User-Agent: Microsoft-Entourage/12.36.0.130206Date: Mon, 27 Jan 2014 11:01:39 -0700Subject: An Aid To Interplanetary Trajectory DesignFrom: Daniel Adamo <adamod@earthlink.net>Message-ID: <CF0BED14.1477B%adamod@earthlink.net>Thread-Topic: An Aid To Interplanetary Trajectory DesignThread-Index: Ac8bkjVG3f8bbm0WLkSbOy4TnJ0yXA==Mime-version: 1.0Content-type: multipart/mixed;	boundary="B_3552815982_4425808"> This message is in MIME format. Since your mail reader does not understandthis format, some or all of this message may not be legible.--B_3552815982_4425808Content-type: multipart/related;	boundary="B_3552815982_4386903"--B_3552815982_4386903Content-type: multipart/alternative;	boundary="B_3552815982_4424574"--B_3552815982_4424574Content-type: text/plain;	charset="US-ASCII"Content-transfer-encoding: 7bitATIG Members-I hope you're enjoying a happy and prosperous 2014.  This year, I findmyself designing yet another precision round-trip trajectory from Earth toMars and back.  I expect to be sharing details of this design and itsassociated mission concept with you in the near future.During the patched conic phase of interplanetary trajectory design, I'vefound planet-centered departure or arrival hyperbolic trajectories can oftenbe conveniently defined using asymptotic velocity imposed by theheliocentric transfer trajectory, together with specified periapsis distanceand declination.  The attached PDF details how to define and sampleplanet-centered hyperbolic trajectories using these data in a variety ofmission design contexts.  For those wishing to implement this technique, anumeric example is included for the context of arrival at Mars.As always, questions and comments on the attached documentation are welcome.-Dan--B_3552815982_4424574Content-type: text/html;	charset="US-ASCII"Content-transfer-encoding: quoted-printable<HTML><HEAD><TITLE>An Aid To Interplanetary Trajectory Design</TITLE></HEAD><BODY><FONT FACE=3D"Arial"><SPAN STYLE=3D'font-size:10pt'>ATIG Members-<BR><BR>I hope you're enjoying a happy and prosperous 2014. &nbsp;This year, I find= myself designing yet another precision round-trip trajectory from Earth to =Mars and back. &nbsp;I expect to be sharing details of this design and its a=ssociated mission concept with you in the near future.