© Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México igebde ihn topee xetfrPluto. for except atmosphere, no with bodies single required. the is from tech- exploration and their bodies technologies for these new niques of to Furthermore, development distance the large Sun, 2002). the Jewitt to & due earlier (Luu the System from these Solar material since theo- System, preserved the Solar probably the improve bodies of to formation the step of important ries an is (KBOs) eit eiaad srnmayAstrofísica y Astronomía de Mexicana Revista ne,II Russia. IKI, ences, 2 1 e er g hs bet eetogtt be to thought were objects these ago years few A Objects Belt Kuiper the of exploration The pc eerhIsiueo h usa cdm fSci- of Academy Russian the of Brazil. Institute INPE, Research Research, Space Space for Institute National PIA RJCOIST UPRBL OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL with o h 0ya rjcois hr r loatrisi th in asteroids additional also low are with there encountered be trajectories, 20-year the For rnlsmjrstaetra ucnol rnfrni co empa transferencia “cónicas la de buscando enfoque trayectorias el mejores en las basa tran se gr modelo influencia El la trayect intermedios. para Las posibilidades Quaoar. distintas y Makemake considerando Haumea, (KBO): Kuiper de turón mission. aauavnaad azmet ne nevl 0323,y 2023-2034, intervalo el en lanzamiento de ventana una para eeai aal atr nl ea eeceta transfer una encuentran requieren que Se años meta. 20 la de en menos captura la para necesaria h agtojc.Terslsso rnfr ihduration with transfers show results total The a spend object. target the n rycoi aacd n elsojtsK con KB objetos los de uno cada para trayectoria una niete22-04itra,addseadn the disregarding and interval, 2023-2034 the inside eta,l ulamnaí lvlrcetfiod amisión. la de Words: científico as Júpit Key valor con el encuentros de aumentaría para atracción también cual la usarse lo empleando podrían central, años años, 20 10 de de rias menos de duración h oe sbsdo h pthdcnc”apoc.Tebes The total approach. minimum “patched-conics” the the for traj searching on by These based found intermedi is of Quaoar. model possibilities and The different Makemake, considering Haumea, obtained (KBO): Objects Belt .INTRODUCTION 1. ∆ ebsa rycoisd rnfrni nr aTer tr y Tierra la entre transferencia de trayectorias buscan Se h rsn ae erhsfrtasesfo h at oth to Earth the from transfers for searches paper present The V ne 0k/ n uainblw1 er,uigteJptrs Jupiter the using years, 10 below duration and km/s 10 under .M Sanchez M. D. uprbl bet:idvda:Mkmk uprbl obj belt Kuiper — vehicles Haume Makemake space — individual: individual: Quaoar objects: individual: objects: belt belt Kuiper Kuiper — numerical methods: ∆ V eevdJn 221;acpe oebr1 2018 14 November accepted 2018; 22 June Received ne 0k/.Teei looetaetr o aho h KBO the of each for trajectory one also is There km/s. 10 under 1 .A Sukhanov A. A. , , 55 ABSTRACT RESUMEN ∆ 95 (2019) 39–54 , ∆ V V eo u 0k/.Tmins encuentra se También km/s. 10 que menor oicesn h cetfi euno the of return scientific the increasing so , ∆ 1,2 e r rie yoeo oesalmos like moons, small more or Quaoar and one bod- Makemake, by these Haumea, of orbited several are that tech- ies discovered observational was of it advances niques, the with However, ciiy n xml fti osblt stepo- the (Barucci is Quaoar possibility in geological cryovolcanism this of recent presence of be tential present compa- example can also sizes One fact could with activity. This Pluto KBOs to other 2016). rable that al. indication million et 10 an (Moore than has (less old) Pluto activity years spacecraft, that surface recent discovered Horizons of Pluto, New signs by the passing that when is point esting V n .F .A Prado A. B. F. A. and , 3 rnfrfragvnluc window, launch given a for transfer http://www.cbat.eps.harvard.edu/minorsats.html ∆ V ∆ eurdfrtecpueat capture the for required t lntgaiyassists. gravity planet ate vttrad o planetas los de avitatoria V una n anbl htcould that belt main e niscndrcó de duración con encias eo u 0k/ y km/s 10 que menor eodsdlcinturón del teroides eo 0yasthat years 20 below mds.S encuen- Se lmadas”. epeinola despreciando sojtsdlCin- del objetos es ∆ r a trayecto- Las er. rjcoisare trajectories t e fteKuiper the of ree V ra eobienen se orias oa mínima, total 1 coisare ectories wingby. ects: — a 3 ∆ nte inter- Another . V s 39 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México nlntos( inclinations inwr on.Isedo h ulconsumption fuel the the namely total considered, of was Instead parameter equivalent consump- an found. fuel minimum were transfer the tion optimal of The terms in 2058. trajectories in to launch flight with direct was Haumea exception only The interval. 2034 bodies. these 1 Table of ( moons plane. masses ecliptic the the presents to also respect with given are h o at akn ri n l necessary all and orbit parking Earth low the 06,adQaa Fae ta.21) h val- The 2013). ( axes al. semi-major al. et the of et (Fraser ues Parker Quaoar 2013; and (Brown Makemake 2016), 2017), Ortiz 2009; al. charac- Brown et physical & exploration. (Ragozzine and Haumea spacecraft orbital of for teristics some target presents en- which 1 good Table is TNO, a densest core it the makes is its probably 2013). probably al. Quaoar et (Fraser Then, and material Quaoar silicate density by Haumea, formed high tirely from differently a thin Like but a has by orbit. ice, covered Weywot. eccentric core of an rocky named layer a in has moon, be Quaoar to Haumea, small 2016). seems a al. moon et This has (Parker also 1” moon, desig- (136472) Quaoar discovered general “S/2015 its recently and is a yet, nation name has official also no has It which Eris. and planet 2009). an- dwarf al. is this et Haumea of (Pinilla-Alonso of characteristic core important rocky depleted other the carbon surrounds of layer that thin ice The ring ellipsoid 2017). discovered al. recently triaxial moons, et a (Ortiz two a and possesses Hi’iaka, is h), and it Namaka (3.9154 rotation because fast TNOs, with the intrigu- most of the this ing probably to candidate is