• Non ci sono risultati.

End-of-life disposal concepts for Libration Point Orbit and Highly Elliptical Orbit missions

N/A
N/A
Protected

Academic year: 2021

Condividi "End-of-life disposal concepts for Libration Point Orbit and Highly Elliptical Orbit missions"

Copied!
24
0
0

Testo completo

(1)

Permanent link to this version

http://hdl.handle.net/11311/943355

RE.PUBLIC@POLIMI

Research Publications at Politecnico di Milano

Post-Print

This is the accepted version of:

C. Colombo, E.M. Alessi, W. van der Weg, S. Soldini, F. Letizia, M. Vetrisano, M. Vasile, A. Rossi, M. Landgraf

End-of-life disposal concepts for Libration Point Orbit and Highly Elliptical Orbit missions

Acta Astronautica, Vol. 110, 2015, p. 298-312 doi:10.1016/j.actaastro.2014.11.002

The final publication is available at https://doi.org/10.1016/j.actaastro.2014.11.002

Access to the published version may require subscription.

When citing this work, cite the original published paper.

© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license

(2)

END-OF-LIFE DISPOSAL CONCEPTS FOR LIBRATION POINT

ORBIT AND HIGHLY ELLIPTICAL ORBIT MISSIONS

Camilla Colombo1, Elisa Maria Alessi2, Willem van der Weg3, Stefania Soldini4, Francesca Letizia5, Massimo Vetrisano6, Massimiliano Vasile7, Alessandro Rossi8, Markus Landgraf9

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

1 Introduction

/LEUDWLRQ3RLQW2UELWV /32V DQG+LJKO\(OOLSWLFDO2UELWV +(2V DUHRIWHQVHOHFWHGIRUDV WURSK\VLFV DQG VRODU WHUUHVWULDO PLVVLRQV DV WKH\ RIIHU YDQWDJH SRLQWV IRU WKH REVHUYDWLRQ RI WKH (DUWKWKH6XQDQGWKH8QLYHUVH7KHQHLJKERXUKRRGRIWKH/DJUDQJLDQFROOLQHDUOLEUDWLRQSRLQWV /DQG/RIWKH6XQ±(DUWKV\VWHPKDVEHHQUHFRJQLVHGDVDYDQWDJHORFDWLRQIRUDVWURSK\VLFV DQG VRODU PLVVLRQV VLQFH WKH HQG RI WKH V ZLWK WKH 1$6$ ,6(( PLVVLRQ ,QGHHG RUELWV DURXQG/DQG/DUHUHODWLYHO\LQH[SHQVLYHWREHUHDFKHGIURPWKH(DUWKDQGHQVXUHDQHDUO\FRQ VWDQWJHRPHWU\IRUREVHUYDWLRQDQGFRPPXQLFDWLRQJHRPHWU\EHFDXVHWKH/DQG/OLEUDWLRQRU ELWV DOZD\V UHPDLQ FORVH WR WKH (DUWK DW D GLVWDQFH RI URXJKO\  PLOOLRQ NP 0RUHRYHU / LV VLWXDWHGRQWKH6XQ±(DUWKOLQHEH\RQGWKH(DUWKDQGWKXVLWLVVXLWDEOHIRUKLJKO\SUHFLVHWHOH 

0DULH &XULH 5HVHDUFK )HOORZ 'HSDUWPHQW RI $HURVSDFH 6FLHQFH DQG 7HFKQRORJ\ 3ROLWHFQLFR GL 0LODQR ,WDO\ (PDLOFDPLOODFRORPER#SROLPLLW 3RVWGRFWRUDO5HVHDUFK)HOORZ,)$&&156HVWR)LRUHQWLQR,WDO\ 3K'FDQGLGDWH$GYDQFHG6SDFH&RQFHSWV/DERUDWRU\8QLYHUVLW\RI6WUDWKFO\GH*ODVJRZ8. 3K'FDQGLGDWH$VWURQDXWLF5HVHDUFK*URXS8QLYHUVLW\RI6RXWKDPSWRQ8. 3K'FDQGLGDWH$VWURQDXWLF5HVHDUFK*URXS8QLYHUVLW\RI6RXWKDPSWRQ8. 3K'FDQGLGDWH$GYDQFHG6SDFH&RQFHSWV/DERUDWRU\8QLYHUVLW\RI6WUDWKFO\GH*ODVJRZ8. 3URIHVVRU$GYDQFHG6SDFH&RQFHSWV/DERUDWRU\8QLYHUVLW\RI6WUDWKFO\GH*ODVJRZ8. 6HQLRU/HFWXUHU,)$&&156HVWR)LRUHQWLQR,WDO\ 0LVVLRQ$QDO\VW(6$(62&'DUPVWDGW*HUPDQ\

(3)

  VFRSHVUHTXLULQJJUHDWWKHUPDOVWDELOLW\$OVRVLQFHWKH6XQWKH(DUWKDQGWKH0RRQDUHDOZD\V EHKLQGWKHVSDFHFUDIW//32HQVXUHDFRQVWDQWJHRPHWU\IRUREVHUYDWLRQZLWKKDOIRIWKHHQWLUH FHOHVWLDOVSKHUHDYDLODEOHDWDOOWLPHV2QWKHRWKHUKDQGKLJKO\HOOLSWLFDORUELWVDERXWWKH(DUWK JXDUDQWHHORQJGZHOOLQJWLPHVDWDQDOWLWXGHRXWVLGHWKH(DUWK¶VUDGLDWLRQEHOWWKHUHIRUHORQJSH ULRGVRIXQLQWHUUXSWHGVFLHQWLILFREVHUYDWLRQDUHSRVVLEOHZLWKQHDUO\QREDFNJURXQGQRLVHIURP UDGLDWLRQV 1RJXLGHOLQHVFXUUHQWO\H[LVWIRU/32DQG+(2PLVVLRQV¶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

,QWKLVDUWLFOHDQDQDO\VLVRISRVVLEOHGLVSRVDOVWUDWHJLHVIRU/32DQG+(2PLVVLRQVLVSUH VHQWHG DV D UHVXOW RI D (XURSHDQ 6SDFH $JHQF\¶V *HQHUDO 6WXG\ 3URJUDPPH VWXG\ ZLWKLQ WKH *UHHQ236LQLWLDWLYH(QGRIOLIHGLVSRVDORSWLRQVDUHSURSRVHGZKLFKH[SORLWWKHPXOWLERG\G\ QDPLFVLQWKH(DUWKHQYLURQPHQWDQGLQWKH6XQ±(DUWKV\VWHPSHUWXUEHGE\WKHHIIHFWVRIVRODU UDGLDWLRQ SUHVVXUH WKH (DUWK¶V JUDYLW\ SRWHQWLDO DQG DWPRVSKHULF GUDJ 7KH RSWLRQV DQDO\VHG LQ WKLVVWXG\DUH(DUWKUHHQWU\RULQMHFWLRQLQWRDJUDYH\DUGRUELWIRU+(2VZKLOHVSDFHFUDIWRQ /32VFDQEHGLVSRVHGWKURXJKDQ(DUWKUHHQWU\RUFDQEHLQMHFWHGRQWRWUDMHFWRULHVWRZDUGVD 0RRQLPSDFWRUWRZDUGVDQKHOLRFHQWULFSDUNLQJRUELWE\PHDQVRILPSXOVLYHGHOWDvPDQRHX YUHVRUWKHHQKDQFHPHQWRIVRODUUDGLDWLRQSUHVVXUHZLWKVRPHGHSOR\DEOHOLJKWZHLJKWUHIOHFWLYH VXUIDFHV2QWKHEDVH RI WKH RSHUDWLRQDO FRVW FRPSOH[LW\DQGGHPDQGLQJGHOWDv PDQRHXYUHV VRPHGLVSRVDORSWLRQVZHUHSUHOLPLQDU\DQDO\VHGDQGODWHUGLVFDUGHGVXFKDVWKH+(2GLVSRVDO WKURXJKWUDQVIHUWRD/32RU+(2GLVSRVDOWKURXJK0RRQFDSWXUH 7KHDUWLFOHVXPPDULVHVWKHG\QDPLFDOPRGHOVFRQVLGHUHGIRUHDFKGLVSRVDOGHVLJQLQWKHFDVH RI+(2VWKHORQJWHUPYDULDWLRQRIWKHRUELWLVSURSDJDWHGWKURXJKVHPLDQDO\WLFDOWHFKQLTXHV FRQVLGHULQJWKHLQWHUDFWLRQRIWKHOXQLVRODUSHUWXUEDWLRQVZLWKWKH]RQDOKDUPRQLFVRIWKH(DUWK¶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ǻv UH TXLUHPHQWV DVZHOO DVWKHVXVWDLQDELOLW\FRQWH[W6RPHJHQHUDO UHFRPPHQGDWLRQVDUHGUDZQLQ WHUPVRIV\VWHPUHTXLUHPHQWVDQGPLVVLRQSODQQLQJ

(4)

 

2 Selected

missions

7KHVHOHFWHGPLVVLRQVIRUWKHGHWDLOHGDQDO\VLVRIGLVSRVDOVWUDWHJLHVDUH,17(*5$/ FXUUHQW  DQG;001HZWRQ FXUUHQW LQWKH+(2FODVV+HUVFKHO SDVW 62+2 FXUUHQW DQG*DLD FXU UHQW LQWKH/32FODVV

 0LVVLRQFRQVWUDLQWV

7DEOHVXPPDULVHVWKHPDLQPLVVLRQFRQVWUDLQWVIRUWKHVHOHFWHGPLVVLRQVLQWHUPVRIDYDLO DEOH RQERDUG SURSHOODQWDQG HTXLYDOHQW ǻv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cR DQHTXLYDOHQWUHIOHFWLYLW\FRHIILFLHQW R c LVFRPSXWHGFRQVLGHULQJWKHFRQWULEXWLRQRIDOO WKHSDUWVRIWKHVSDFHFUDIW DQGWKHDUHDWRPDVVUDWLRAm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ǻY >PV@ GDWH  )DLOXUHV &RQVXPSWLRQ SHU\HDU>NJ@ 3RLQWLQJFRQVWUDLQWV F%2/5  0D[$P (2/ >PNJ@ 62+2 /32        ORVV RI J\URVFRSHV  ƒ  6(9DQJOHƒ   +HUVFKHO /32  