<BR><BR>During the patched conic phase of interplanetary trajectory design, I've fo=und planet-centered departure or arrival hyperbolic trajectories can often b=e conveniently defined using asymptotic velocity imposed by the heliocentric= transfer trajectory, together with specified periapsis distance and <I>decl=ination</I>. &nbsp;The attached PDF details how to define and sample planet-=centered hyperbolic trajectories using these data in a variety of mission de=sign contexts. &nbsp;For those wishing to implement this technique, a numeri=c example is included for the context of arrival at Mars.<BR><BR>As always, questions and comments on the attached documentation are welcome=.<BR><BR>-Dan<BR><BR><IMG src=3D"cid:3473665300_102819322" ></SPAN></FONT></BODY></HTML>--B_3552815982_4424574----B_3552815982_4386903Content-Type: image/jpeg; name="image.jpg"Content-ID: <3473665300_102819322>Content-Transfer-Encoding: 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FV51RpY39MVkgsgkTJUKq2N8ceS00NzBnTLnKj8MpZV41dgs9K6OVG9YPV7Vj6enBATpsNrXvK/qzAZysXDaRG6cIqgIkGuBDXjZD2FKf0D+oyXBLnEpS9VhHlz0xfqxb6yBFfHbXv5Bd2Rr/+thHlE7OW9rCt4Xi5iTrTldLYH11XYTw/B+HZgdt49uNn06mqLGe4f7kIN6YXq2CJ4J38X2AEFtMS8G+eSnFVDYvAT6bYEDDmL5Jxu8lN1Op+mTDQsAE4CMUTKK7KY102daeeYS7xKcIPwvz/T2W1Iamr59IMjc9K+TJpNn2rqi4pzrX6p7Mrv3lhdVCpXnyjPhbba5I0qIFO03VHSq1XH1TdRr++Vy/ImstEgp0arZaaZnK2vIu9asMr+Qi4qSzwTA/+eh+n58AtyUbXzoDVTo3E+1LQSG1Xk0ryyEGr/vIikiNV18FM0brzwHavma5D+BJHTHE7wK0Y6gFTTC1d1PI+tGCHxTMFtRh8pXMbHP1aHekbs4b+aGgvfa9+tCDTjhp0XUjXhANHAFtw42iJG0o8Bhxdtf4JaRD6qQW0UVfDsUVfne4dhRiUceIuTYCKmmhYFp3791ggyJIjnblfLaeop5w1i/kujO6UNQz60oDFXVPb7TW0uaVENsi2f1gk/UPoA5oIiJQzPJzho/wPq5GDXotsQhpK7Gg24HRZdn02WnF4dRhe3YxldoQIgzWLNGcPrQPBAIERcgRtm0OcKZSYIMJpIPfbMOQ7//amgI0HV/J0p+7hRdnPD/Ax7QcY8Pbn/Sf4jfYT/0Ua1M/8rfc30JlAOsNpHj0LX9X+/hkm5wT4jvHguvln4PGiqwb+Nrfxz/M/mQrpHf7dui9RNXAwyfq3/PAmyIbkjDauKVtrLGE4FDuR2AavDPkg2tRH/DscoRthiqYcAVgSpjM6GOKt0XC3xRhv4Z82vCKizQJGclN59WhSJnMeejHe4yy6N4Kw4NcN8gx0z0lnlpPnH43CmuUN/BRnb4H1U7O8Cb0HL9Arr4zO/QKJuiTjvKw958LY5lthNnoR7VswlnTFLlKYl7mJnoG+YE+ToV7WnlsBfm5EXgbfmAg+TMZ8N78I3hrtS9RfxHteoMEYgRr4ksw3tZWcL8V807YR84NgPh/vJnn6Yi46NeIlpiLTdWkGrtQHjK8l+Lm7d5H8NG0snpH0X0l+WgP8L7d42w664csxvwPlAT7Iz1+vM7e9xs7WDNjVvtwQ+jYWz6B//uM6QxgQ5f2C1A8j6sMEbOj+oQJN7XTDny/gDnzv6uPQ9AifU3akCVvjq0OaQ7l96BJCtNpJZCCvm/tJYye2tSo4a3WJXEALnwc204JB7Dbp2OZftdwaBEOczZ+N9uqgy02jPxttsgXHI4Wx3vTtER6tGyNRijDTND3kRhsiQwZ2bxxhiSF78lpHoKMUzRQqQZwukcybUreQkZtApjNyMOISGTlKZ30HJwFuhMt8uc8IKKHFfUbaBxAuMedaMAR8bZrIKw7LiTzu3mFKIg8IiUQZ0QVXBf+67pOJMmzXsMsnM3vpJJCEtNAYDSIF2+sAvIdSX/S+3gXvy7tYlqP2We+XFYcT+27grP2LYuftgX1BcBX+GTjBj/BX+Mnzw2d198Y7g9IVO3on/sCP8+/nk7rnPqQzpOlARiF98Ze47wfxBBWTcXbfQT74cfr0nULC1A7rJON6x1DqXrzTn4Wmx4Avn/gLrz0W9yJfOn21gM5PydAmfCxIpC1t/CTxMeXekmQg1WLgkeZJBnfAXD6pH3gsSkbHfxQuslvPj94pfoQJDV+WCAJ3xTwRp54bAto9u/cMe+K/AT/h3JsWyVnEWpkHbPTHmTG3G4Zd4tm62qxqMJ+SvTvwsNp4oEzziZnCDRAqJ3J3SoIdwmx+WIY+hUsKgEEwq9I1lLQXg3UWBJNjEpuPdw6D2GHfE16NbLCRQAdsX2Kq/2ENjID3Yp2lBqEO4O1lqSyeszr/MOUQyw+UBQumMI9ZnpSbWmN/NGa6dopkXCghN7WGsq8GkzEJIoc75eb+LALDw2e28O9QnqnF0pT62MNEzyAyWI4JSWlKDLrElnYlSWk0In4Wb1OSYyaKJkLwMjV80pRQFzVXFqXmGnMTRTSdRl6IaLo1DethXUNpDKptYC+5vpd0tOin7XoZDScrCw0T6NEmvm+81DWSCEOP3E8D3x+FWs6yWF7oHi2x0ClT4tGIyxkjBZexFzvuLu3Ff/wzh3q/Cxv7+UE06Mkt+uLAC4HXftiLPsuimT7DW9tRqVtPA6wAN6Ph+6xW+GnZp7iruxD6ZrXtekLoesEuYbx41z2LeaSCpcH4kG5HkwwkGEg8JO74XUoQa7gEKNwarwHYcAhAI5uN8rrUlvnmbl3B1wPSVKXWY+QUHM0703wWU5BbwiIuyIvEhhzVCNIihpzl5EcosfHD+fF0x1ICS4r7OJ9EiJiJLIjnU+C0zNZdLBFuPoRuBgjoYk1yd/8bIOXT4/39+eEnP7nc+SntUmDXspvMKgcmDjEx+h1jv32nRNC4DRZ6QncZSp30A2bWdrhuWMTqmA057iKwh1tgHTkWsow/yKoShvOf+Nv8B8whN3kb2np4275IapwkVCixkprTDdllAoSmt1NqxcF4Cxc9tTd00OYI27jeVzRm8fW3wt9pDcFkadSo7EKSdcFD3LHHgBuoYIAZnMRxpV0QsFuvPNdcmmAdM9/IpZFl4JhYHGYKVqTlbXBZPz5yq3hpAuTlojjI6lP3kjyUqVI8VR+pLnHkaTE0rChxVM4PkcrgB3hVh66DB8XwPzO6Ww7FIe5uXSLqEkqajO/1GZgvce7zTpZG2mbmeXh4lP2OqT2J38wtvJzTXmhT9cdGI83l6I41BVnavLlYr8FIDu8/1zeVBl5DR47dHLAcoWUvDYRjDC0NSmTmbnt/+wmb0WqIDaZYW2qQaKHjMY9JDG5SwpjuUU9iUGYLNMRwa4+2bIv5FOiLddqGStBo2Ou0CfuwkmNLiGU9yLhrQXBIpOzx4bRraapoaYpDLFsSS7Gs7PwoVIgM8dJkEYeq+ZW1ITt1CEPhrvhp/snLQdx3KYHgJ5gtjJ9eFQYmV4kKx3wBAWVr4mb67mioQHULLZ7SKLbDQ5AVzpGxwL079VJ/pX7v9WJSQ6a2NaIR1bJdntRVWEXffyVOHOub8+mtkkoP3k+Z7e/EbeCWMLnyiWeZdxbMHSneYvGchh5QSj9UnvKNnc8Wmj0bVxvEO7FGkRIqToxjQwbYy4JOLdjdiPUuDyx4BGGt8VTKMzxEMp2LtaMoFeqBhhaFMHZy1qkK6up+fYhVixryDLAgjChXelllSpc+tikBMzVCXmSX5orZ4VliXSHYUPXNLpnVkcCKvLHVgNQCb/o8qXtrlmo45lWP8BRPFW1aKat0yy7EIRt2mdIxrmi/8xVLdQn3DgZyC+8RlbLK6OOAqiUNcSxWj3Wh0LIzrTuwhc0Wv7bke0rRUo1AjKS7otqbUlUNl6GiRs9vdPM6/0z0WdES0H1utHsiuldu60VLLUoCXRq2F4PnF1YMkZntQ+/jNbaLcZEZE/GQ6pdarrgNw3wTTa0rj7qMiZThb3loAX5WwpGD7pkYE99b6ueTNF7AeWyaw5sSp19YBIKA6eugV/CZKsO8EXiYVqyxKYY7tv4vHgmq1UNfYR4umuWYUaNDAwa1BKGXIMhRwdekBL9wJfjYzPJGRvtQhfAC1UGiLBLKhZQMqvFRZmlrI6VtTx1x+pwpto+OjBQE7avKj/1S7Sp1BfloqCvQW3UF+WjRhHuNbbA3Yxm1iGg4jQ3XgriarLyg2eohvxQFtBp7UmbqtwEXWogWLDJCUiw5BK0WUcXKJgt9prGB7pRBC1Wb2A+20f1EJzQ2H11r9Uxjo0l6n2vs7c69uRUxDoU0Vdk7bz4a2/2VOKfhmAJ/xrsFPb1NfawfIB4YRYVpWYK/iPoF+A6nrGD/2A004s7Egc4TWl7hoRAUBypRHe33gQh+VomVsybm1BtYk0vUz4/T7MCPaohr2GMXkD8t8nJLek5+hfgT3CHTDjhw4WYgSP+8kmw8htxO6hY78WonN/MNOVtKI0Yh46lQE+rMsKCdqieg2xU83iNRl1vBup5yKjpYl9wjtwdm98iaHFRsjbovsT3ihLT9taBfr7czwjDtkMU2HY47XW1nzEfDzlht7Yz5aBNdFHvo2P0NDipZn+iJvpXBTGCd2I0x6VvBDPwjChYkTs42IXvxHFty7SEqs1RHtCeyXVDNmo0thMg2fNS8yDZ/1Xu5cOLF35XgumTK7yIXOIKXb2BCxPgtppk9Az+8wRnsmJ/O592KIC9HdAx5rFTtMAcch2dDiALZMheicOmpZABMH3HUX0Yzy1PWpjtCRUPMrHjwFpTKsSZiFHUNi6TBwcR8tPp7pJ7WYok1ZB8lQ8zsHOo2FlOFcBBH13NNaW+uVlA2SEHjcgLSbxQAxzmEjFNRwVRFeSrUsgQXjDtjtWSqtmxwyaRvXCKwHzk6djDh2fhMeALZmahLFxR0sCzcPoMJ9NYwBxWoPpQN5PHUb3c8NwIQRZCrHFrh1oYrG18XsTS+hW4gLKGfiHdPGcFoe9Z0Alks+8C2yIV1Hsp+4qlCvSRDLOBfaQTeyG5j0gP0zIbfTzqZqF+I6hp6amAxDUTfP2VGHT9gsCJWwDZpgJ55BZn8iCzFGpm2CrLoFleAfhGorvLuGliSe7IOalzMQYeH8IkOWeGTv2PAhkoyKY78xxpXJgUnIFC8W+nMF2VDt3KAOVNmTHaoS9RKA+tyCfoKVLe4CClAi8o6zIJ7+3ndYH9CMcyMIVG6jkz8fD1isEBsPoYs+g84mowtkAJg0pZl0hc5l6pZ9QdjxEcgljfn7cpDiXNVyENmgcGYN1vGfDbYRD4mtrzNRqXrXvgqo