a Haumea just as classification. is (IAU) Quaoar but Union planets, recognized Astronomical dwarf were International Objects Makemake the Trans-Neptunian and by as Haumea classified they (TNOs). be and KBOs because also the targets of can representatives as PRADO good chosen & are were SUKHANOV, they SANCHEZ, bodies Quaoar. three (136108) (50000) present These and to The Makemake, trajectories (136472) optimal Haumea, with KBOs. for us the bod- searches provide of paper these to features of necessary detailed are more more Pluto or beyond one ies planetology. to comparative missions out Spacecraft carry to bodies, about of these knowledge distance our not improve were large significantly data to the observational enough Sun, to the due from KBOs However, the 2015). al. et 40 eaaye h ae fluc nte2023- the in launch of dates the analyzed We aeaei h hr ags N,atrPluto after TNO, largest third the is Makemake ∆ V hc stesmo h launch the of sum the is which , I r prxmt.Teinclinations The approximate. are ) m a ,dniis( densities ), ,ecnrcte ( eccentricities ), ρ ,adthe and ), ∆ e and ) V ∆ V in s fteegnsaentkoni dac h u fthe of sum the advance in known not and characteristics are the engines engines since different the Although by of summed. made simply be be cannot will maneuvers space deep ino h ehdcnb on nsvrlpubli- several in found be can method & descrip- the The Strange of 2008). 1999; al. tion et Sukhanov Solórzano 1977; 1982; 2002; Longusky Penzo al. several et & of D’Amario planning (Kohlhase the missions for interplanetary used was and technique considered. andăE- are E-V-E-E-S schemes V-E-DV-E-S which transfer Also E-V-V-E, in paper. areăanalyzed except this 2023-2034 schemes, in launch these for maneu- of areăpossible propulsive Jupiter, All space Venus, deep Earth, ver. respec- a for anăasteroid, means stand and tively.ăDV A Neptune, P, Uranus, V, N, Saturn, E, U, where S, Belt, 2005), J, E-A-J-P-Kuiper Farquhar & scheme (Guo the Horizons with New the E-V-V-E-A- scheme and the J-S, with (Per- 1995), Cassini Flanagan E-A-DV-E-A, & al. alta scheme with et the (Wenzel with 1982), Ulysses 1992), al. E-V-E-E-A-A-J, et E-J-S- scheme 1 scheme (D’Amario the Voyager the Galileo the with space, in 1977), Outer as Penzo outer such & the space, (Kohlhase to outer missions and in planets used This widely anymore. was century this technique in reproduced 1977), be cannot Penzo & (Kohlhase space, 2 always the Earth-Jupiter-Saturn-Uranus-Neptune-Outer Voyager by not the used of are combination mission the combinations example, Some For realistic a possible. flight. in interval, of time plan- time proposed these of the combinations of within feasible design ets, find the to in than is difficulty less main trajectories flight The plan- of time of years. total number 20 with smaller to- trajectories a planets for of leaving ets years the flight, 20 of of trajectory with time number single tal trajectories the a for Thus, maximized in was consid- limited. bodies is be of flight may number of the flybys. time the limited ered, since during the view, acquired since be of However, could point data scientific scientific more of the are time from missions the interesting multi-body shortens Furthermore, lowers and/or which flight. consumption planets, fuel the maneu- the of include assists capture considered gravity schemes the transfer various the account of Most into ver. taking made for should optimization required be be new is a capture will trajectories, If specific planets these capture. dwarf without launch by the given flown that the for assuming schemes windows transfer possible ious flight. the during steol a oetmt piaiyo h transfers. the of optimality estimate to way only the is 4 h ehdo ace-oisi well-known a is patched-conics of method The nfc hsi o ut orc eas h anhand launch the because correct quite not is this fact In 4 hswsdn osdrn var- considering done was This ∆ V s © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México rmtefe osmto on fve.A men- As view. minimum of this point above, optimal consumption tioned are fuel found the trajectories were speci- from the windows Thus, were the for. within months, sought transfers several to optimal up sometimes and fied windows, and time few arrival extended a that and means swingby, This launch, window. launch a given a n h nldsiain hoiga pia tra- minimum optimal the as with Earth one choosing the the destination, jectory between final trajectories the and possible all gen- problem erates this be- solve Quaoar. to trajectories and implemented software Makemake, of The Haumea, sets and generate Earth Solar to tween the used of planets is the System, to spacecraft the of proaches Solar the of exploration future the System. in to impor- missions targets are future which tant for Quaoar, and useful Makemake, be trajecto- Haumea, can transfer here The shown ries (1968). Escobal like cations, oevle n h pia rnfr ( by transfers limited optimal was the flight and of the make values time to the some not long order In too time. transfers arrival the prop- to Or- numerically agated then Asteroid and Bowell’s Database Edward Elements bital planets the dwarf from the taken DE405 of were JPL elements the Orbital using calculated ephemerides. were planets the of launch the ssoni h etscin hn h minimum the Then, flight, of section. time next of km/s the ∆ years 22 in 20 to km/s shown to 10 as 10 from with vary can trajectories veloc- it in arrival high: the too since is planet, ity dwarf the around bit eswt iia total minimal with fers rd hntasesicuiggaiyassso the of consid- assists gravity is including transfer transfers planet Then dwarf ered. the the to First, Earth section. direct this in presented are planets dwarf calculated. were flight OEPYIA N RIA HRCEITC FHUE,MKMK,ADQUAOAR AND MAKEMAKE, HAUMEA, OF CHARACTERISTICS ORBITAL AND PHYSICAL SOME V Haumea Makemake uor13–1.5 – 1.3 Quaoar h ace-oi ehiu,mkn ls ap- close making technique, patched-conic The l ye ftetaetre on o aho the of each for found trajectories the of types All ∆ ognrt h pia rjcoycmrssthe comprises trajectory optimal the generate to Body V ∆ eurdt lc h pccati ls or- close a in spacecraft the place to required V n i-oremnues h orbits The maneuvers. mid-course and .METHODOLOGY 2. .RESULTS 3. < 4 . 