     +HOLXPILQLVKHG  &RQVWUDLQWVGXH WR WKHU PDO PDQ DJHPHQWDQG VWDU WUDFNHUV RSHUDWLRQ 6XQVKDGH SRLQWLQJ WRZDUGV WKH 6XQ   *DLD /32   (2/   (2/  1$ 1$ 6SLQSUHFHVVLQJD[LV ZLWK DQ DQJOH RI ƒDURXQG VF6XQOLQH  

(5)

  ,17(*5$/ +(2        7HOHVFRSHQHYHU SRLQWV FORVHU WKDQ ƒIURPWKH 6XQ   ;00 +(2      5HDFWLRQZKHHO GHJ UDGDWLRQ  7HOHVFRSH QHYHU SRLQWV FORVHU WKDQ ƒIURPWKH 6XQ   

 0LVVLRQVFHQDULRV

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±(DUWK0RRQEDU\ FHQWUH 0LVVLRQ 2UELW /3 7 [ \ ] Y[ Y\ Y] &- 62+2 +DOR6RXWK /    ±    

+HUVFKHO +DOR1RUWK /      ±  

 1.008 1.009 1.01 1.011 -0.005 -0.003 -0.001 0.001 0.003 0.005 -0.0016 -0.0007 0.0002 0.0011 0.002 0.0029 z HORIZONS CR3BP initial condition x y z 0.989 0.9895 0.99 0.9905 0.991 0.9915 -0.004 -0.002 0 0.002 0.004 -0.0008 -0.0005 -0.0002 0.0001 0.0004 0.0007 z HORIZONS CR3BP initial condition x y z D  E 

)LJXUH  +DOR RUELW SUHGLFWHG E\ WKH -3/ +25,=216 V\VWHP UHG  DQG RUELW UHSUR GXFHG LQ WKH &5%3 XVHG IRU WKH GLVSRVDO DQDO\VLV EOXH  1RQGLPHQVLRQDO XQLWVV\QRGLF UHIHUHQFHV\VWHPFHQWUHGDWWKH6XQ±(DUWK0RRQEDU\FHQWUH$ +HUVFKHOE 62+2

(6)

  1.51e+08 1.511e+08 1.512e+08 -250000 0 250000 -60000 -30000 0 30000 60000 90000 z (km) x (km) y (km) z (km)  -100000 -80000 -60000 -40000 -20000 0 20000 40000 60000 80000 100000 -300000 -100000 0 100000 300000 z (km) y (km) D  E 

)LJXUH  /LVVDMRXV RUELW VHOHFWHG WR VLPXODWH WKH HYROXWLRQ RI *DLD 6\QRGLF UHIHUHQFH V\VWHPFHQWUHGDWWKH6XQ±(DUWK0RRQEDU\FHQWUH$ 'UHSUHVHQWDWLRQDQGE \]SUR MHFWLRQ



7KHG\QDPLFVRI+(2ZLWKKLJKDSRJHHDOWLWXGHLVPDLQO\LQIOXHQFHGE\WKHHIIHFWRIWKHWKLUG ERG\SHUWXUEDWLRQGXHWRWKHJUDYLWDWLRQDODWWUDFWLRQRIWKH0RRQDQGWKH6XQDQGWKHHIIHFWRIWKH (DUWK¶V REODWHQHVV )RU WKH DQDO\VLV RI +(2 GLVSRVDO WKH VXLWH PlanODyn ZDV GHYHORSHG WR SURSDJDWHWKH(DUWKFHQWUHGG\QDPLFVE\PHDQVRIWKHDYHUDJHGYDULDWLRQRIWKHRUELWDOHOHPHQWV LQ .HSOHULDQ HOHPHQWV 7KH SHUWXUEDWLRQV FRQVLGHUHG DUH VRODU UDGLDWLRQ SUHVVXUH DWPRVSKHULF GUDJZLWKH[SRQHQWLDOPRGHORIWKHDWPRVSKHUH]RQDOKDUPRQLFVRIWKH(DUWK¶VJUDYLW\SRWHQWLDO XSWRRUGHUWKLUGERG\SHUWXUEDWLRQRIWKH6XQDQGWKH0RRQXSWRGHJUHHRIWKH/HJHQGUH SRO\QRPLDO 7KH FRGH ZDV VXFFHVVIXOO\ YDOLGDWHG DJDLQVW WKH HSKHPHULGHV RI WKH ,17(*5$/ PLVVLRQIURP1$6$+25,=216DQGRIWKH;001HZWRQPLVVLRQJLYHQE\(6$ VHH)LJ XUH 



D  E 

)LJXUH  +(2 SHULJHH DOWLWXGH HYROXWLRQ %OXH DFWXDO HSKHPHULGHV 5HG SURSDJDWLRQ ZLWK3ODQ2'\QF\DQSURSDJDWLRQZLWK67(/$VRIWZDUH$ ,17(*5$/DQGE ;00 1HZWRQ

(7)

 

3 HEO disposal through Earth re-entry

+(2PLVVLRQVFDQEHGLVSRVHGLQDGHILQLWHZD\WKURXJKUHHQWU\LQWRWKH(DUWK¶VDWPRVSKHUH 7KLVFDQEHDFKLHYHGE\H[SORLWLQJWKHQDWXUDOORQJWHUPSHUWXUEDWLRQVWRWKHRUELWGXHWRWKHLQ WHUDFWLRQEHWZHHQOXQLVRODUSHUWXUEDWLRQDQGWKHJHIIHFWDVH[SODLQHGLQ5HI 7KHGLVSRVDOVWUDWHJ\WRUHHQWU\LVGHVLJQHGFRQVLGHULQJDVLQJOHPDQRHXYUHSHUIRUPHGGXULQJ WKHQDWXUDORUELWHYROXWLRQRIWKHVSDFHFUDIW7KHYDULDWLRQLQRUELWDOHOHPHQWV'kep GXHWRDQLP SXOVLYHPDQRHXYUHDWDJHQHULFWLPHtLVFRPSXWHGWKURXJK*DXVV¶SODQHWDU\HTXDWLRQVZULWWHQLQ ILQLWHGLIIHUHQFHIRUPDV  'kep G kep t

m fm'Y

  

ZKHUH fmLVWKHWUXHDQRPDO\DWZKLFKWKHPDQRHXYUHLVJLYHQDQG'Y WKHYHORFLW\FKDQJHGH

ILQHGE\LWVPDJQLWXGHLQSODQHDQGRXWRISODQHDQJOHV7KHQHZVHWRIRUELWDOHOHPHQWVDIWHUWKH PDQRHXYUHkepd

 kepd kep t

m  'kep  

LVSURSDJDWHGIRUWKHDYDLODEOHLQWHUYDORIWLPHWRSHUIRUPWKHGLVSRVDOZLWKPlanODyn7KHQWKH HYROXWLRQRIWKHSHULJHHDOWLWXGHhp

t VWDUWLQJIURPWKHGHYLDWHGFRQGLWLRQLQ(T  LVFRP

SXWHGDQGWKH PLQLPXP SHULJHH DOWLWXGHhpPLQRI WKHSHULJHH KLVWRU\ FDQ EH GHWHUPLQHG DVWKH

PLQLPXPSHULJHHDOWLWXGHWKDWWKHVSDFHFUDIWUHDFKHVZLWKLQWKHDOORZHGDYDLODEOHWLPHVSDQIRU UHHQWU\'tGLVSRVDO'XHWRWKHQDWXUDORVFLOODWLRQVRIWKHRUELWEHFDXVHRISHUWXUEDWLRQVWKHHIIHFW RIWKHGLVSRVDOPDQRHXYUHZLOOEHGLIIHUHQWGHSHQGLQJRQWKHWLPHLWLVDSSOLHG7KHUHIRUHGLIIHU HQWVWDUWLQJGDWHVIRUWKHGLVSRVDOPDQRHXYUHZHUHVHOHFWHGZLWKLQDZLGHGLVSRVDOZLQGRZ)RU HDFKLQLWLDOFRQGLWLRQFRUUHVSRQGLQJWRDFHUWDLQWLPHWKHPDQRHXYUHPDJQLWXGH'v DQGGLUHFWLRQ DQGWKHSRLQWRQWKHRUELWZKHUHWKHPDQRHXYUHLVSHUIRUPHG fmZHUHGHWHUPLQHGWKURXJKJOREDO RSWLPLVDWLRQ$Q\UHDFKHGDOWLWXGHEHORZNPLVDFFHSWHGDQGWKHWRWDOǻvLVPLQLPLVHG 2QFHDILUVWJXHVVVROXWLRQZDVIRXQGWKURXJKJOREDORSWLPLVDWLRQDQGFRQVLGHULQJWKHDYHUDJHG G\QDPLFVZLWKPlanODyn, LQDVHFRQGVWDJHDKLJKILGHOLW\RSWLPLVDWLRQLVSHUIRUPHG$IXOOG\ QDPLFDOPRGHOLVFRQVLGHUHGZULWWHQLQD&DUWHVLDQUHIHUHQFHIUDPHFHQWUHGDWWKH(DUWK7KHKLJK ILGHOLW\PRGHOLQFOXGHVWKHKLJKHUWHUPVXSWRWKHWKGHJUHHVIRUVHFWRULDODQGWHVVHUDOKDUPRQLFV RIWKH(DUWKDQG0RRQJUDYLW\ILHOGWKHJUDYLWDWLRQDOSHUWXUEDWLRQVRIWKH6XQWKH0RRQDQGWKH SODQHWV RI WKH VRODU V\VWHP VRODU UDGLDWLRQ SUHVVXUH DQG DWPRVSKHULF GUDJ ZLWK DQ H[SRQHQWLDO PRGHO RI WKH (DUWK¶V DWPRVSKHUH *LYHQ WKH IDFW WKH PRGHO XVHG IRU GHVLJQLQJ WKH UHHQWU\ LV EDVHGRQWKHSURSDJDWLRQRIWKHPHDQRUELWDQGRQO\VRPHSHUWXUEDWLRQVHIIHFWVDUHFRQVLGHUHGLI RQHSHUIRUPVWKHUHHQWU\PDQRHXYUHDWWKHQRPLQDOWLPHWKHRUELWFRXOGQRWUHHQWHUEHFDXVHWKH RVFXODWLQJ WUXH DQRPDO\ GRHV QRW FRUUHVSRQG WR WKH RSWLPDO WUXH DQRPDO\ fm IRXQG WKURXJK