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mdFzbNsjPUaL0kynaP/MhRIyypE9pKt1EFhLkpFKaS6TcK6KkoG7QLUSRW49fuXDo1M/tuXZT+Kdq8kmj8Ixt/ZdnLeduT3/FPgncaSa/QYCczT0Qpu+k33jW8uXs9Fcoh2wG4fwne5qpJlMepkmAEOBhgAaw6P3yUG84HAglgf0lJk5MmBjoMwmjfYFNNVnyEO0CdANeBijQ4hCpACEPiW4aTyqY+xKj8kypZKK2drBwcWWq0FtYHHinJl0m6WOAkEnZRxNSUr0TSgKnaoaiAVrIJ4gBEnqr8il5hPwm05FEQWGgTx6QmxNV6tCabNlLTpkgF2A2oANwDGDF7HrpHcDHAB2g0HC5O/GnrepTchdfxTvR6310l51DmWqn0mkRnaJTioWHhEas93N2IndpIKn397aNXop5b+I1RsOT8vucbUxI7xfdibJgKAlUYqJe2Mmo9vrGp7Dbm8JjXCZOeFLcucGHD8NOGuCY6N4vQ9I9EQN92lvlmxY4LG8yElXZab8a8s4P5ieh5/wlYPio11sSHIGq4ZjlT8nNsFHczIcYbaUBp0Gbc0Ug08CXzQmMM/CMWYEhwImGYDpQKM03IzDcWxc1mRKBoCGTKAwON1grpgWGH0KH0yiofxYa6Z0WzPFedEXA6fWVB6zewmAmxk/qA6ECb3Ews6o0GLjfu8d70Pu8V7F4LwY1UBnIrZpYVVklc7zZ6HDfBG+lVzksNxuJvHYKOdWhqjF5db0qMtRJQWj1Sa9qqr1JIpEKppFqxUJbt00stHZbxbi94E/bW4qB3wql71XHBcZ5/I2GSp2JiUETjTOM0pnId6G3vzyR7w8G8mEMI2I7D3zr8kDAVxSsSdc/kp00GYqdBvYD/xUiVUEXJHurGwKwcmdvaVUAduiEO80qotTs3xdUDOoll5YbGIY0kTuYg1ooc2xwnG9SIDDOF6zE+KdD6T4MnubLcwfiT2Eolp1GIh8UK1ErVGuptdoqd4lucUS8LJRdslsekS9LZTW4tkupylJZLS+XC6VlaM1F4iRcvBD5LsA7AEmlyKsBq81aN2KI6XLk6BGbQCnyarNUbUSxSVn4DYqxPlgmZEKcRNKQ0EtodAXTJA6xYKY0FmSn7GzsF8OH2UM1GeJ7wkPl5OBpZl5h5nmh0eWO7eWO75c72ssdsXJHc7ljZrmjqNwxodxR4xQXkYscIs/I+ayZP2Pms828KDTa5TjlcjzlctztcmxwOVa4HK0ux0KXo97lqHHwdK4kB00z80lmPtbI+dy+obOGUtoRPkezyCF7YNqRpIqRCV+5mhQjEr5qIHsi/5BakyuslG9nUC2ALoAyiCWpitHOVGbsAnyGPPxt4McTvkI1yY+lUJfRZ81I3k0+Q5p/TvnsBf4ZdZn1n1CZiR8ZxA8mPCsh/WMD1aTxA+QxBsEAQXOQ6xK+EpBXJsquVWuG8VUY0xi7nQpMtjBCxGCvHhTzJPIfUg+zm/IxTZVpn2+Deg7y3oT6ZTBp54T63wVJ0ZVQ3/clGbX3QNuZUI+XoRbKUP9cdlz9U9lW9RVfUvAB9T99L6kveZMKGJ8ABxgf95md7M1HI/gfKlug3ut7SL0r1Xe8wGS6GcbsCmWpN0GldZ7jage6WeK5Vl2Q6upKjzmDuSfMjpswH/R/edBsvMxndJylzihbpjb4utS6spfU6Z4FapWK9gPq5ILjaoXHnEKJxxQvzIdymMlET5c6vqxLnVtxmH9DNo4D/KESW6ftGtty21JbxBayVdouthXbxtncthH24XanfYg9055ut9utdsUu7GQfkdSPhfzGUTjC6jSQFacUk2KWncIoI0NOgu2CLiUtS0ZEpKlWq/BHkja9Uav0R7S02VdEe5jvjHFE619MkUUu7YsmT5LT58zTLJ5a1oZHKNJcmwNmTWxJMjVHk6wbErfkacProjjEOHTLHXkGjt1yRyxGo66rzqkePn3Y5Ib6/yVrMRtb6v1ffTlfFc1SzlhtR6Qpqu0ZG9MCRkEfG4toM5pc86N9YqP4Xri