006 4 m . ∆ PIA RJCOIST UPRBL BET 41 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL 4 (kg) V × × o htlmtdtm of time limited that for ) × 10 10 10 ∆ 21 21 21 V osntconsider not does ∆ V ρ . . 601 90S21 167)1 (136472) S/2015 29.0 0.15 46 3.2 – 1.4 eurd for required, (g/cm i.e. .8 301 82Nmk,Hi’iaka Namaka, 28.2 0.19 43 1.885 . 400 . Weywot 8.0 0.04 44 4.2 trans- 3 ) AL 1 TABLE a (AU) rf eoiyaddcesstelaunch the space- decreases the and increases velocity which craft considered, are planets eraetelaunch the decrease ofidtase rjcoiswt esta 0years 20 than total less with a possible and trajectories be transfer not may find about it to is consequently, dura- maneuvers and, the EVEdvE years, because and 3.5 EVEE flight, the of of time tion may total maneuvers the these increase However, maneuver-Earth). space and (Earth-Venus-Earth-deep (Earth-Venus-Earth- EVEdvE Earth EVEE and Earth) as in such maneuvers used, are assist Venus gravity multiple of h total the il o l h wr lnt.Tetpso trajec- of types The following: the planets. worth are dwarf is tories pos- the It are all trajectories for flight. of sible of types all time a not with of that Jupiter mentioning years by 60 passing of Haumea maximum represent- to the trajectory, Earth example, B the For type ing a is constraints”. EJH60y “no trajectory where for flight, of stands time in- the “nc” planets in the constraint the of the and letter of volved first name the involved, The indicates planets transfer. trajectory the direct of the transfers with number of beginning the types by The ordered made inclination are consumption. if the fuel maneuver maneuver of the expensive assist cost very using a gravity the is minimize This which to change, also 1. used plane, Table is ecliptic in planets the seen dwarf in- to as all orbital inclination since the considerable spacecraft, changing have the for of responsible clination one the is Haumea. to flight direct and interval the 2023-2034 for the 2058 in transfers for searching rjcoyta nldsteEE maneuver EVEE the includes that Trajectory - D iettaetr,wt oconstraint. no with trajectory, Direct - A at otedafpae asn ySaturn. by passing planet dwarf the to Earth - C at otedafpae asn yJupiter. by passing planet dwarf the to Earth - B rjcoyta nldsteEEv maneuver EVEdvE the includes that Trajectory - E h atpae ntewyt h wr planet dwarf the to way the in planet last The n h uie rvt assist. gravity Jupiter the and assist. gravity Jupiter the and ∆ I e V ∆ salmti h rsn eerh when research, present the in limit a is V esta 0k/.Ti au for value This km/s. 10 than less dg Moon(s) (deg) ∆ V h lsia combination classical the , ∆ V To . © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México twl enmee ln h yeo h transfer, type, the of same type the the of g. along transfer numbered be one will than it more is there If PRADO & SUKHANOV, SANCHEZ, 42 at oHue rnfralw odces the decrease to allows transfer Haumea to Earth direct the for trajectory the shows transfer. 1 Figure flight. of hog h anbl ihhg eoiy h addi- the velocity, high with tional pass However, belt flight main of the mission. time smaller through the with of trajectories the output increas- since asteroids), scientific (or the and asteroid encounter ing belt to main possible as- a it main observe makes the This by belt. pass teroid trajectories transfer all KBOs, nraetomc h total the much too increase hnHue spsigb h ieo oe.In nodes. of line the by 2, passing trans- Table of is direct date Haumea just launch a (11.03.2100), when the of is date with arrival A), the scenario, and (23.01.2058) (type best the EHnc using the fer the 2, presented of Table trajectory inclination first in the the high Then, very change orbit. the to spacecraft is maneuvers reason of The cost plane. line, ecliptic node the the with at Haumea reaches i.e. spacecraft consumption fuel the to minimum transfer if its direct have would the degrees, body 28.2 this about is plane tic year. day, = yyyy = and dd month where the = dd.mm.yyyy, in mm format presented in dates the are All results to summarized subsection. shown, are last also results the in The are trajectories transfers. the the 4). illustrate of (Table Quaoar some and of (Ta- 3), Plots (Table Haumea Makemake to give 2), trajectories subsections the ble each for three for results next main shown the The are results target. The individual encounters asteroids. possible the include with trajectories 20-year the velocity, rjcoyta nldsteEE maneuver EVEE the includes that Trajectory - G rjcoyta nldsteEEv maneuver EVEdvE the includes that Trajectory - H h aea ,btwt aunisedof instead Saturn with but E, as same The - F rjcoyta nldsteEE maneuver EVEE the includes that Trajectory - I 1 2 n oon. so and A2, A1, , h nescino h amaobtlplane orbital Haumea the of intersection the , h diino h uie wnb uigthe during swingby Jupiter the of addition The ic ama aeae n uorare Quaoar and Makemake, Haumea, Since ic nlnto fteHue ri oteeclip- the to orbit Haumea the of inclination Since n h uie n aungaiyassists. gravity Saturn and Jupiter the and assists. gravity Uranus and Jupiter the and assists. gravity Uranus and Jupiter the and Jupiter. ∆ V ∆ ∆ V V eurdt none natri could asteroid an encounter to required T L 3.1 stetotal the is stelaunch the is rnfr oHaumea to Transfers . ∆ V ∆ ∆ n O stetime the is TOF and , V V hsi h only why is This . , V A stearrival the is e. ottesm stetotal the as same the most ihluc n25.I h J6ytase,teto- the transfer, EJH60y the In tal transfer 2058. EHnc in the launch with with compared if flight, of time the etudr1 km/s. 10 under kept h eraeo the EHnc. transfer of the decrease to The compared km/s 1.43 of ference e iha additional trans- the an during with reached be fer Just that could trajectory. that asteroids 20-year asteroid the the one in for encountered be search could to transfer vEJH20y hw nTbe2 hr sdces ntetotal the in decrease EJH20y is the there with 