JOREDO RSWLPLVDWLRQ )RU WKLV UHDVRQ WKH VROXWLRQV FRPSXWHG ZLWK PlanODyn LV WKHQ UHILQHG WR HQVXUHDUHHQWU\DOVRLQWKHKLJKILGHOLW\PRGHO7KHUHIRUHWKHVFRSHLQWKHVHFRQGVWDJHRIWKH GHVLJQSURFHVVLVWRLGHQWLI\VXLWDEOHLQLWLDOFRQGLWLRQVW\SLFDOO\ILQGLQJWKHLQVWDQWRIWLPHLQWKH QHLJKERXUKRRGRIWKHQRPLQDOVROXWLRQDWZKLFKDPDQRHXYUHRIWKHVDPHPDJQLWXGHZLOORIIHU WKHPRVWIDYRXUDEOHILQDOFRQGLWLRQV$WZRVWHSRSWLPLVDWLRQZDVSHUIRUPHG7KHILUVWRSWLPLVD WLRQVWHSFRQVLVWVLQUXQQLQJDEURDGVHDUFKLQWUXHDQRPDO\ZLWKDVWHSRIGHJUHHWRREWDLQWKH RSWLPDOFRQGLWLRQVZKLFKSRVVLEO\OHDGWRUHHQWU\E\DSSO\LQJWKHQRPLQDOǻvPDQRHXYUHFRP SXWHG LQ (T   7KH VHFRQG RSWLPLVDWLRQ VWHS DSSOLHV D TXDVL1HZWRQ PHWKRG WR UHHQWHU WKH

(8)

 

VSDFHFUDIW EHORZ  NP E\ RSWLPLVLQJ WKH ǻv PDQRHXYUH SHUIRUPHG DW WKH LGHQWLILHG RSWLPDO LQLWLDOFRQGLWLRQ

,QWKHIROORZLQJVHFWLRQRQO\,17(*5$/GLVSRVDOWKURXJK(DUWKUHHQWU\LVSUHVHQWHGDVIURPWKH DQDO\VLV;00UHHQWU\UHVXOWHGXQIHDVLEOHZLWKWKHDYDLODEOHRQERDUGIXHORYHUDWLPHSHULRGRI \HDUV

 ,17(*5$/GLVSRVDOWKURXJK(DUWKUHHQWU\

,17(*5$/ RUELW IXWXUH HYROXWLRQ ZDV SUHGLFWHG XQWLO  VHH )LJXUH   7KH LQWHUYDO GLVSRVDO

't FRQVLGHUHGIRUWKHGLVSRVDOGHVLJQLVIURPWR7KHPD[LPXP v'  DYDLODEOHIRUWKHPDQRHXYUHVHTXHQFHVLVHVWLPDWHGWREHPVLQDVLQ7DEOH :LWKLQWKHFRQVLGHUHG'tGLVSRVDOUHHQWU\EHORZNPLVSRVVLEOHZLWK'v DVOLWWOHDVPVDV YLVLEOHLQ)LJXUHWKDWVKRZVWKHUHTXLUHG v' IRU(DUWKUHHQWU\DVIXQFWLRQRIWKHWLPHWKHPD QRHXYUHLVSHUIRUPHGEHWZHHQDQG EOXHOLQH 7KHGLVSRVDOVROXWLRQVFDQ EHJURXSHGLQIRXUIDPLOLHVRILQLWLDOFRQGLWLRQVWKDWSUHVHQWVLPLODUG\QDPLFVEHKDYLRXULQWHUPV RIHYROXWLRQRIRUELWDOHOHPHQWVIROORZLQJWKHPDQRHXYUH,QGHHGWKUHHMXPSVLQWKHUHTXLUHG'v  IRUUHHQWU\DUHYLVLEOHIURPWKHEOXHOLQHLQ)LJXUHD7KHEHVWVROXWLRQVEHORQJVWRIDPLO\ ZKLFK KDYH D UHHQWU\ LQ  ZLWK D v' EHWZHHQDQGPV GHSHQGLQJRQWKH\HDUDQG PRQWKWKHPDQRHXYUHLVJLYHQEHWZHHQDQGWKHILUVWKDOIRI )DPLO\GLVSRVDORS WLRQVLQVWHDGQHHGDKLJKHU'vWREHJLYHQEHWZHHQWKHVHFRQGKDOIRIDQGWKHILUVWKDOIRI WRUHDFKWKHPLQLPXP SHULJHH EHWZHHQ  DQG  TXLFNHU UHHQWU\ &RORPER HWDO VKRZHGWKHGHSHQGHQFHVRQWKHGLIIHUHQWIDPLOLHVRIUHHQWU\FRQGLWLRQVXSRQWKHRUELWDOHOHPHQWV ZLWKUHVSHFWWRWKHPDLQGLVWXUELQJERG\LHWKH0RRQ7KHRSWLPDOPDQRHXYUHDOORZVLQFUHDV LQJWKHDPSOLWXGHRIWKHRVFLOODWLRQVLQDQRPDO\RIWKHSHULJHHPHDVXUHGZLWKUHVSHFWWRWKH(DUWK 0RRQSODQHDQGWKHUHIRUHLQHFFHQWULFLW\VRWKDWWKHHFFHQWULFLW\FDQEHLQFUHDVHGXSWRWKHFULWL FDOHFFHQWULFLW\

 eFULW 

R(DUWKhpUHHQWU\

a

ZKHUHR(DUWKLVWKH UDGLXV RI WKH (DUWKa LV WKH VHPLPDMRU D[LV DQG WKH WDUJHW SHULJHHDOWLWXGH UHHQWU\ p h LVVHWWRNP,QSDUWLFXODUZKHQWKHQRPLQDORUELWHFFHQWULFLW\LVORZWKHRSWLPLVHG UHHQWU\PDQRHXYUHWHQGVWRIXUWKHUGHFUHDVHLWDVDFRQVHTXHQFHWKHIROORZLQJORQJWHUPSURSD JDWLRQZLOOUHDFKDKLJKHUHFFHQWULFLW\FRUUHVSRQGLQJWRDUHHQWU\,QWKLVFDVHWKHPDQRHXYUHLV PRUHHIILFLHQW LHORZHUǻvLVUHTXLUHGDVLQIDPLO\ 2QWKHRWKHUVLGHZKHQWKHQRPLQDOHF FHQWULFLW\LVKLJKWKHUHHQWU\PDQRHXYUHDLPVDWIXUWKHULQFUHDVLQJLW,QWKLVFDVHWKHUHTXLUHG 'v LVKLJKHUZKLOHWKHWDUJHWPLQLPXPSHULJHHLVUHDFKHGDIWHUDVKRUWHUWLPH )LJXUHE )XU WKHUGHWDLOVRQWKHRSWLPLVDWLRQRIWKHUHHQWU\PDQRHXYUHDVIXQFWLRQRIWKHLQLWLDORUELWDOSDUDPH WHUVDUHJLYHQLQ5HI ,Q)LJXUHDUHILQHGVROXWLRQVZLWKWKHKLJKILGHOLW\PRGHORIWKHG\QDPLFVDUHVKRZQZLWKDUHG OLQH (VSHFLDOO\ IRU WKH EHVW UHHQWU\ FRQGLWLRQV WKHUH LV D YHU\ JRRG DJUHHPHQW EHWZHHQ WKH QRPLQDOVROXWLRQVDQGWKHUHILQHGVROXWLRQV7KHUHDUHFDVHVIRUZKLFKWKHPDJQLWXGHRIWKHPD QRHXYUHVLVLQWKHRUGHURIPVZKLFKLVWKHPD[LPXPDYDLODEOHǻvIRU,17(*5$/ VHH7D EOH ,QWKHZRUVWFDVHVLQVWHDGDQDGGLWLRQDO'v LQWKHRUGHURIPVZLWKUHVSHFWWRWKH QRPLQDOPDQRHXYUHLVUHTXLUHG

(9)

   40000 5000 6000 7000 8000 9000 10000 11000 20 40 60 80 100 120 140 MJD2000 time [days] Δ velocity [m/s] Nominal Optimised D  E  )LJXUH5HTXLUHGǻYWRGHRUELW,17(*5$/7KHEOXHOLQHUHIHUVWRWKHQRPLQDOVROX WLRQVIURPWKHJOREDORSWLPLVDWLRQWKHUHGOLQHVWRWKHRSWLPLVHGVROXWLRQV 

4 HEO disposal through injection into a graveyard

sta-ble orbit

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lanODyn $ JUDYH\DUG RUELW LV GHVLJQHG LPSRVLQJ WKDW DIWHU WKH PD QRHXYUHWKHYDULDWLRQRIWKHHFFHQWULFLW\LQWLPHVWD\VOLPLWHGWKDWLV'e t

e t PD[ e t

PLQLV PLQLPLVHGZKHUHe t

PD[DQGe t

PLQDUHUHVSHFWLYHO\WKHPD[LPXPDQGPLQLPXPHFFHQWULFLW\ UHDFKHGGXULQJWKHQDWXUDOHYROXWLRQDIWHUWKHGLVSRVDOPDQRHXYUHLVJLYHQ,QRUGHUWRDQDO\VHD ZLGHUDQJHRIGLVSRVDOGDWHVGLIIHUHQWVWDUWLQJGDWHVIRUWKHGLVSRVDOZHUHVHOHFWHG6LQFH(DUWK UHHQWU\ZDVVKRZQWREHXQIHDVLEOHZLWKWKHDYDLODEOHRQERDUGSURSHOODQWWKHVHOHFWHGGLVSRVDO RSWLRQIRU;00LVWKHWUDQVIHULQWRDJUDYH\DUGRUELW7KLVRSWLRQLVQRWVKRZQIRU,17(*5$/ DVZKHUHSRVVLEOHUHHQWU\KDVWREHSUHIHUUHGWRJUDYH\DUGRUELWGLVSRVDO