+T9xgoFi0jxvExnCj0c4N9bHzbAioG8CGoAYy2Dop32BDdHeabAvM3rA8NhpsXgMZbLtJNdlU3m2wIcwMvp4uNVzfoyIDj9JBXSZPl9KR4vGaPCe+xmNx0gmT54TFaQ6XbbIUFKCbMmSxaM+4AjD0FIwzyXO+IntS5I0p8kaTfPVX5GCKvCdF3gPyN4z3/6621f470fDyplqOzI722Kk2VgezGHiUs2O6GQfD9k/blHeQx8g3KMMf09I9tVqGp5aqq3P8zqlceqU1U7OizQYwwmaKO+fGvIMKweQGeyaaHYOk4priGoOEcDZIQ9A8dJCUc+MUNwbZPUhyonkYBkEclzQhLq8Ka4UtQJ76GOWEl9fjbxCtwbdu3bo1a9YiX7cOAr6miDZtzrxoj88X1nJb6mP+cM7y+rX/wggU0QohVG0I2WxhLQShNWv8ppzfvy5VQN9G8Zvf2lSbMYSf/BAa/BiYMDcghkmT+tu9+WPMU3e/P5jj8wf79FNyc8/woMEf4zXG/CCP3lJ9GCWjjIVuuRPwLVIBY+Q1lEOkvwt434CBS/WzFuzGA+36n+R0MN8zCED4vLSb7uQM2ohbepgC9DN6ga6iDppD3bi5n+LXaQa84aXv0kQK0Tkaxa3UwBWo3UnZ+gugXKF/IE5gv7mfNuO2v47+QIvpN7ie7uQgFVAl/Y6m6csoy3KULqZb6R79j2RTyunndFR/Sx+gmfQTOspTuUluskyn79D1dAPdztlcyJV8A/kwh/X0JPULZ9p+vJRm0WXUTFFaRvtwqgi8H2ZTN78m6zBSlLbxRdyv78UB7IVkMdXwxcKvH6R8KsSRPoWq6Ra6m+6j17mEp8kypY+yoVMr9fEQHsXj+Ij+Y1KRZtF8zPR22kF76EV6kVVuFqWyxfLLgfdpCK3GDDfSNnqNPuF0/g6vF0n52EC1vkLv1Z+FdAXGqceeux5c90K7R+kA9dOvYJOjPJZn8738kbLWEji3eeD3A8f0UfonNBRznUvtdDV10lb45yF6mt6k43SaFbbzMH5aTBJvyiHKQ5ZsnfTb4DUX3lI1sNZ6uo22IPVB4tfs4gkc5LX8BzFEDBUrxY2iS/xNbsUt4s/KX/Q6fbf+DGz+AV5LHiQfNcKrG+G17fDdXnqc9lOSnqO/0in6DJZcwdu4h/fzP8QI8Zh4TTlrOWo5pT+on6UMWNtLRTQJKQgLzqBLMJeraSc89Ty9RG/Rl/Ql5/FkvpFv4zjfyffwDn6HvxC34lL4ttwhfyk1+ZzCSkBZYdlmOWadY2sd2DGwU49Auyz0XY64mQ4btiEW1yAmfgw7JugJOoK5/YPOwC5Z0LaAp3Ajr+cbeDNv54f5DTFTrBCrRYdkOVZ65Hi5RVGVLuX3ypuW6y3bBnwDMb3EPBvTEQ1TMO8o0kJailGuR9oGO3TTYXjrt4jaDxDNn9MZjCbg5wweyW4ez2GkufB6lBdwK7fzRv4pd/Gb/JFwihwxTmwXd4ufilfEX+Q18i75gOyVr8oBRbdkWAJIEUsM+nZZPrXOtW611doW2R61/+5c4bnnzr09kDkwcmD8QNPA9wcO6VH9Ov27+iP6o/pjerfebyxUXI7vprGILxfSeCrByonQt2gB5n8VXYOYjNMP6IdIj0KHXtpHzyLifk+v0Nv0DtIJeh+e/dDU6XM6C51y2MNliJcKns+LeCl38PVmuonv4/v5Adb4CPfzC/wqv85H+RjSF/wPPi2GiyxRKipEvZghLheNYrFoEx14XN4nHhC/EE+Ig+LX8PIfxOviPTEgx8ATYTlTXikXwCIb8FR6RD4h/0u+Jo/Kd+Vp2EaBj9yKR/EqVcoy5WblmGUC7LTEssKyC+lpa4Z1BV5KvdYXre/brLYJtpm22bZf2BI2HSulm36EVfq1DxG3myeKKzBLyc+IfXwXvyQSykkxhGN8vSRRrBQhxmfRCbFVenm6XM95WMd30CVCwoZDxINiBqLb+BqxioOIw2bLq8pIfhR3qVtxm51NL2PfiYBnCx0kr36UhtEP9atoP2djRbXp92MtbOII92MNLRPXiL