2, transfer Table in this in launch compare shown for we transfer If Fig- EVEEJH20y 2023. example, the an shows As 4 ure maneuver. EVEdvE or EVEE total the rela- the since for flight, found of solution time best short lat- the tively The is trajectory. transfer EJH10y the ter shows 3 Figure and transfer. EJH60y the is for transfer as EHnc same the the for of almost time time arrival the arrival the in the since variations flight, that to sensitive indicates more This is de- velocity a km/s. has 1.43 which of velocity, arrival crease the by followed was at wnbslast ml eraeo h to- the two of the decrease small between a maneuver tal to space The leads swingbys deep 5. Earth Figure the in of shown is use maneuver space deep the higher km/s 1.93 a velocity. for to arrival one leading the situation, the than EJH20y EJH20y larger of the the is increment as EVEEJH20y velocity in time spacecraft mid-course of the period same transfer, the in planets f14 msaddces f36 msi h launch the in km/s 3.69 of ∆ decrease and km/s 1.43 of sE n 4 h additional The 2, E4. Table and in shown E3 are as encounter asteroid the trans- with the fer and transfer encounter, Characteristics EVEdvEJH20y the original the of EVEdvEJH20y. of date trajectory the includes the asteroid, 6 and the Figure of QZ. orbit 1986 the (11023) is asteroid This launch iia obnto,btuigJptrisedof larger instead a have total Saturn Jupiter involve that transfers using the all Saturn, but with combination, compared However, similar the allows using maneuver. Haumea interval to EVEdvE 2023-2034 transfers of the possibility in another assist gravity urn km/s. 0.10 is asteroid anhwnoswt rnssigyatrJupiter, after swingby Uranus with windows launch V ∆ h launch The iue2sosteEH0 rnfrtrajectory, transfer EJH20y the shows 2 Figure h VdEH0 rnfrtaetr htuses that trajectory transfer EVEdvEJH20y The h xsec fluc idw ihteSat- the with windows launch of existence The ∆ oee,snetesaerf asdb more by passed spacecraft the since However, . V V ∆ aey f01 ms eue h EVEd- the used We km/s. 0.11 of namely, , V ∆ erae rm82 mst .4k/,adif- a km/s, 6.84 to km/s 8.27 from decreased scnb eni al .Teeaealso are There 2. Table in seen be can as , V h ria eoiy h total the velocity, arrival the , ∆ V a erdcdb en fthe of means by reduced be can ∆ V ∆ tluc s14 ms al- km/s, 1.43 is launch at < V ∆ V h aeproportion same The . ∆ . mswsfound. was km/s 0.5 V eesr o the for necessary ∆ ∆ V V ∆ and was V © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México h ria velocity, arrival the l ,oecnseta h aetp ftrajectory of type same total the the of that values Ta- see larger with has can 2 the one Table for 3, Comparing ones ble the Haumea. than to ex- fuel larger transfers the slightly transfers, are the penditures all for that, Makemake, to ie nTbe3 where 3, Table in given years. 25 transfers than smaller all flight in of km/s time 10 by total have of passing that limit trajectories our Transfer exceed Uranus 2. also Table as flight, in of time shown same the with trajectories other re ae h ulcnupinlre.I a be can It total larger. the consumption from seen, fuel de- This one the by makes Haumea. larger inclination gree, than an Sun astronomi- with the associated three fact, from is Makemake farther units flight. cal of time the is u hyas aealretotal large a have also they but neape o h rnfrtp ,wihi di- a is total which the body, A, the type to transfer transfer the rect for example, an yeTaetr anhdate Launch Trajectory Type 3EEJH0 30.0639 94 37 30.00 40.00 55.30 13.76 6.50 3.91 19.44 11.27 5.75 3.91 3.92 3.90 03.08.2026 14.08.2026 05.08.2026 EVEEJUH30y EVEEJUH40y G3 EVEEJUHnc G2 G1 2EEJ1y2.522 .32.070 15.00 20.00 7.09 5.87 20.20 13.13 3.63 3.62 24.05.2023 21.05.2023 EVEEJH15y EVEEJH20y D2 D1 1En 30.0882 .282 42.26 8.24 4.22 8.24 23.01.2058 EHnc A1 1EEvJHc1.522 .265 .549.92 5.25 6.50 3.62 13.05.2023 EVEdvEJUHnc H1 hrceitc ftetasest aeaeare Makemake to transfers the of Characteristics 2EH0 50.0873 62 .919.99 42.42 9.39 7.39 16.27 4.80 7.32 7.39 15.07.2028 13.07.2027 ESH20y ESHnc C2 C1 4EH0 11.0597 50 .810.00 20.00 37.54 59.99 9.98 7.30 8.24 6.84 25.05 11.20 4.52 2.88 9.79 7.30 6.96 01.10.2025 6.84 18.08.2024 17.08.2024 21.09.2025 EJH10y EJH20y B4 EJH40y B3 EJH60y B2 B1 5EEvJ1y2.522 .32.070 15.00 19.89 20.00 29.92 7.08 59.97 5.76 5.86 5.09 20.20 4.41 13.27 13.13 7.11 3.63 3.15 3.62 3.62 24.05.2023 3.61 3.61 12.05.2023 21.05.2023 14.05.2023 EVEdvEJH15y 14.05.2023 EVEdvEJH20y+ast E5 EVEdvEJH20y E4 EVEdvEJH30y E3 EVEdvEJH60y E2 E1 4EEvS2y2.122 .72.81.020.00 25.00 30.00 46.94 10.30 6.65 5.65 5.03 22.28 15.66 10.82 4.43 4.27 4.07 4.11 4.18 23.11.2024 16.12.2024 10.12.2024 30.11.2024 EVEdvESH20y EVEdvESH25y F4 EVEdvESH30y F3 EVEdvESHnc F2 F1 YE FOTMLTAETRE OSN PCCATT HAUMEA TO SPACECRAFT A SEND TO TRAJECTORIES OPTIMAL OF TYPES 3.2 rnfr oMakemake to Transfers . ∆ ∆ V V T ∆ PIA RJCOIST UPRBL BET 43 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL o h rnfrtrajectories transfer the for V stetotal the is L stelaunch the is ∆ V ∆ o aeae As Makemake. for V ∆ oprdwith compared V ∆ V s82 km/s 8.24 is n TOF and , ∆ V , V A AL 2 TABLE is ∆ V L km/s , in hwta auni oeeceti em of terms in efficient simula- more total our the is swingby, reducing Saturn Jupiter that show or tions Saturn the before transfer 8. The Figure years. transfers in 10 shown of Both is flight B3 of km/s. time a 17.72 considered is which Makemake), h 3tp ftase (Earth-Jupiter-Makemake) total transfer a of that has note type variation, vari- this B3 trajectories of large of example the Very an types As different noted. for 3. are costs Table the in in shown ations is as swingby, ftetotal the of rjcoisuigteJptrsigysedless spend swingby Jupiter total the using trajectories 7. Figure the in Makemake for shown for is km/s A1 Transfer 8.33 and flight. Earth-Makemake flight Earth-Haumea the for oHue,a2-ertase sfail famis- having a designed, is if bodies total feasible the multiple is by transfer passing 20-year sion a Haumea, to oee,i ecnie h VdEmaneuver EVEdvE the consider we if However, iial owa cusfrHue,transfer Haumea, for occurs what to Similarly ∆ V