 ;001HZWRQJUDYH\DUGRUELWGLVSRVDO

;001HZWRQPLVVLRQLVSODQQHGWREHGLVSRVHGDIWHU7KHLQWHUYDO'tGLVSRVDOFRQVLGHUHG IRU WKH GLVSRVDO GHVLJQ LV IURP  WR  DQG IRU HDFK VWDUWLQJ GDWH DQDO\VHG D JUDYH\DUGRUELWZDVGHVLJQHGZLWKWKHUHTXLUHPHQWWREHVWDEOHIRU\HDUSHULRG7KHPD[LPXP v ' DYDLODEOHIRUWKHPDQRHXYUHVHTXHQFHVLVHVWLPDWHGWREHPVLQFRQVLGHULQJ D\HDUFRQVXPSWLRQRINJDVSHFLILFLPSXOVHRIVDQGWKHFXUUHQWSURSHOODQWPDVVVKRZQLQ 7DEOH+RZHYHULQRUGHUWRNHHSWKHJHQHUDOYDOLGLW\RIWKLVVWXG\WRGLIIHUHQW+(2VWKHVHDUFK IRURSWLPDOWUDMHFWRULHVIRUGLVSRVDOZDVQRWOLPLWHGWRWKHRQERDUGSURSHOODQWUDWKHUDOLPLWRQ

(10)

 

WKH GHOWDY RI WKUHH WLPHV WKH DYDLODEOH GHOWDY RQERDUG ZDV FRQVLGHUHG ZKLFK FRUUHVSRQGV WR PVRQ

)LJXUHVKRZVWKHRSWLPDOPDQRHXYUHIRUDWUDQVIHULQWRDJUDYH\DUGRUELW7KHUHGOLQHUHSUH VHQWVWKHQRPLQDOHYROXWLRQRI;00RYHU'tGLVSRVDO(DFKVWDUWLQJWLPHFRQVLGHUHGIRUSHUIRUPLQJ WKHGLVSRVDOPDQRHXYUHLVLQGLFDWHGE\DEODFNFLUFOHLQ)LJXUHD7KHPDQRHXYUHLVUHSUHVHQWHG LQWKHSKDVHVSDFHRIHFFHQWULFLW\LQFOLQDWLRQDQGDQRPDO\RIWKHSHULFHQWUHZLWKUHVSHFWWRWKH (DUWK0RRQSODQH$VLWFDQEHVHHQIURP)LJXUHDWKHPDQRHXYUHDLPVDWPRYLQJWKHRUELWWR ZDUGVWKHFHQWUHRIWKHOLEUDWLRQORRSLQWKHHFFHQWULFLW\ZSKDVHVSDFH7KHPDJQLWXGHRIWKH PDQRHXYUHLVDOZD\VFORVHWRWKHPD[LPXPERXQGVHWDQGIURP)LJXUHDLWLVYHU\FOHDUWKDWD KLJKHUDYDLODEOH v' ZRXOGDOORZUHDFKLQJDPRUHVWDEOHRUELW LHFHQWUHRIWKHOLEUDWLRQ ,WKDV WR EH QRWHG WKDW WKH GHVLJQHG JUDYH\DUG RUELW UHGXFHV DW OHDVW WKH RVFLOODWLRQV LQ HFFHQWULFLW\ SUHYHQWLQJWKHVSDFHFUDIWIURPDQXQFRQWUROOHGUHHQWU\ZLWKLQWKH\HDUSHULRG,QGHHGLWZDV YHULILHGWKDWDIWHUWKHPDQRHXYUHLVSHUIRUPHGWKHPLQLPXPSHULJHHUHPDLQVDERYHNP



D  E 

)LJXUH  ;00 JUDYH\DUG GLVSRVDO PDQRHXYUHV EHWZHHQ  DQG  3KDVH VSDFH HYROXWLRQ LQ WKH HFFHQWULFLW\ȦLQFOLQDWLRQ SKDVH VSDFH (DUWK0RRQ SODQH  D  Ȧ HFFHQWULFLW\ DQG E  HFFHQWULFLW\LQFOLQDWLRQ 5HG QRPLQDO SUHGLFWHG RUELW EODFN OLQHV ǻY PDQRHXYUHV7KHVKDGHGDUHDLQGLFDWHVHFFHQWULFLWLHVEH\RQGWKHFULWLFDOHFFHQWULFLW\IRUUH HQWU\ DWSHULJHHDOWLWXGHRINP   $VDQH[DPSOHDGLVSRVDOWUDMHFWRU\LVVKRZQZKRVHPDQRHXYUHLVSHUIRUPHGRQ ZKLFKFRUUHVSRQGVWRWKH\HDU;00KDVEHHQFXUUHQWO\H[WHQGHGWR7KHHYROXWLRQRIWKHWUD MHFWRU\DIWHUWKHPDQRHXYUHLVVKRZQZLWKDF\DQOLQHLQ)LJXUH

(11)

  D  E  )LJXUH;00JUDYH\DUGGLVSRVDOPDQRHXYUHLQ3KDVHVSDFHHYROXWLRQLQWKHHF FHQWULFLW\ȦLQFOLQDWLRQSKDVHVSDFH (DUWK0RRQSODQH D ȦHFFHQWULFLW\DQGE HFFHQ WULFLW\LQFOLQDWLRQ5HGQRPLQDOSUHGLFWHGRUELWEODFNOLQHVǻYPDQRHXYUH7KHOLJKWEOXH OLQHUHSUHVHQWVWKHHYROXWLRQRIWKHRUELWDOHOHPHQWVZLWKUHVSHFWWRWKH(DUWK0RRQSODQH DIWHUWKHGLVSRVDOPDQRHXYUHLVSHUIRUPHGIRUWKHIROORZLQJ\HDUV 

5 LPO disposal through Earth re-entry

 +HUVFKHODQG62+2GLVSRVDOWKURXJK(DUWKUHHQWU\

7KH UHHQWU\ IRU +HUVFKHO DQG 62+2 /32 PLVVLRQV ZDV GHVLJQHG FRQVLGHULQJ WKHLU HSKHPHULGHVIURPWKH+25,=216V\VWHPZLWKRQHGD\WLPHVWHS)RU+HUVFKHOWKHLQLWLDOSR VLWLRQDQGYHORFLW\ZHUHFRQVLGHUHGIURPWR)RU62+2WKHODWHVWDYDLO DEOHGDWD WR ZHUHXVHGWRVLPXODWHWKHH[SHFWHGRUELWXQWLO WKHIRUHVHHQ HQGRIOLIH GDWH IRU62+2 )RU WKLV 62+2 RUELW LV DVVXPHGWR EH SHULRGLFLQWKH V\QRGLF&5%3UHIHUHQFHIUDPHZLWKSHULRGHTXDOWRGD\V

$ GLIIHUHQWLDO FRUUHFWLRQ SURFHGXUH LV LPSOHPHQWHG WR ILQG WKH FKDQJH LQ WKH LQLWLDO YHORFLW\ VXFKWKDWWKHVSDFHFUDIWLQMHFWVIURPWKHDFWXDO/32LQWRWKH(DUWKZDUGEUDQFKRIWKHXQVWDEOH LQYDULDQWPDQLIROGRIWKH/32FRPSXWHGLQWKH&57%3IURPWKHLQLWLDOFRQGLWLRQVLQ7DEOH 7KHDFWXDOLQLWLDOFRQGLWLRQIRUWKHQRPLQDOPLVVLRQIURPWKHUHDOHSKHPHULGHVLVWUDQVIRUPHGLQWR DQRQGLPHQVLRQDOV\QRGLF6XQ±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

(12)

 LVSURSDJDWHGLQDUHDOLVWLFG\QDPLFDOPRGHODFFRXQWLQJIRU6XQ(DUWK0RRQDQGDOOWKHSODQHWV IURP0HUFXU\WR3OXWRVRODUUDGLDWLRQSUHVVXUHDWPRVSKHULFGUDJEHORZDQDOWLWXGHRINP H[SRQHQWLDOPRGHO [JHRSRWHQWLDOLIWKHGLVWDQFHZLWKUHVSHFWWRWKHFHQWUHRIWKH(DUWKLV OHVVWKDQNP:KHQHYHUDQRUELWJHWVWRDQDOWLWXGHORZHUWKDQNPLQOHVVWKDQD\HDU WKHUHHQWU\DQJOHLVHYDOXDWHGDV  WDQ VLQ  FRV e f e f I   ZKHUHeLVWKHHFFHQWULFLW\DQGf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ctober 23, 2012, 18:00 October 20, 2012, 18:00 October 5, 2012, 18:00 November 17, 2012, 18:00 November 27, 2012, 18:00 December 4, 2012, 18:00 -16 -14 -12 -10 -8 -6 -4 -2 0 re-entry angle (deg)

0 5 10 15 20 25 30 35 40 re-entry cost (m/s) 160 180 200 220 240 260 280 300 320 340 -20 -15 -10 -5 0

re-entry angle (deg) 0 10 20 30 40 50 60 70 80 re-entry cost (m/s) 50 100 150 200 250 300 350 400 D  E  )LJXUH5HHQWU\IHDVLEOHVROXWLRQV$ +HUVFKHOPLVVLRQWKHFRORXUEDUUHIHUVWRWKHWR WDOWLPHRIIOLJKW GD\V IURPWKHOLEUDWLRQSRLQWRUELWWRWKH(DUWK% 62+2PLVVLRQWKH FRORXUEDULQGLFDWHVWKHVWDUWLQJGDWHRQWKH/32IRUWKHUHHQWU\ \HDUVIURP- 

 *DLDGLVSRVDOWKURXJK(DUWKUHHQWU\

7KH SURFHGXUH GHYHORSHG IRU *DLD LV VOLJKWO\ GLIIHUHQW ZLWK UHVSHFW WR WKH RQH DSSOLHG IRU 62+2DQG+HUVFKHODV*DLDFDQQRWUHHQWHUQDWXUDOO\VLQFHWKHPLQLPXPGLVWDQFHWRWKH(DUWK ZLWKRXWSHUIRUPLQJDQ\PDQRHXYUHLVDERXWNP7KHQRPLQDORUELWZDVDVVXPHGWREHD /LVVDMRXVTXDVLSHULRGLFRUELW VHH)LJXUH SURSDJDWHGIRUDERXW\HDUVWRDFFRXQWIRUWKH \HDUVRIQRPLQDOGXUDWLRQRIWKHPLVVLRQSOXVPRQWKVWRSHUIRUPWKHUHHQWU\SKDVH$VDWWKH