8qZ6UTEfqufANxcwJrv5x3WF+k+cKPaJtGu2gU3m3j4aUN7BIlNI/ul1vgaTflUqGy0oI9nD/Fk2aP2CG2in3687jY/Q373jxlBi58x7DvF+L6/CE9jrm9IF4VW3m/YuVH+HLMYQz+tbAAsVwgHqQ2uY4VsUn8XTlKb4jJYp4s4k+VMilpNvx0M8X4Q7bTXt4hTrOb7uFN0P49/lC8R2vp76yLc3K7aOfn+Lc8Svi5Vk6iAfEuL8JsCugjSzaumRVYR1bE1QmxRy7F8+BVy9PyLWWWPEAKP8UV4qx0iXqeJSv1k+S1npaOgdf0OqoXuv4jJePcx7DONfSG/qwsVlqVS8/sP/OyyOYfyVWWqP7pwEbLzWI6LbV8YJtGG0QddoiXcRZ1UyF/LEbD7ipaqmCpbOUHZ86IOTRWnOLPaT1vx+oogCbN2Dm6aRluHD7Yzood+j76Eq+bp2mWXId95gA9i2i/AXt7lliMc6adG3F1LmG8qJB2Iho+UZbTBtoE/z+J07QLpXzLzwdC9B/Y976NtfhH3oZVN1NMVqLUhLP0JhpHFKppDlVPnzZ1StXkyoqLyoOBskmlJcVF/sKJE8b7vAWecW6Xmj92TN7o3JzsUSNHZA0f5hw6xJGZkZ5mt1ktisTTqCjsaWhxab4WTfF5Zs4sNuqeVjS0fq2hRXOhqeFCHs1lyLWCdAFnCJxLv8EZSnGGznOy0zWVphYXucIel/ZSvceV5HlzoijfUe+JubSTZnmWWf6BWXag7HZDwBXOaa93adziCmsN17XHwy31xUXck5Fe56lrSy8uop70DBQzUNKyPR09nD2dzYLIDlf14GHugIraaE89bmYeiK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qwYARsAzgBAnLvgNy18gDwacBZgKDbgXcDerWcuBlyzMWo7hDLgjkOKNuS/nK1uOKkWAxRq2Jxvz2tuOe7nClCU8TF/aao4diq8S7SeRf1myK10kX9yWnhGFzLK6PEAroVwCkOOBNQCqgBSGJBMLPQcUJMpZVGUqMcnbxTdEqdslRUw2JOiWKajh3ooBhRQD4w5DqafGy039Ru6jIJm8lpKjKppukmuU10ih4hHKJQVIhpoknIA6HTQcPYEkTqBGVsyW5zrzlgPm0+a5YDymnlrDKoXFRkp1KkqMp0xa+0K13KbqVXMe1Wdhu439xu7jILm9lpLjKr5ulm2WFgvZVbRQumScA2QDtgN0CCjJtQ7hQ3ApqwGk0Q240oJ2BCzgY4i/QgYhk5K/is4LOi1IpSK0oJWKNMB/gB7QCNqlylXKmj8V/UKIBsUKPQUhRxtBOFcqQAk5GzIGdBzgKus/wSRmgDdgKmA4ReNogUtAb4Cq1omO5HrJBGvwjgej2NpgIEv6Q2Z5/OZYFc1pvLducy1VdRWaxmAMXExDS5mzxNOU0HpDZ3m6ctp+2ANM09zTMtZ9oBqcJd4anIqTggFboLPYU5hQckh9vhceQ4Dkg99UfqT9WfqZea6tvqO+vFaCxdf9BbVKzHGR4tPhq0JxePtlZex49gOk3A+wHnAIIcwIWACkAbQOJHgB38KZQ+hdKnaBqgCSCjxlOobwXW6BpNK98PkPXUOaT4NXQchvxwcGzJtMrJMLlNgP0AgbYPo/5hnTucOqKXB4AH9fJpwBp/L0Ab5eGrdQQM3DxtHMAOQAWgCdAOkOmMmIvDYa7WMrAD0A44ApDEPIS5Yi5/CuEwPyzyVcvIeAclJOC0iYk22iptPBI6YGGP6/g+Hd+h4wodZ6pRky1fT7Y8N9ny48mWbCR4DlWiwh4du1RzpeXpSsu0SktupQWtJZKLLDxex4qG2Z90PFXH+Wqcy/KNy/J3l+VvLstDLssql+UHLq1eKvauhcfp2KxhtlfHk3WcpZodlpcdlrkOy2iHpdLC9jGMgap0nK7jFA2zL5621ljJdJJ9QTVojwV9uY4BTnrEQkFfpWOADQV9ExBdDvr2IfpX0PcTx7PsG6YfaezrYOZ5R2U8+5JNknDEsb8Px39