V ∆ A oprdt rnfr sn h Saturn the using transfers to compared V ∆ km/s , ∆ V rud1 ms hrfr,regarding Therefore, km/s. 10 around V f1.3k/,wihi lothalf almost is which km/s, 10.43 of o h rnfrC (Earth-Saturn- C3 transfer the for ∆ V ntesm a stransfers as way same the In . ∆ V T msTF years TOF, km/s , © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -6 -2 nFgr .Treatriscnb encountered be can asteroids Three shown 9. is transfer transfer Figure F2 This the in in Makemake, chosen. encountered to is be (EVEdvESM20y) Earth can from that way asteroids the of search online. the viewed be g can are figure olive distances color in The The Haumea right. years. of 20 the orbit ecli to on the the constrained trajectory and in transfer blue, Haumea whole in to the shown (red) are trajectory planets transfer the Optimal 2. Fig. ca figure s color is The Earth units. the astronomical from in ecli departure given the The are in olive. distances Haumea in The to Haumea (red) of orbit trajectory the transfer Optimal 1. Fig. PRADO & SUKHANOV, SANCHEZ, 44 -1.5 -4 8.02.2026 8.02.2026 23.01.2058 Jupiter Jupiter -1 Earth -2 -0.5 18.08.2024 18.08.2024 -1.5 -0.5 0.5 1.5 -6 -4 -2 -2 -1 2 0 2 4 6 0 1 Earth Earth Sun 0 0 Sun 0.5 2 1 4 1.5 2 6 -50 -50 iha additional an with h iso.Teatrisae 918 91ER23, of 1981 additional gains (96168) an scientific are: with asteroids the The considering mission. much the too not is vni srnmcluis h oa ieo ih was flight of time total The units. astronomical in iven tcpae h ri fteErhi hw nbu and blue in shown is Earth the of orbit The plane. ptic ono h etadtewoetaetr nteright. the on trajectory whole the and left the on hown tcpae nldn uie wnb.Teobt of orbits The swingby. Jupiter a including plane, ptic h at oJptrflgti hw ntelf and left the on shown is flight Jupiter to Earth The . evee online. viewed be n -40 -40 -30 -30 21.09.2044 21.09.2044 Haumea Haumea -20 -20 Jupiter -10 -10 ∆ ∆ V V -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 fls hn1k/,which km/s, 1 than less of fol .4k/;(12062) km/s; 0.04 only of 0 0 10 10 27.04.2100 Haumea 20 20 30 30 40 40 50 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -6 -6 he seod r hw nFgrs1,1,ad12, and 11, 10, Figures in these respectively. shown reaching are trajectories asteroids transfer three The km/s. 0.14 additional an with vi FB10, d be can The 1998 figure right. color The the on years. 20 trajectory to whole constrained the the is and and flight blue, left of in time the marked on are ecli shown planets the the in is of Haumea to orbits (red) The trajectory swingby. transfer Optimal 4. Fig. n 152)20 T4 ihadditional with UT44, 2001 (135420) and 4.02.2028 4.02.2028 7.10.2026 7.10.2026 Jupiter Jupiter Jupiter Jupiter i.3 h aea nFgr ,btwt 0ya ieo flight of time 10-year a with but 2, Figure in as same The 3. Fig. -4 -4 21.05.2023 21.05.2023 22.11.2023 22.11.2023 -2 -2 Venus Venus Earth Earth -6 -4 -2 -6 -4 -2 6 0 2 4 6 0 2 4 PIA RJCOIST UPRBL BET 45 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL Sun Sun 0 0 14.10.2024 14.10.2024 14.10.2026 14.10.2026 2.10.2025 2.10.2025 ∆ Earth Earth 2 2 Earth Earth V f01 km/s; 0.12 of 4 4 ∆ V of 6 6 tcpae nldn h VEmnue n h Jupiter the and maneuver EVEE the including plane, ptic -50 -50 ie nTbe4 where 4, Table in given stearvlvelocity, arrival the is O stetm fflgt h ri fQuaoar of orbit The flight. of time the is TOF ri fHue noie h eatr rmteEarth the from departure The olive. in Haumea of orbit hrceitc ftetasest uorare Quaoar to transfers the of Characteristics wdonline. ewed sacsaegvni srnmcluis h total The units. astronomical in given are istances -40 -40 27.09.2035 27.09.2035 Haumea Haumea h oo gr a evee online. viewed be can figure color The . -30 -30 5.02.2043 5.02.2043 Haumea Haumea 3.3 -20 -20 rnfr oQuaoar to Transfers . Jupiter Jupiter -10 -10 -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 ∆ ∆ 0 0 V V T L stetotal the is stelaunch the is 10 10 20 20 30 30 ∆ ∆ V 40 40 V and , , V 50 50 A © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -3 -4 hsnme lcsisobtbtenteobt of orbits of eccentricity the the between because Makemake, orbit and and its units, Haumea astronomical places 44 number of this axis semi-major a has astronomica online. in viewed given be depar are can The distances figure olive. The color in The right. Haumea orbit years. of the The orbit on swingby. the trajectory Jupiter and ecli the green, the and in in asteroid encounter, Haumea asteroid to (red) QZ trajectory 1986 transfer Optimal 6. Fig. figu ri color the The on years. trajectory 20 whole to constrained the a is and blue flight left in of ecli the marked time the on total are The shown in planets is Haumea the Earth of to orbits the (red) The trajectory swingby. transfer Jupiter Optimal 5. Fig. PRADO & SUKHANOV, SANCHEZ, 46 30.09.2025 30.09.2025 -3 29.09.2025 29.09.2025 -2 dv dv 15.05.2023 15.05.2023 14.04.2027 14.04.2027 1986 QZ 1986 QZ -2 dv dv 21.05.2023 21.05.2023 Earth Earth -1 18.10.2023 18.10.2023 Earth Earth -1 20.10.2023 20.10.2023 Venus Venus -3 -2 -1 3 0 1 2 Sun 0 Venus Venus -2 -1 -3 0 1 2 3 4 Sun 0 13.08.2024 13.08.2024 11.11.2026 11.11.2026 10.11.2026 10.11.2026 1 12.08.2024 12.08.2024 Earth Earth Earth Earth 1 Earth Earth Earth Earth 2 2 3 3 tcpae nldn h VdEmnue,te(11023) the maneuver, EVEdvE the including plane, ptic -50 -50 u otelwriciaincmae oHaumea to compared inclination lower case, this the of In to degrees. inclination 8 due orbital is plane the ecliptic the However, to Quaoar low. is Quaoar uefo h at ssono h etadtewhole the and left the on shown is Earth the from ture dteobto amai lv.Tedpruefrom departure The olive. in Haumea of orbit the nd tcpae nldn h VdEmnue n the and maneuver EVEdvE the including plane, ptic ecnb iwdonline. viewed be can re nt.Tettltm fflgti osrie o20 to constrained is flight of time total The units. l ftepaesaemre nbu,teobto the of orbit the blue, in marked are planets the of s h.Tedsacsaegvni srnmclunits. astronomical in given are distances The ght. -40 -40 15.05.2043 15.05.2043 21.05.2043 21.05.2043 -30 -30 Haumea Haumea Haumea Haumea -20 -20 13.02.2028 13.02.2028 13.02.2028 