed luna ex a ehicula ac i i y, in: 2023 IEEE Ae osp. Con , Big Sky, Mon ana, 2023, pp. 1–8. [77] M.E. Landis, P.O. Hayne, J.P. Williams, B.T. G eenhagen, D.A. Paige, Spa ial dis ibu ion and he mal di e si y o su ace ola ile cold aps a he luna Poles, Plane . Sci. J. 3 (2022), h ps://doi.o g/10.3847/PSJ/ac4585. [78] J.K. De Wi , W.B. Edwa ds, M.M. Sco -Pando , J.R. No c oss, M.L. Ge nha d , The p e e ed walk o un ansi ion speed in ac ual luna g a i y, J. Exp. Biol. 217 (2014) 3200–3203, h ps://doi.o g/10.1242/jeb.105684. [79] C. Ol ho , EVA walk-back limi calcula ion using he i ual spacesui , in: 48 h In . Con . En i on. Sys , 2018 u-i . dl.o g/handle/2346/74208%0Ah ps:// u-i . dl. o g/bi s eam/handle/2346/74208/ICES_2018_259.pd ?sequence=1. [80] W.C. Liu, B. Wu, An in eg a ed pho og amme ic and pho oclinome ic app oach o illumina ion-in a ian pixel- esolu ion 3D mapping o he luna su ace, ISPRS J. Pho og amm. Remo e Sens. 159 (2020) 153–168, h ps://doi.o g/10.1016/j. isp sjp s.2019.11.017. [81] B. Wu, W.C. Liu, A. G umpe, C. W¨ ohle , Cons uc ion o pixel-le el esolu ion DEMs om monocula images by shape and albedo om shading cons ained wi h low- esolu ion DEM, ISPRS J. Pho og amm. Remo e Sens. 140 (2018) 3–19, h ps://doi.o g/10.1016/j.isp sjp s.2017.03.007. [82] K. Mehlho n, P. Sande s, Algo i hms and Da a S uc u es: he Basic Toolbox, Sp inge Be lin Heidelbe g, 2008, h ps://doi.o g/10.1007/978-3-540-77978-0. E. Pe˜ na-Asensio e al.