(13)



WLPHRIWKHVWXG\*DLDKDGQRWODXQFKHG\HWWZRLQLWLDOHSRFKVIRUWKHILUVWSRLQWRQWKH/LVVDMRXV RUELW ZHUH DVVXPHG QDPHO\  DQG  WR UHIOHFW WKH RSWLRQV IRU WKH PLVVLRQ ODXQFK

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ǻvOHVVWKDQPV1HYHUWKHOHVVLQVRPHFDVHVWKHPDQRHXYUHLVQHDUO\]HURLWWXUQV RXWWKDW*DLDFDQDUULYHWRWKH(DUWKDWQRH[SHQVHE\WUDYHOOLQJWKURXJKHLWKHUDKHWHURFOLQLFRU KRPRFOLQLFFRQQHFWLRQWRDYHU\KLJKDPSOLWXGH/32)XUWKHUGHWDLOVRQWKH/32GLVSRVDORSWLRQ WKRXJK(DUWKUHHQWU\DUHJLYHQLQ5HI D  E  )LJXUH2SWLPDOVROXWLRQVIRU*DLDUHHQWU\LQWHUPVRIUHHQWU\FRVWDQGUHHQWU\DQJOH IRU  R c A m PNJZLWKLQLWLDOHSRFKRQWKH/32RQ7KHFRORXUEDUUH SRUWV D WKHLQLWLDOHSRFKRIWKHUHHQWU\WUDMHFWRU\ \HDUIURP- DQG E WKHWRWDOWLPH RIWUDQVIHU GD\V 

6 LPO disposal towards a Moon impact

'LVSRVDO RSWLRQV YLD OXQDU VXUIDFH LPSDFW DQG PLVVLRQ H[WHQVLRQ E\ FDSWXUH LQWR OXQDU RUELW ZHUHVWXGLHGLQWKHFRXSOHGUHVWULFWHGWKUHHERG\SUREOHP ,QRUGHUWRDSSUR[LPDWHWKHWUDMHFWRU\LQERG\G\QDPLFVWUDMHFWRULHVOHJVGHULYLQJIURPWKH XQVWDEOHLQYDULDQWPDQLIROGVOHDYLQJWKH/32LQWKH6XQ± (DUWK0RRQ &5%3DQGWKHVWDEOH PDQLIROGVRID/32DURXQG/LQWKH(DUWK±0RRQ&5%3DUHFRQQHFWHGLQWRDVLQJOHWUDMHFWRU\ 7KH6XQ± (DUWK0RRQ &5%3KDVDVSULPDULHVWKH6XQDQGWKH(DUWK±0RRQEDU\FHQWUH &RQQHFWLRQEHWZHHQWKHWZRPRGHOVLVDFFRPSOLVKHGYLDWKHXVHRID3RLQFDUpVHFWLRQZKHUHWKH

(14)



WZRSKDVHVSDFHVPXVWLQWHUVHFW7KHLQLWLDORUELWDOSKDVHVD DQGSE EM

D RIERWK&5%3VFRQWURO WKH JHRPHWU\ RI WKH FRQQHFWLRQ 7KLV FDQ EH UHGXFHG WR D VLQJOH SDUDPHWHUD DEM DSE DV

RQO\WKHUHODWLYHSKDVLQJEHWZHHQ6XQ(DUWKDQG(DUWK±0RRQV\VWHPVLVQHFHVVDU\ $VWXG\ZDVXQGHUWDNHQWRFUHDWHDPDSRIFRQGLWLRQVQHDUWKH/OLEUDWLRQSRLQWRIWKH(DUWK 0RRQV\VWHPZKLFKFDQEHUHDFKHGIURPWKH6XQ±(DUWKV\VWHPDQGOHDGWRDORQJHUGXUDWLRQ TXDVLSHULRGLFRUELWDERXWWKH0RRQRUDQLPSDFWRQWKHOXQDUVXUIDFH7KHUHVXOWLQJVHWRILQLWLDO FRQGLWLRQVDERXWWKH(DUWK0RRQ/OLEUDWLRQSRLQWWKHLUFRUUHVSRQGLQJRUELWOLIHWLPHDQGWKHLU FDWHJRU\RIGHFD\ LH0RRQLPSDFWRUOXQDUFDSWXUHRUH[LWYLDOLEUDWLRQSRLQWV VHUYHVDVWKH EDVLVRIGHVLJQLQJWUDQVIHUVIURP6XQ±(DUWKOLEUDWLRQSRLQWRUELWWRZDUGVWKH0RRQ7KH6XQ± (DUWK/32XQVWDEOHPDQLIROGVDQGWKHWUDMHFWRU\DUFVIORZLQJWRZDUGVFKRVHQOXQDUWDUJHWVWDWHV DUHFRPSXWHGRQFHDQGVWRUHG2QFHWKLVLVFRPSOHWHGWKHWUDQVIRUPDWLRQRIWKHOXQDUWDUJHWVWDWH DUFVIURP(DUWK±0RRQWR6XQ±(DUWKV\QRGLFEDU\FHQWULFUHIHUHQFHIUDPHFDQEHTXLFNO\SHU IRUPHGIRUWKHHQWLUHGRPDLQRIWKHRUELWDOSKDVLQJDQJOHD 7KHORZHVWSRVVLEOHSURSHOODQWFRVWϬ ZDVVRXJKWIRUDQXPEHURI/32V VHH7DEOH 

7DEOH  2YHUYLHZ RI ORZHVW SURSHOODQW FRVW VROXWLRQV H[SUHVVHG LQ PV LQ WKH FRXSOHG &5%3)RUVRPHFDVHVWKHSUREOHPLVFRQVLGHUHGWREHSODQDUVRWKHSRVLWLRQDQGYHORFLW\ DORQJWKH]D[LVLVQHJOHFWHG /327\SH &DSWXUHǻY ,PSDFWǻY +HUVFKHO 1$ 1$ +HUVFKHO3ODQDU PV PV *DLD PV PV *DLD3ODQDU 1$ 1$ 62+2 PV PV 62+23ODQDU PV PV 

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ǻvFRVWD PHWULFQDPHGWKHCYDOXHPD\DOVREHXVHGXVLQJWKHRUELWDOHOHPHQWVRIWKHVSDFHFUDIWVWDWH MXVWEHIRUHLPSDFWDV 

   0RRQ 0RRQ 0RRQ          v C e r h a P P P        ZKHUHvDQGrDUHUHVSHFWLYHO\WKHVSDFHFUDIWYHORFLW\DQGSRVLWLRQhLVWKHDQJXODUPRPHQWXP DQGeWKHHFFHQWULFLW\7KHCYDOXHSURYLGHVDQLQGLFDWLRQRIWKHUREXVWQHVVRIWKHWUDQVIHUWKH ORZHUWKHYDOXHWKHPRUHEDOOLVWLFWKHFDSWXUHDWWKH0RRQLVDQGWKXVWKHPRUHUREXVWWKHWUDQV IHULVLQFDVHRIFRQWLQJHQFLHV,QWKHFDVHRIPLVVLQJWKHOXQDUVXUIDFHDWUDMHFWRU\ZLWKORZC YDOXH ZLOOEHTXDVLFDSWXUHG E\ WKH 0RRQDOORZLQJ IRU IXUWKHUVPDOO PDQRHXYUHV WRLPSDFW WKH

(15)

 VSDFHFUDIWXSRQWKHOXQDUVXUIDFH7KLVYDOXHLVXVHIXODVDQRWKHUSDUDPHWHUWRFRPSDUHRQHSDU WLFXODUWUDQVIHUZLWKDQRWKHU)XUWKHUGHWDLOVRQWKHGHVLJQVWUDWHJ\RIGLVSRVDOWUDMHFWRULHVWRZDUGV D0RRQLPSDFWDUHJLYHQLQ5HI,QWKHIROORZLQJVHFWLRQWKHFDVHVFHQDULRVRI+HUVFKHO6RKR DG*DLDDUHSUHVHQWHG

 +HUVFKHOGLVSRVDOWKURXJK0RRQLPSDFW

+HUVFKHO GLVSRVDO WKURXJK 0RRQ LPSDFW ZDV GHVLJQHG IURP  WR  $Q RYHUYLHZRIWKHVROXWLRQVIRXQGIRU+HUVFKHOLVVKRZQLQ)LJXUHZKLFKVKRZVWKHGDWHRIGH SDUWXUHIURPWKH/32RQWKHxD[LVDQGWKHWLPHRIIOLJKWDQGWKHCYDOXHEHIRUHOXQDUVXUIDFH LPSDFWRQWKHyD[LV(DFKVROXWLRQLVFRORXUFRGHGDFFRUGLQJWRWKHǻvFRVWLQPVWREULQJWKH VSDFHFUDIWRQWRLWVOXQDULPSDFWWUDMHFWRU\  3500 4000 4500 50 60 70 80 90 100 T [MJD2000] ToF [day] Δ v [m/s] 32.79 35 40 45 50 55 60 65 70 75 80 85 90 95 99.62 3500 4000 4500 −0.5 0 0.5 1 1.5 2 2.5 3 T [MJD2000] C3 [km 2/s 2] Δ v [m/s] 32.79 35 40 45 50 55 60 65 70 75 80 85 90 95 99.62 D  E  )LJXUH$ 7LPHRIIOLJKWDQGE &YDOXHWRLPSDFWWKH0RRQDVDIXQFWLRQRIWKHWLPH RIGHSDUWXUHIURPWKH+HUVFKHO/32LQ0-'6ROXWLRQVDUHFRORXUFRGHGDFFRUGLQJWR WKHǻYFRVWLQPV 

 62+2GLVSRVDOWKURXJK0RRQLPSDFW

7KHGDWHVFRQVLGHUHGIRUWKHDQDO\VLVRIGLVSRVDOPDQRHXYUHVIRU62+2WR0RRQLPSDFWDUH IURPWR6XFKZLQGRZGRHVQRWFRUUHVSRQGWRWKHGLVSRVDOZLQGRZKRZ HYHULWLVDSSURSULDWHWRVWXG\WKHEHKDYLRXURIWKHVROXWLRQVSDFHDQGWKHUHTXLUHGǻv)LJXUH VKRZVWKHVROXWLRQVIRU62+2