13.02.2028 Jupiter Jupiter -10 -10 -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 0 0 10 10 20 20 30 30 40 40 50 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -2 aeo ama hstase eursatotal the a In requires transfer comparisons. this for used Haumea, compared 10-year be of are a can case 4 considering flight and of and transfer swingby time the Jupiter 3, fact, fact a this exemplify using This 2, To Tables other. each if Makemake. with seen to be or can Haumea to transfers oQaa aefe osmto,epesdb the by expressed consumption, total Earth fuel have from Quaoar trajectories to transfer all Makemake, and color The units. Ear astronomical the in from given departure e are The the distances olive. in The in Makemake Makemake right. to of (red) orbit trajectory the and transfer Optimal 7. Fig. yeTaetr anhdate Launch Trajectory Type 1En 01.0483 .283 68.39 8.33 3.42 8.33 10.12.2034 EMnc A1 3EM0 60.0382 18 77 10.00 19.99 34.52 17.72 7.87 7.31 31.88 13.60 7.21 8.26 7.86 7.31 16.09.2033 15.08.2031 15.07.2028 ESM10y ESM20y C3 ESMnc C2 C1 3EM0 31.051.12.81.310.00 20.00 53.36 10.43 7.36 6.39 25.78 13.95 3.24 10.41 6.57 6.39 03.10.2025 12.07.2034 23.06.2034 EJM10y EJM20y B3 EJMnc B2 B1 5EEvS2yat 11.0442 28 19 20.00 20.00 20.00 37.68 20.00 11.97 11.96 11.83 5.00 11.87 22.83 21.97 22.25 7.390 21.97 4.24 4.30 4.28 4.21 4.29 21.11.2024 13.11.2024 16.11.2024 EVEdvESM20y+ast3 22.11.2024 17.11.2024 EVEdvESM20y+ast2 F5 EVEdvESM20y+ast1 F4 EVEdvESM20y F3 EVEdvESMnc F2 F1 -1.5 ∆ V YE FOTMLTAETRE OSN PCCATT MAKEMAKE TO SPACECRAFT A SEND TO TRAJECTORIES OPTIMAL OF TYPES mle hnteoe eurdfrthe for required ones the than smaller , -1 -0.5 -1.5 -0.5 0.5 1.5 -2 -1 0 1 2 PIA RJCOIST UPRBL BET 47 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL 0 10.12.2034 10.12.2034 Sun Earth Earth 0.5 1 1.5 ∆ AL 3 TABLE V 2 ∆ V L km/s , -50 banatase oQaa ihaflgttm f8 of time flight a with total Quaoar and years to transfer a obtain hc ae tavr ovnettre.Fgr 13 Figure transfer. Earth-Jupiter-Quaoar target. 8-year convenient the very flight, shows of a decade it a makes than less which in reached be can Quaoar ii f1 msfrtetotal the for km/s 10 of limit ∆ f99 mst eeeue.FrMkmk,the Makemake, For executed. be is to value km/s 9.98 of lpi ln.Teobto h at smre nblue, in marked is Earth the of orbit The plane. cliptic gr a evee online. viewed be can figure hi hw ntelf n h hl rjcoyo the on trajectory whole the and left the on shown is th V 8 = -40 . ∆ 34 -30 V V A ms ic,i hsppr efie a fixed we paper, this in Since, km/s. km/s , 10 = -20 ∆ V . 43 -10 .3k/.Ti en that means This km/s. 9.73 = -50 -40 -30 -20 -10 30.04.2103 30.04.2103 Makemake ms hl o uori is it Quaoar for while km/s; 50 10 20 30 40 ∆ 0 V 0 T msTF years TOF, km/s , 10 ∆ V ti osbeto possible is it , 20 30 40 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -8 -3 oeecet ntrso total of terms in are efficient, transfers more Earth-Jupiter-Quaoar the all Haumea, aunQaa rnfr.Ti atcnb enin seen be can fact This transfers. Saturn-Quaoar h oa ieo ih scntandt 0yas h oo figu ri color the The on years. trajectory 20 whole to constrained the is and flight left of blue, the time in on total marked e The shown are the is planets in the Earth Makemake of the to orbits (red) The trajectory swingby. Saturn transfer Optimal 9. Fig. figu color The years. in 10 Makemake to of constrained orbit e is the flight the and of in blue, time Makemake in total to marked The are (red) planets trajectory the transfer of Optimal 8. Fig. PRADO & SUKHANOV, SANCHEZ, 48 ntecs fQaa,smlryt htof that to similarly Quaoar, of case the In 18.09.2026 18.09.2026 -6 -2 Jupiter Jupiter 15.04.2026 15.04.2026 -4 Earth Earth -1 -2 -2 -1 -8 -6 -4 -2 -3 8 0 1 2 3 0 2 4 6 Sun Sun 0 0 13.06.2025 13.06.2025 16.11.2024 16.11.2024 4.06.2027 4.06.2027 26.07.2028 26.07.2028 3.10.2025 3.10.2025 Venus Venus ∆ 2 V Earth Earth Earth Earth 1 Earth Earth hnteEarth- the than , dv dv 4 2 6 8 3 n h ri fMkmk noie h eatr from departure The olive. in Makemake of orbit the and -50 -50 EEvJ2y sue osac o osbeas- possible for search E1 to transfer the used combined Therefore, is if Haumea, (EVEdvEJQ20y) swingby. efficient Jupiter for more a occurred is with what transfer to EVEdvE Similarly the 4. Table lpi ln,icuigteEEv aevradthe and maneuver EVEdvE the including plane, cliptic 3.10.2035 3.10.2035 Makemake Makemake 15.11.2044 15.11.2044 lpi ln,icuigaJptrsigy h orbits The swingby. Jupiter a including plane, cliptic Makemake Makemake ecnb iwdonline. viewed be can re online. viewed be can re lv.Tedsacsaesoni srnmclunits. astronomical in shown are distances The olive. h.Tedsacsaegvni srnmclunits. astronomical in given are distances The ght. -40 -40 -30 -30 -20 -20 31.07.2033 31.07.2033 Jupiter -10 -10 Saturn -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 0 0 10 10 20 20 30 30 40 40 50 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -3 -3 s61 ms n hsfc ae tpsil ofind to possible it makes fact this and km/s, 6.13 is nti ae lhuhtetotal the although Jupiter. to case, Earth this from In way the in encounters th teroids with but 10, Figure in as same online. viewed The be F4. can type figure Transfer 11. Fig. online. astrono viewed in be given can ma are figure are distances color planets The The the dep olive. of years. The in orbits Makemake The encounter. of right. orbit asteroid the ER23 on 1981 trajectory the whole in (96168) Makemake the to (red) and trajectory swingby transfer Optimal 10. Fig. -2 -2 14.04.2026 14.04.2026 15.04.2026 15.04.2026 Earth Earth Earth Earth -1 -1 -1 -3 -2 -1 -3 -2 3 0 1 2 3 0 1 2 PIA RJCOIST UPRBL BET 49 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL Sun Sun 0 0 11.06.2025 11.06.2025 14.06.2025 14.06.2025 17.11.2024 17.11.2024 24.07.2028 24.07.2028 6.06.2027 6.06.2027 13.11.2024 13.11.2024 3.06.2027 3.06.2027 28.07.2028 28.07.2028 Venus Venus Venus Venus ∆ Earth Earth Earth Earth Earth Earth 1 1 V Earth Earth dv dv dv fti transfer this of 1981 ER23 1981 ER23 27.12.2028 27.12.2028 24.01.2029 24.01.2029 1998 FB10 1998 FB10 2 2 3 3 citcpae nldn h VEmnue,teJupiter the maneuver, EVEE the including plane, ecliptic -50 -50 