(16)

 −100040 0 1000 2000 3000 4000 5000 50 60 70 80 90 100 T [MJD2000] ToF [day] Δ v [m/s] 15.38 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99.79 −1000−6 0 1000 2000 3000 4000 5000 −4 −2 0 2 4 6 T [MJD2000] C 3 [km 2/s 2] Δ v [m/s] 15.38 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99.79 D  E  )LJXUH$ 7LPHRIIOLJKWDQGE &YDOXHWRLPSDFWWKH0RRQDVDIXQFWLRQRIWKHWLPH

RI GHSDUWXUH IURP WKH 62+2 /32 LQ 0-' 6ROXWLRQV DUH FRORXUFRGHG DFFRUGLQJ WR WKHǻYFRVWLQPV 

 *DLDGLVSRVDOWKURXJK0RRQLPSDFW

6ROXWLRQVIRU*DLDGLVSRVDOWKURXJK0RRQLPSDFWDUHVKRZQLQ)LJXUH 5000 5500 6000 6500 7000 7500 40 50 60 70 80 90 100 T [MJD2000] ToF [day] Δ v [m/s] 5.66 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99.92 5000 5500 6000 6500 7000 7500 −4 −3 −2 −1 0 1 2 3 T [MJD2000] C 3 [km 2/s 2] Δ v [m/s] 5.66 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 99.92 D  E  )LJXUH$ 7LPHRIIOLJKWDQGE &YDOXHWRLPSDFWWKH0RRQDVDIXQFWLRQRIWKHWLPH RIGHSDUWXUHIURPWKH*DLD/32LQ0-'6ROXWLRQVDUHFRORXUFRGHGDFFRUGLQJWRWKH ǻYFRVWLQPV

7 LPO disposal towards an heliocentric parking orbit

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

(17)



ǻvQHFHVVDU\LVFRPSXWHGIURPWKH-DFRELFRQVWDQW7KHVSDFHFUDIWLQLWV/32FDQEHSODFHGRQ RQHRIWKHXQVWDEOHPDQLIROGOHJVWKDWIORZIURPWKH/322QHEUDQFKZLOOOHDGWRZDUGVWKH6XQ UHDOPRIWKH(DUWK6XQV\VWHPZKLOHWKHRWKHUWRZDUGVWKHRXWHUSDUWRIWKH(DUWK6XQV\VWHP$V WKHVSDFHFUDIWPRYHVDZD\IURPWKH/32WKHǻvWRFKDQJHWKH-DFRELFRQVWDQWFDQEHFRPSXWHG DWDQ\WLPHDORQJDQ\SRLQWRIWKHPDQLIROGDV'vreq vactualvreq ZHUHvactualLVWKHDFWXDOYHORF

LW\RIWKHVSDFHFUDIWDORQJWKHPDQLIROGDQGWKHUHTXLUHGYHORFLW\FDQEHGHWHUPLQHGIURP  

  

    req J closed S E v x y z x y C r r P P §  ·     ¨  ¸ © ¹     ZKHUHxyzDQG x  y DQGzDUHUHVSHFWLYHO\WKHSRVLWLRQVDQGYHORFLWLHVLQWKH6XQ±(DUWK 0RRQ&57%3ZLWKJUDYLWDWLRQDOSDUDPHWHUP  7KLVSURFHGXUHZDV DSSOLHGWRVWXG\62+2+HUVFKHODQG*DLDGLVSRVDO)RUDSHULRGRI \HDUVDIWHUOHDYLQJWKH/32WKHǻvWRFORVHWKHVXUIDFHVRI+LOOLVFRPSXWHGIRUERWKEUDQFKHVRI XQVWDEOHPDQLIROG,QWKHIROORZLQJVHFWLRQVDYDOXHIRUWKHǻvFDQEHUHDGIRUHDFKSORWEDVHGRQ WKH SRVLWLRQ IURP ZKHUH LW GHSDUWHG IURP WKH /32 VKRZQ RQ WKH yD[LV  DQG RQ WKH WLPH DIWHU KDYLQJGHSDUWHGWKH/32 VKRZQRQWKHxD[LV 6RPHFRQGLWLRQVDUHILOWHUHGRXWGXHWRRQHRIWKH IROORZLQJUHDVRQVWKHWUDMHFWRU\DSSURDFKHVWKH(DUWKZLWKLQNPRUSRUWLRQVRIDJLYHQDUF RQDPDQLIROGPD\EHZLWKLQWKHLQQHUUHJLRQQHDUWKH(DUWK LHEHWZHHQWKHOLEUDWLRQSRLQWV/ DQG/ 

 +HUVFKHOGLVSRVDOWKURXJKKHOLRFHQWULFSDUNLQJRUELW

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 t (year) Δ v (m/s) 25 50 75 100 125 150 0 π

Curvilinear coordinate on LPO

2π 1.5π 0.5π 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 t (year) Δ v (m/s) 25 50 75 100 125 150 0 π

Curvilinear coordinate on LPO

2π

1.5π

0.5π

D  E 

)LJXUH  ǻY FRVW IRU +HUVFKHO PLVVLRQ WR FORVH WKH VXUIDFHV RI +LOO DV IXQFWLRQ RI WKH WLPHDIWHUGHSDUWXUHIURPWKH/32DQGSRVLWLRQRIGHSDUWXUHRQWKH/32'LVSRVDOWRZDUGV D WKHLQQHUSDUWRIWKHVRODUV\VWHPDQGE WKHRXWHUSDUWRIWKHVRODUV\VWHP

(18)

 

 62+2GLVSRVDOWKURXJKKHOLRFHQWULFSDUNLQJRUELW

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 π t (year)

Curvilinear coordinate on LPO

Δ v (m/s) 25 50 75 100 125 150 2π 1.5π 0.5π 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 t (year) Δ v (m/s ) 25 50 75 100 125 150 0 π

Curvilinear coordinate on LPO

2π 1.5π 0.5π D  E  )LJXUHǻYFRVWIRU62+2PLVVLRQWRFORVHWKHVXUIDFHVRI+LOODVIXQFWLRQRIWKHWLPH DIWHUGHSDUWXUHIURPWKH/32DQGSRVLWLRQRIGHSDUWXUHRQWKH/32'LVSRVDOWRZDUGVD  WKHLQQHUSDUWRIWKHVRODUV\VWHPDQGE WKHRXWHUSDUWRIWKHVRODUV\VWHP

 *DLDGLVSRVDOWKURXJKKHOLRFHQWULFSDUNLQJRUELW

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 1 2 3 4 5 6 t (year)

Time after LPO injection (year)

Δ v (m/s) 25 50 75 100 125 150 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 0 1 2 3 4 5 6 t (year)

Time after LPO injection (year)

Δ v (m/s) 25 50 75 100 125 150 D  E  )LJXUHǻYFRVWIRU*DLDPLVVLRQWRFORVHWKHVXUIDFHVRI+LOODVIXQFWLRQRIWKHWLPHDI WHUGHSDUWXUHIURPWKH/32DQGSRVLWLRQRIGHSDUWXUHRQWKH/32'LVSRVDOWRZDUGVD WKH LQQHUSDUWRIWKHVRODUV\VWHPDQGE WKHRXWHUSDUWRIWKHVRODUV\VWHP

(19)





8 LPO disposal towards the outer solar system through

solar radiation pressure

,QWKHSUHYLRXVVHFWLRQLWZDVLQYHVWLJDWHGWKH/32(QG2I/LIH (2/ GLVSRVDOZKLFKDLPV WRFORVHWKH+LOO¶VFXUYHVWRSUHYHQWWKHVSDFHFUDIW¶V(DUWKUHWXUQ2OLNDUDHWDOSURSRVHGDVLPL ODUVWXG\WKDWLQFOXGHVDVHQVLWLYLW\DQDO\VLVRQWKHHIIHFWLYHQHVVRIXVLQJWKHUHVWULFWHGWKUHHERG\ SUREOHP DV DQ DSSUR[LPDWLRQ RI WKH VSDFHFUDIW¶V G\QDPLFV 7KH FORVXUH RI WKH ]HURYHORFLW\ FXUYHVLVSHUIRUPHGZLWKDWUDGLWLRQDOǻvPDQRHXYUHDQGWKHFXUYHVFDQEHFORVHGHLWKHUDW/RU LQ/7KXVWKHVSDFHFUDIWFDQEHFRQILQHGLQVLGHWKHVRODUV\VWHP /FORVXUH RURXWVLGHWKH6XQ (DUWKV\VWHP /FORVXUH 

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xD[LVWKHUHIRUHWKH FORVXUH RI WKH +LOO¶V FXUYHV RFFXU DW WKH VRFDOOHG SVHXGR /LEUDWLRQSRLQW ZLWK VRODU UDGLDWLRQ SUHVVXUH 6/ +RZHYHUGXHWRWKHFRQVWUDLQVLQWKHDFFHOHUDWLRQRI653WKHVSDFHFUDIWLVDOZD\V FRQILQHGWRVWD\RQWKHULJKWVLGHRIWKHSVHXGR/LEUDWLRQSRLQWWKXV653FDQEHH[SORLWHGRQO\ ZKHQWKH/32GLVSRVDOLVWRZDUGWKHRXWHU6XQ±(DUWKV\VWHPRULQRWKHUZRUGVZKHQWKHFOR VXUHLVSHUIRUPHGDW6/7KLVVWUDWHJ\ZDVVWXGLHGIRU+HUVFKHO*DLDDQG62+2$IWHUWKH LQMHFWLRQRIWKHVSDFHFUDIWRQWRWKHXQVWDEOHWUDMHFWRU\WKDQNVWRDǻvPDQRHXYUH TXDVLSURSHO ODQWIUHHVWUDWHJ\ IURPDVWDUWLQJSRLQWRIWKHSHULRGLFRUELWWKHPLQLPXP(2/DUHDUHTXLUHGWR FORVHWKH+LOO¶VFXUYHVLQ6/LVIRXQGWKURXJKQXPHULFDORSWLPLVDWLRQ )LJXUHVKRZVWKHUHVXOWVLQWKHFDVHRI*DLDLQWHUPRIUHTXLUHGDUHDWRPDVVDQGHTXLYDOHQW ǻv7KHHTXLYDOHQWǻvLVDWKHRUHWLFDOYDOXHQRWDFKLHYDEOHZLWKDWUDGLWLRQDOSURSXOVLRQZKLFK TXDQWLILHVFKDQJHVLQWKHHQHUJ\RIWKHV\VWHP7KLVPDNHVHDVLHUWRFRPSDUHWKLVVWUDWHJ\ZLWK WKHWUDGLWLRQDOSURSXOVLRQEDVHGVWUDWHJ\)URPRXUDQDO\VLVVSDFHFUDIW¶VVLPLODUWR*DLDUHTXLUHV DPLQLPXPRIPVSDQ LHVTXDUHIODS RIDGGLWLRQDODUHDIURPLWVRULJLQDOPVXQVKDGHWR SHUIRUPWKHFORVXUHDW6/,QVWHDG+HUVFKHODQG62+2UHTXLUHDGHOWDDUHDRIPVSDQDQG  PVSDQ UHVSHFWLYHO\ ,NDURV PLVVLRQ GHPRQVWUDWHG WKH GHSOR\PHQW RI D P VSDQ RI D VTXDUHGVDLOWKHUHIRUHVSDFHFUDIWVLPLODUWR*DLDFDQSRWHQWLDOO\EHPRUHOLNHO\WRXVHDQ(2/ GHYLFH &XUUHQWVWXGLHVDUHDLPHGDWLQFOXGLQJWKHHIIHFWRIWKH(DUWK¶VHFFHQWULFLW\LQWRWKHGHVLJQRI WKH(2/DUHDLQRUGHUWRGHWHUPLQHDQDUHDPDUJLQWKDWSUHYHQWWKHRSHQLQJRIWKH]HURYHORFLW\ FXUYHVGXHWRSHUWXUEDWLRQVUHODWHGWRWKHIXOOERG\G\QDPLFV 