ia nt.Tettltm fflgti osrie o20 to constrained is flight of time total The units. mical ih oalwterae ocmaeti yeof type this of compare time to of years reader 20 the of allow limit flight, to the of flight times keep shorter to in decided type we same the of transfers kdi le h riso h seodi re,adthe and green, in asteroid the of orbits the blue, in rked 17.11.2044 13.11.2044 17.11.2044 13.11.2044 Makemake Makemake Makemake Makemake ruefo h at ssono h etadthe and left the on shown is Earth the from arture 102 98F1 seodecutr h color The encounter. asteroid FB10 1998 (12062) e -40 -40 -30 -30 -20 -20 19.07.2033 19.07.2033 3.07.2033 3.07.2033 -10 -10 Saturn Saturn -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 0 0 10 10 20 20 30 30 40 40 50 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -4 ∆ 14 Figure in shown is example. Makemake, E1 an Haumea, as transfer The bodies Quaoar. three and the for transfer th with but 10, Figure in as online. same viewed The be can F5. figure type Transfer 12. Fig. PRADO & SUKHANOV, SANCHEZ, 50 h seod(535 93U6cnb ece with reached additional be can an UO6 1993 (155385) asteroid The eod(47)20 E2 a evstdwt an with visited be can UE122 additional 2001 (64378) teroid V yeTaetr anhdate Launch Trajectory Type 1En 70.0388 .883 68.46 8.39 3.98 8.84 27.03.2023 EQnc A1 1EQc0.722 .143 .145.06 19.99 7.51 10.10 13.36 4.39 7.43 7.51 19.07.2029 04.07.2024 ESQ20y ESQnc C2 C1 4EQy3.222 .32.497 7.99 9.98 19.63 42.74 9.73 8.34 6.82 6.70 26.64 20.59 9.21 3.08 9.73 8.34 6.82 31.12.2028 6.70 26.12.2028 22.11.2027 23.11.2027 EJQ8y EJQ10y B4 EJQ20y B3 EJQnc B2 B1 3EEvJ2yat 30.0641 07 .619.81 19.98 19.99 7.26 6.13 6.39 10.71 10.54 10.54 4.16 4.12 4.14 13.06.2026 19.06.2026 16.06.2026 EVEdvEJQ20y+ast2 EVEdvEJQ20y+ast1 E3 EVEdvEJQ20y E2 E1 w seod a erahdwt nadditional an with reached be can asteroids Two 3EEvJQ0 50.0642 88 76 20.00 25.00 30.00 17.68 8.71 5.39 28.85 20.61 13.22 4.22 4.24 4.21 05.06.2026 05.06.2026 06.06.2026 EVEdvEJSQ20y EVEdvEJSQ25y I3 EVEdvEJSQ30y I2 I1 faon ms au hti o o large. too not is that value a km/s, 1 around of -3 ∆ YE FOTMLTAETRE OSN PCCATT QUAOAR TO SPACECRAFT A SEND TO TRAJECTORIES OPTIMAL OF TYPES V 19.04.2026 19.04.2026 -2 ∆ f11 ms h rnfr htcon- that transfers The km/s. 1.13 of V Earth Earth fol .6k/,wieteas- the while km/s, 0.26 only of -1 -3 -2 -1 4 0 1 2 3 Sun 0 11.06.2027 11.06.2027 16.06.2025 16.06.2025 21.11.2024 21.11.2024 3.08.2028 3.08.2028 Venus Venus Earth Earth 1 dv dv Earth Earth 2001 UT44 2001 UT44 12.02.2029 12.02.2029 2 AL 4 TABLE 3 ∆ V L km/s , -50 o87 ms n,fial,wt ii f2 years, 20 of limit a with finally, total the and, km/s; 8.71 to rwho h total the of growth total the years, 25 to limit this ing n aunsigy.I rnfrwt 0years 30 total with the transfer flight, a of Jupiter In time both of allows swingbys. also geometry Saturn Quaoar orbital and to The transfers respectively. the Fig- 16, of in and shown are 15 asteroids ures these by passage the tain 21.11.2044 21.11.2044 Makemake Makemake 152)20 T4atri none.Tecolor The encounter. asteroid UT44 2001 (135420) e -40 V ∆ -30 A V km/s , osu o1.8k/.Ti sensitive This km/s. 17.68 to up goes -20 26.08.2033 26.08.2033 -10 ∆ Saturn -50 -40 -30 -20 -10 V 10 20 30 40 50 ∆ 0 V napro ffieyasof years five of period a in 0 T ∆ msTF years TOF, km/s , V 10 s53 ms reduc- km/s; 5.39 is 20 ∆ V 30 sincreased is 40 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -8 -3 hs rnfr.Ti loidctsta h trajec- total a the and that years 25 indicates using for also tory window This launch limited transfers. a these Jupiter only of allows alignment ca Saturn the figure and that color indicates right The flight the of years. on time 20 trajectory to whole constrained the is a flight and blue ecl of left in time the the marked total on in are shown planets Quaoar the is to of Earth (red) orbits The trajectory swingby. transfer Jupiter Optimal 14. Fig. i given oli are in online. distances Quaoar viewed The of be right. orbit can ecl the the figure the on and color in trajectory blue whole Quaoar in the to marked and are (red) planets trajectory the transfer of Optimal 13. Fig. sarr opportunity. rare a is -6 1.08.2030 1.08.2030 -2 8.02.2030 8.02.2030 11.01.2027 11.01.2027 Jupiter Jupiter -4 Venus Venus Earth Earth -1 -2 19.06.2026 19.06.2026 -2 -1 -8 -6 -4 -2 -3 8 0 1 2 3 0 2 4 6 PIA RJCOIST UPRBL BET 51 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL Sun Sun 0 0 31.12.2028 31.12.2028 25.12.2028 25.12.2028 Earth Earth 10.11.2027 10.11.2027 ∆ Earth Earth 2 V dv dv 1 Earth Earth esta 0km/s 10 that less 4 2 6 8 3 -50 -50 hsppri rsne ee iue1 hw h to- the shows 17 Figure tal here. presented is paper this es h rnfr r ersne ytertype, their by represented are transfers The fers. dteobto uori lv.Tedpruefo the from departure The olive. in Quaoar of orbit the nd srnmcluis h ieo ih s8yas The years. 8 is flight of time The units. astronomical n pi ln,icuigteJptrsigy h orbits The swingby. Jupiter the including plane, iptic e h eatr rmteErhi hw nteleft the on shown is Earth the from departure The ve. pi ln,icuigteEEv aevradthe and maneuver EVEdvE the including plane, iptic evee online. viewed be n h itne r ie natooia nt.The units. astronomical in given are distances The . ∆ h umr falotmltasessonin shown transfers optimal all of summary The -40 -40 V safnto ftetm fflgtfraltrans- all for flight of time the of function a as -30 -30 3.4 umr ftetransfers the of Summary . -20 -20 25.04.2031 25.04.2031 Jupiter -10 -10 Jupiter -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 0 0 10 10 30.12.2036 30.12.2036 Quaoar Quaoar 20 20 10.06.2046 10.06.2046 Quaoar Quaoar 30 30 40 40 50 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México -3 -3 o aeae n re nsfrQaa.Fgr 18 Figure Quaoar. the ones for shows blue ones Haumea, green to and transfers Makemake, for for ones red the with including but 15, Figure online. as viewed same be The can E3. figure type Transfer 16. Fig. astronomica online. in viewed given be depa are can The distances figure olive. The color in The right. Quaoar years. of the orb orbit on The ecl the trajectory the and encounter. asteroid