(20)



D  E 

)LJXUH*DLDGLVSRVDOWKURXJK653$ 5HTXLUHGDUHDWRPDVVUDWLRIRUWKHFORVXUHRI WKH+LOO¶VFXUYHVDQGE HTXLYDOHQWǻY



9 HEOs and LPOs disposal strategies trade-off

%DVHG RQ WKH DQDO\VLV RQ WKH VHOHFWHG PLVVLRQV VRPH SUHOLPLQDU\ JXLGHOLQHV IRU IXWXUH DQG FXUUHQWPLVVLRQVFDQEHGUDZQDVDJHQHUDORXWSXWRIWKLVVWXG\

ƒ 7KHH[WHQVLRQRIDPLVVLRQVKRXOGEHFRQVLGHUHGLQWKHFRQWH[WRIWKHVXVWDLQDELOLW\RIWKH ZKROH SURJUDP +(2 DQG /32 PLVVLRQV DUH QRW VXVWDLQDEOH ZLWKRXW D SODQQHG HQGRIOLIH GLVSRVDODV+(2DQG/32UHJLRQVZLOOEHVHOHFWHGIRURWKHUIXWXUHPLVVLRQV0RUHRYHUE\ RSWLPLVLQJWKHGLVSRVDOSKDVHRIWKHPLVVLRQWKHVDPHRUVOLJKWO\KLJKHUPLVVLRQFRVWFRXOG DOORZ H[WUD RXWSXW IURP WKH VFLHQWLILF DQG RSHUDWLRQDO SRLQWRI YLHZ (QGRIOLIH GLVSRVDO VWUDWHJLHVVKRXOGWKHUHIRUHEHFRQVLGHUHGDVDQH[WHQVLRQRIWKHPLVVLRQ

ƒ 2QWKHRWKHUKDQGLWVKRXOGEHFRQVLGHUHGWKDWWKHFRVWRIWKHGLVSRVDOLVQRWRQO\WKHDGGL WLRQDO GHOWDv EXW DOVR WKH FRVW IRU RSHUDWLRQV DQG WKH UHVRXUFHV UHTXLUHG WR PDLQWDLQ WKH PLVVLRQWHDP0RUHRYHUWKHH[WHQVLRQRIDPLVVLRQLVVXEMHFWHGWRVHYHUDOFRQVWUDLQWVVXFK DVEXGJHWDQGJHRUHWXUQFRQVWUDLQWV6RPHRIWKHPVXFKDVPLVVLRQFRQVWUDLQWVDQGGLVSRVDO UHTXLUHPHQWVKDYHEHHQWDNHQLQWRDFFRXQWLQWKHSUHVHQWVWXG\LQGHHGVRPHVWUDWHJLHVZHUH GLVFDUGHGEDVHGRQWKHRSHUDWLRQDOFRVWWKH\ZRXOGUHTXLUH ƒ 5HJXODWLRQVSUHVFULEHSURWHFWHGUHJLRQVIRU*(2DQG/(2DQG*116SURWHFWHGUHJLRQVDUH FXUUHQWO\XQGHUGHILQLWLRQ,WLVLPSRUWDQWWRKLJKOLJKWWKDWVSDFHLVQRWGLYLGHGLQWRGHILQLWH UHJLRQV /32PD\QDWXUDOO\WUDQVIHUWR+(2ZKLFKGXULQJUHHQWU\FRXOGLQWHUDFWZLWKWKH 0HGLXP(DUWK2UELW0(2DQGWKHQWKH/(2HQYLURQPHQW 7KHUHIRUHWKHGLIIHUHQWGLVSRV DOVWUDQVIHUVSURSRVHGLQWKLVVWXG\DUHLQVWULFWUHODWLRQDPRQJWKHPDVLWLVSRVVLEOHWRWUDQV IHUIURPRQHOHJWRDQRWKHU

 +(2VGLVSRVDO

;00 SHULJHH LV PXFK KLJKHU WKDQ ,17(*5$/ DQG WKLV PDNHV PRUH GLIILFXOW D GLVSRVDO WKURXJKUHHQWU\3UHGLFWLQJWKHIXWXUHLWLVPRUHOLNHO\WRH[SHFWPRUHPLVVLRQVZLWKKLJKSHULJHH WR EH RXWVLGH WKH UDGLDWLRQ EHOW 7KLV PHDQV WKDW PRUH VFHQDULRV VXFK DV /32V RU KLJK SHULJHH +(2V DUH H[SHFWHG DQG WKH WUDGHRII EHWZHHQ D VDIH HQYLURQPHQW IRU REVHUYDWLRQV DQG D JRRG FRQILJXUDWLRQIRUGLVSRVDOVKRXOGEHFRQVLGHUHG7KLVLVVXHKLJKOLJKWVWKHLPSRUWDQFHWRSODQLQ

(21)



DGYDQFHWKHGLVSRVDOVWUDWHJ\LQGHHGWKHH[SORLWDWLRQRIOXQLVRODUSHUWXUEDWLRQFDQGHFUHDVHWKH UHTXLUHGPDQRHXYUHIRUUHHQWU\+RZHYHUGXHWRWKHORQJSHULRGIRUWKHQDWXUDORVFLOODWLRQVWKH PDQRHXYUHVKRXOGEHSODQQHGLQDGYDQFH7KURXJKWKHJUDYLWDWLRQDORIWKH0RRQ+(2VFDQDOVR LQMHFW WR WUDQVIHU RUELWV ZKLFK UHDFKHV /32V LQ WKH (DUWK ± 0RRQ DQG WKH (DUWK ±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

 /32VGLVSRVDO

7KHUH DUH VHYHUDO FRQVLGHUDWLRQV WR WDNH LQWR DFFRXQW ZKHQ FKRRVLQJ EHWZHHQ LPSDFWLQJ D VSDFHFUDIW IURP D /32 XSRQ WKH (DUWK¶V RU 0RRQ¶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ǻvVKRXOGEHWDNHQLQWRDFFRXQWWRFRQVLGHUWKH HIIHFW RI SHUWXUEDWLRQV RQ WKH ORQJWHUP HYROXWLRQ RI WKH RUELW 7KH RSWLRQ RI /32 GLVSRVDO WR ZDUGVWKHRXWHUVRODUV\VWHPWKURXJKVRODUUDGLDWLRQSUHVVXUHLVQRWIHDVLEOHIRUFXUUHQWVSDFHFUDIW EXWFRXOGEHHDVLO\LPSOHPHQWHGRQIXWXUHVSDFHFUDIWDVLWLVDQRFRVWVROXWLRQDVORQJDVWKHUH IOHFWLYHDUHDRQERDUGWKHVSDFHFUDIWFDQEHIXUWKHUH[WHQGHGDWWKHHQGRIPLVVLRQ$IWHUWKHGH YLFH GHSOR\PHQW WKH GLVSRVDO FDQ EH FRPSOHWHO\ SDVVLYH LI WKH GHYLVHG LV VHOIVWDELOLVHG WR EH

(22)



6XQSRLQWLQJDWWLWXGH,WLVH[SHFWHGWKDWLIWKHGHYLFHLVGHSOR\HGIXUWKHUIURPWKHQRPLQDO/32 WKHDUHDWRPDVVUHTXLUHPHQWVZRXOGEHGHFUHDVHG

10 Conclusions

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

Acknowledgments

7KLVZRUNZDVLQLWLDWHGDVSDUWRIDVWXG\IRUWKH(XURSHDQ6SDFH$JHQF\QDPHG³(QG2I /LIH'LVSRVDO&RQFHSWVIRU/DJUDQJH3RLQWDQG+LJKO\(OOLSWLFDO2UELW0LVVLRQV´ &RQWUDFW1R )026 7KHDXWKRUVZRXOGOLNHWRDFNQRZOHGJHWKH(6$VWDII.0HU]IURPWKH (6$'HEULVRIILFHDQG,&DUQHOOLIURPWKH(6$*63RIILFH&&RORPERDFNQRZOHGJHVWKHVXS SRUW UHFHLYHG E\ WKH (8 0DULH &XULH JUDQW  6SDFH'HE(&0  6SDFH 'HEULV (YROXWLRQ &ROOLVLRQULVNDQG0LWLJDWLRQ ZLWKLQWKH(XURSHDQ)3IUDPHZRUN7KHDXWKRUVDFNQRZOHGJHWKH XVHRIWKH,5,',6+LJK3HUIRUPDQFH&RPSXWLQJ)DFLOLW\DQGDVVRFLDWHGVXSSRUWVHUYLFHVDWWKH 8QLYHUVLW\RI6RXWKDPSWRQLQWKHFRPSOHWLRQRIWKLVZRUN

References

 3HUR]]L ( )HUUD]0HOOR 6 HGLWRUV Space manifold Dynamics '2,  BVSULQJHU

 (LVPRQW1$'LWULNK$9-DQLQ*.DUUDVN9.&ODXVHQ.0HGYHGFKLNRY$,.X OLN 6 9 9WRUXVKLQ 1 $ <DNXVKLQ 1 , ³2UELW GHVLJQ IRU ODXQFKLQJ ,17(*5$/ RQ WKH 3URWRQ%ORFN'0 ODXQFKHU´ $VWURQRP\ DQG $VWURSK\VLFV 9RO  1  SS /±/ 1RYGRL

 &RORPER&/HZLV+/HWL]LD)6ROGLQL6*|VVQLW]HU/$OHVVL(05RVVL$'LPDUH / 9DVLOH 0 9HWULVDQR 0 YDQ GHU :HJ : 0F,QQHV & 0DFGRQDOG 0 /DQGJUDI 0 (QGRIOLIHGLVSRVDOWUDMHFWRULHVIRUOLEUDWLRQSRLQWDQGKLJKO\HOOLSWLFDORUELWPLVVLRQVThe

64th International Astronautical Congress%HLMLQJ&KLQD,$&$3

 $UPHOOLQ 5 'L /L]LD 3 5DVRWWR  0 'L 0DXUR * /DQGJUDI 0 ³'LVSRVDO 6WUDWHJLHV IRU 6SDFHFUDIWLQ/DJUDQJLDQ3RLQW2UELWV´The 24th

AAS/AIAA Space Flight Mechanics Meeting

(23)

  &DQDOLDV(*RPH]*0DUFRWH00DVGHPRQW--$VVHVVPHQWRIPLVVLRQGHVLJQLQFOXG LQJXWLOLVDWLRQRIOLEUDWLRQSRLQWVDQGZHDNVWDELOLW\ERXQGDULHV(XURSHDQ6SDFH$JHQF\WKH $GYDQFHG&RQFHSWV7HDP$ULDGQD)LQDO5HSRUW D >/DVWDVVHVVHG'HFHP EHU@  &RORPER&/HWL]LD)6ROGLQL6/HZLV+$OHVVL(05RVVL$9DVLOH09HWULVDQR0 9DQGHU:HJ:(QG2I/LIH'LVSRVDO&RQFHSWVIRU/DJUDQJH3RLQWDQG+LJKO\(OOLSWLFDO 2UELW0LVVLRQV)LQDO5HSRUW(6$(62&FRQWUDFW1R)0269HUVLRQ ±)HEUXDU\  &RORPER&/HWL]LD)$OHVVL(0/DQGJUDI0(QGRIOLIH(DUWKUHHQWU\IRUKLJKO\HO OLSWLFDORUELWVWKH,17(*5$/PLVVLRQThe 24th

AAS/AIAA Space Flight Mechanics Meeting

-DQ6DQWD)H1HZ0H[LFR

 $OHVVL(0&RORPER&/DQGJUDI0³5HHQWU\'LVSRVDODQDO\VLVIRU/LEUDWLRQ3RLQW2UELW 0LVVLRQV´ 24th

International Symposium on Space Flight Dynamics ISSFD 2014 /DXUHO

0DU\ODQG0D\

 9DQGHU:HJ:9DVLOH0(DUWK6XQ/DQG/WR0RRQ7UDQVIHUV([SORLWLQJ1DWXUDO'\ QDPLFVThe 64th

International Astronautical Congress%HLMLQJ&KLQD,$&&

 2OLNDUD = *RPp] * DQG 0DVGHPRQW - - ³(QGRIOLIH GLVSRVDO RI OLEUDWLRQ SRLQW RUELWV VSDFHFUDIW ´ The 64th

International Astronautical Congress ,$&& %HLMLQJ &KLQD

6HSWHPEHU

 6ROGLQL6&RORPER&:DONHU6/DQGJUDI0³/LEUDWLRQ3RLQW2UELWPLVVLRQVGLVSRVDODW WKH HQGRIOLIH WKURXJK VRODU UDGLDWLRQ SUHVVXUH´ 2nd

International Academy of Astronautics Conference on Dynamics and Control of Space Systems '<&266  ,$$$$6'\&R66

5RPH,WDO\0DUFK

 -RUED $ ³1XPHULFDO FRPSXWDWLRQ RI WKH QRUPDO EHKDYLRXU RI LQYDULDQW FXUYHV RI Q GLPHQVLRQDO PDSV´ Nonlinearity 9RO  SS   GRL  



.RRQ:6/R0:0DUVGHQ-(5RVV6'³/RZHQHUJ\WUDQVIHUWRWKH0RRQ´Celes-tial Mechanics and Dynamical Astronomy9ROQSS

 ´;001HZWRQ8VHUV+DQGERRN´,VVXH (6$;001HZWRQ62& 

 %DXVNH5³2SHUDWLRQDOPDQRHXYUHRSWLPL]DWLRQIRUWKH(6$PLVVLRQV+HUVFKHODQG3ODQFN´

International Symposium on Space Flight Dynamics

 +HFKOHU0&RERV-³+HUVFKHO3ODQFNDQG*$,$2UELW'HVLJQ´7th

International Confer-ence on Libration Point Orbits and Applications3DUDGRUG¶$LJXDEODYD*LURQD6SDLQ

-XQH

 2OLYH-32YHUEHHN79)OHFN%SOHO Monthly Trending Report6HSWHPEHU5HI 62+235*752FW

 -HW 3URSXOVLRQ /DERUDWRU\ ³+RUL]RQV :HE,QWHUIDFH´ >2QOLQH@ $YDLODEOH

KWWSVVGMSOQDVDJRYKRUL]RQVFJL>/DVWDFFHVVHG@

 0HUW].3HUVRQDOFRPPXQLFDWLRQ HPDLO -XO\

 &1(6 ³67(/$ 8VHU¶V JXLGH´ )HE  DYDLODEOH DW KWWSORJLFLHOVFQHVIU67(/$HQ6WHOD8VHU0DQXDOSGI>/DVWDFFHVVHG-XQH@

(24)



 &RORPER&$OHVVL(0/DQGJUDI0(QGRIOLIH'LVSRVDORIVSDFHFUDIWLQ+LJKO\HOOLSWL FDO 2UELWV E\ 0HDQV RI /XQL6RODU 3HUWXUEDWLRQV DQG 0RRQ 5HVRQDQFHV Sixth European

Conference on Space Debris(6$(62&'DUPVWDGW*HUPDQ\$SULO

 3DUPDU³;001HZWRQ0LVVLRQ6WDWXV´LQWK;8*0HHWLQJ

 &DVWHOOL 5 ³2Q WKH 5HODWLRQ %HWZHHQ WKH %LFLUFXODU 0RGHO DQG WKH &RXSOHG &LUFXODU 5H VWULFWHG7KUHH%RG\3UREOHP$SSUR[LPDWLRQ´Nonlinear and Complex DynamicsSS 6SULQJHU1HZ<RUN  )DQWLQR(*RPH]*0DVGHPRQW--5HQ<³$QRWHRQOLEUDWLRQSRLQWRUELWVWHPSR UDU\FDSWXUHDQGORZHQHUJ\WUDQVIHUV´Acta AstronauticaSS  9DQGHU:HJ:-9DVLOH0³&RQWLQJHQF\DQGUHFRYHU\RSWLRQVIRUWKH(XURSHDQ6WXGHQW 0RRQ2UELWHU´Acta Astronautica9ROQSS  $OHVVL(05RVVL$9DOVHFFKL*%$QVHOPR/3DUGLQL&&RORPER&/HZLV+* 'DTXLQ - 'HOHIOLH ) 9DVLOH 0 =XLDQL ) 0HU] . (IIHFWLYHQHVV RI *166 'LVSRVDO 6WUDWHJLHV Acta Astronautica 9RO  -XQH±-XO\  SS ± GRL MDFWDDVWUR +LJKOLJKWV  (QGRIOLIHJXLGHOLQHVQHHGWREHGHILQHGIRU/LEUDWLRQ3RLQW2UELWDQG+LJKO\(OOLSWLFDO2UELW PLVVLRQV 3RVVLEOHGLVSRVDOVWUDWHJLHVDUHSUHVHQWHGDVDUHVXOWRID(XURSHDQ6SDFH$JHQF\VWXG\ 7KH WUDMHFWRU\ GHVLJQ H[SORLWV WKH SHUWXUEHG G\QDPLFV LQ WKH (DUWK HQYLURQPHQW DQG LQ WKH 6XQ±(DUWKDQG0RRQV\VWHP

)LYH(6$PLVVLRQVDUHVHOHFWHG,17(*5$/;001HZWRQ+HUVFKHO*DLDDQG62+2 $WUDGHRIIDQGJHQHUDOJXLGHOLQHVDUHGUDZQEDVHGRQWHFKQLFDOIHDVLELOLW\DQGVXVWDLQDELOLW\  

Riferimenti

Documenti correlati

Estimates of heritability and genetic correlations for milk coagulation properties and individual laboratory cheese yield in Sarda ewes1.

Sicché quando, nel corso del secolo XII, l’organismo comunale di Novara si pose al governo della città, estromettendone l’ordinario diocesano divenuto signore territoriale della

importante documento venne coinvolta direttamente la Penitenzieria Apostolica, sia nella parte dottrinale, che è la più corposa, quanto in quella normativa. La costituzione è

L’integrazione della traiettoria da parte del D-Orbit viene eseguita utilizzando il metodo di Cowell che permette di introdurre, a discrezione dell’utente, parametri

Ces données montrent, d’un côté, que les femmes sont généralement plus inclines que les hommes à parler d’intrigues amoureuses retenues scandaleuses, comme

The aim of the present work is to perform a numerical acoustic properties evaluation of the engine cover by using the hybrid FEM/BEM (Finite Element Model/ Boundary Element

Moreover, the ability of these channel proteins to regulate cell volume, as well as cell migration and apoptosis, all related to the inflammation process, makes them useful tools

The magnetic susceptibility, hence iron con- centration, of the deep cortical layers of patients' M1 subregions corresponding to Pen field's areas of the hand and foot in