in green, UO6 in Quaoar 1993 asteroids to (155385) (red) the trajectory and transfer swingby Optimal 15. Fig. PRADO & SUKHANOV, SANCHEZ, 52 aeclrcd sue nFgr 17. Figure in used as code color same -2 7.02.2030 7.02.2030 2001 UE122 2001 UE122 9.01.2027 9.01.2027 -2 20.09.2030 20.09.2030 9.02.2030 9.02.2030 ∆ 10.01.2027 10.01.2027 11.08.2030 11.08.2030 1993 UO6 1993 UO6 Venus Venus Earth Earth V -1 Venus Venus fluc o l rjcois ihthe with trajectories, all for launch of Earth Earth -1 13.06.2026 13.06.2026 -2 -1 -4 -3 0 1 2 3 22.12.2028 22.12.2028 16.06.2026 16.06.2026 Sun 0 Earth Earth -3 -2 -1 3 0 1 2 Sun 0 6.11.2027 6.11.2027 25.12.2028 25.12.2028 Earth Earth dv dv 1 9.11.2027 9.11.2027 Earth Earth dv dv 1 Earth Earth 2 2 3 4 3 tr rmteErhi hw ntelf n h whole the and left the on shown is Earth the from rture -50 -50 h otitrsigKie etOjcs Haumea, Objects: Belt Kuiper of three interesting to most Earth the the from trajectories spacecraft the pi ln,icuigteEE aevr h Jupiter the maneuver, EVEE the including plane, iptic h 638 01U12atri none.Tecolor The encounter. asteroid UE122 2001 (64378) the t ftepaesaemre nbu,teobt fthe of orbits the blue, in marked are planets the of its nt.Tettltm fflgti osrie o20 to constrained is flight of time total The units. l h rsn ae ie eut fa nlssof analysis an of results gives paper present The -40 -40 -30 -30 -20 -20 .CONCLUSIONS 4. 27.04.2031 27.04.2031 29.04.2031 29.04.2031 -10 -10 Jupiter Jupiter -50 -40 -30 -20 -10 -50 -40 -30 -20 -10 10 20 30 40 50 10 20 30 40 50 0 0 0 0 10 10 20 20 14.06.2046 14.06.2046 3.04.2046 3.04.2046 Quaoar Quaoar Quaoar Quaoar 30 30 40 40 50 50 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México i.1.Total 17. Fig. ettaetre stemnmzto ftetotal the of minimization the more is the or trajectories choose best one to criterion make The to swingby(s). ob- intermediate planets were different trajectories using The tained Quaoar. and Makemake, be can figure color The online. transfers Quaoar. viewed optimal to green: Makemake; Red: transfers to transfers optimal flight. optimal of blue: time Haumea; to the of function a hc osnticuethe include not does which iefrteluc ie o h iso.Tere- The total a mission. using the base- for a trajectories times as identify launch used sults the is interval for 2023-2034 line The neuver. in(AEP n o h nnilspotfrom support financial the for and (FAPESP) Founda- Research tion Paulo São from 2016/14665-2 and 2015/19880-6 for 2014/22295-5, (CNPq); #2016/24561-0, Council Development Grants Technological National and the Scientific from #406841/2016-0 301338/2016-7 grants by and provided support the for be- sometimes a consumed, km/s. only fuel 0.1 with low the made in be increase mission. small can the observations of extra return shown, Those is scientific flight the the increases during some a which belt visiting with main of the transfers possibility of the asteroids longer years, Consider- and 20 of expensive missions. duration less space the deep in of ing account into plans not taken future are be the opportunities should Those and repeated, years. often 10 below flight sfudwt a bodies with the found of mis- each is to the the trajectory with of all one swingby, maneuver for targets Jupiter assist multi-gravity years as a 20 Using considered below sion. bodies flight three of times the with km/s 10 Total ∆V, km/s 10 12 14 16 18 h uhr iht xrs hi appreciation their express to wish authors The 2 4 6 8 0 B4 B3 B3 C3 B4 10 ∆ D2 E5 V ∆ B2 E3 D1 E3 C2 C2 C2 B2 E1 E2 E4 B3 F2 F3 F4 F5 F4 I3 20 o l ye fotmltasesas transfers optimal of types all for V F3 I2 Time offlight,years ne 0k/ n ieof time a and km/s 10 under PIA RJCOIST UPRBL BET 53 OBJECTS BELT KUIPER TO TRAJECTORIES OPTIMAL G3 E2 F2 I1 30 C1 ∆ B2 F1 V G2 40 A1 C1 B1 ftecpuema- capture the of C1 F1 H1 50 B1 G1 ∆ V B1 E1 60 below ∆ A1 A1 V 70 , ezl .P,Mrdn .G,Pg,D . mt,E. Smith, & E., D. Page, G., R. 9 177 Marsden, 39, P., 45, JSpRo, K. AcAau, Wenzel, 2002, 1999, M. A. J. A. Longuski, Sukhanov, & B. J. F. N. A. Strange, Prado, & 4766 A., 137, A. Sukhanov, AJ, H., 2009, R. E. C. M. Solórzano, Brown, & D. Ragozzine, 2009, al. et J. Licandro, R., Brunetto, Practice, N., Eng. Pinilla-Alonso, Control 1995, S. K. Flanagan, Noll, & & F. M., Peralta, W. Grundy, 2017, W., al. M. Buie, et H., B., A. Parker, Sicardy, P., al. Santos-Sanz, et L., R., J. J. Spencer, Ortiz, 63 B., 40, W. ARA&A, McKinnon, 2002, M., 77 C. 21, D. J. SSRv, Jewitt, Moore, 1977, & A. X. 421 P. J. 56, Penzo, Luu, AcAau, & 2005, E. W. C. R. Kohlhase, Bouchez, Farquhar, & & E., Y. Guo, M. Brown, K., Batygin, C., (New W. Astrodynamics, Fraser, of Methods 1968, R. 1982, P. H. R. Escobal, Stanford, & V., D. Byrnes, L7 A., 767, L. ApJ, D’Amario, 2015, 2013, al. E. et M. D., Brown, Perna, M., C. Ore, Dalle A., M. Barucci, Ed- (CAPES). Higher Personnel of ucation Improvement the for Coordination the be can figure color The online. Quaoar. viewed to green: Makemake; transfers transfers to optimal transfers optimal Red: optimal flight. blue: of Haumea; time to the of function a as i.18. Fig. Launch ∆V, km/s .19,AA,9,207 92, A&AS, 1992, J. 205 8, Theory, System and Dyn. Nonlinear 2008, A. 547 496, A&A, 1621 3, L9 825, ApJ, 2016, S. 219 550, Natur, 1284 351, Sci, 2016, 357 222, Icar, 2013, A. Wiley) NY: York, 465 5, JGCD, A107 584, A&A, 10 11 3 4 5 6 7 8 9 0 ∆ V B4 B3 B4 C3 B3 10 tluc o l ye fotmltransfers optimal of types all for launch at D2 E5 B2 E3 D1 E3 C2 C2 C2 B2 E1 E2 E4 B3 F4 F5 F2 F3 F4 I3 REFERENCES 20 F3 I2 Time offlight,years G3 E2 F2 I1 30 C1 B2 F1 G2 40 A1 C1 B1 C1 F1 H1 50 B1 G1 B1 E1 60 A1 A1 70 © Copyright 2019: Instituto de Astronomía, Universidad Nacional Autónoma de México 4SNHZ UHNV PRADO & SUKHANOV, SANCHEZ, Russia the of Institute Research Space Institute Sukhanov: National A. Sanchez: Alexander M. Diogo. and Prado A. B. F. Antonio 54 ats 78 22-1 ã oédsCmo P rzl(ant Brazil SP, ([email protected]). - Campos dos José São 12227-010 1758, nautas, cdm fSine,Mso,179 Russia 117997 Moscow, Sciences, of Academy n nopao [email protected]). onio.prado, o pc eerh-IP,A.dsAstro- dos Av. INPE, - Research Space for