jk+gQ8hcRL0F8kHzMg/hnQd9mjf9R1P8p8o9QhlGr9zBN1+vvZ5P08oeG6z0YzG9Brw8E89ej159SPtO47w3mn0fpT4L5dyC6O5i/AlFP0KMNcFnQl+eojGZLKJNrvAvIw7WR1A/3OBEtr0B+QrhybTBfq1WjdTDAqoPukYiytVE+y9w0Xe/OEXTrk0wjtz64VHLrg04hjx5HMas+eAtl6LEx6N6MVpSnPecd//Cd1CZOXzFrcJ/jo2cxvznIfsgmBQ85Xj+uiSvoOJM/wDzHHL9xn3S8lDnA5gQdp/MHjCCcyh/g7KijD0IOgJezY44j+UscT7l16gE3qFjq/b4CxwPueY77PcgHHZvzn9WGQSsx4zkgN+aPc9T7DjnGewYYyKoPnakRjrHu1Y5yFI8ZYJP6DzlGZg5oQylCG4eOOfLQY5ZbH8r1o0/wMjKwtWq+YY2hxTDHMMNwnaHEUGBwGtIMqYY4Y4zRZowyRhojjEajYpSM3EjGuIHQoOrV3LU4RffaFJhtRpKetsE0MmxA3ZvjzMixdwKxoo7XzapigZg6qptdFRjtrRswhGYGxnjrAsbpP2zoY+zORuQCfPsAo9kNAyykFW1NCcRUNxwnxgq37krR4o1bdzU2srrA6QVU1+IMfD0L84iYMS8gu6uSKGFdRVJFzLjo8vE1/wH59UJ/jfe7X9J3SaSS0gJ762Y1BJ5MawwUa4lQWmNdYMIs5w0Nx/kq3lZbc5y3a1Fjw3G2ga+qnamVsw01jVfZKIO3g418WqSx9VOGxkYZrF9nq9dbg5pm1Nb0ZQBpTC+wSRoT1OcFnWmJzgQdX6W1NV2LwMbTKVNvK5Ona2zQh3Bj1u83FknMqjdmjSS9sVSNqc/jQX/5QI0NfaM9YOjzjNbJh74ju3XycdZIGsNx8rBGvR+m9xNuIifMAy0Y5uFG8Fwjxv/fzKKq/4cWWH/zewsX1C5y1/rdtYsA/sCOda1Jga4Wp7Nv4XsawRkQWf6WBa1a3Lwo8J57UU1gobvG2des1/s38gKN3Oyu6aMFtbMb+haoi2qCzWpzrbu5prH/YGd13TV93XG1r+rO/9BXp9ZYtdbXQb3ev/VVp5EPan3VaX3VaX0dVA/qfdXNrGJ10xv6jFTVWI0F1OJ+bo7AfvCnuBqrEmzt4/TNcZ0r6UcpJyTCsWX2NgYi3VUBC0DbNwWVBZUaCbtTI0Wh2DpMSvrRda6UE+zxYZINxdHuKvJSUu3Smqt/HR0dazRYu9YLvGatRkQCm9Y1qy4wfsa8hoAv4KsNqP6aRqat2trhX3WDajvlO+Pjbb5OX49vv++IT167thHFMacyzmTwpoy2jM6Mnoz9GUcyFI1wQ8Mx1bc/468ZYi20ia3Br1brCl0jxp+WXbMWg+noIHTSAQh3513rrW6ozKAF8HYZPPMCigW4ASWAWQCZ/hv4DcBHgL8DJLoN+CeARwH9WokoEAW1SUtrtB4b0eJxShLF/UVlxWMGEDcvDsez5oXj2qnh2FdZnAR6sKIkotIKx5vRCeBfAd4FfA74F0AWxaJYbxxj1n6NHdThZZAWIbNGQx3eNcyLBNPEvabD6wWDlkcBcpCtLl7kh3/EOtYSRIEFQQQmvbxDq4Y+UHf4pxFgiuU7AfXkAKTidpVCFPoAcB7w6dDk0CV5ObmHloUGRSyYnxoGIg/tpf2USRfZSHqBTsOSH4SrM5320AQ6Q0coitazVyFNNzyMx2EvHLD74ymRyXQ/vUM30Gr6mAZxa66j91kM2qmldtway0OfAdfR9tBxcEVQNf2cTrAVbBbeFappIs+HJDzUEzpNiZQT+nXobeQeoo9ZZqiPJiL1R4qGd95Jd+EavYx+FdJeSTKphR5jG9ln8K38tEMqlbpDy+k6Okq/Z3VITaH18tumo/AO7qJHWSI7HToX+oSew1m6CC1toe0YcZBO8xGiWu4lJ2XRD2gqNYN6K73DYtlIoYayQ1Wh+1H6GH3BvfxlYcA4vDSJmmgXPQxpvEnn4QqYWRl7iB1CeJ39RX4bY6ujtbSBujDyg6h7mI6zkWwkT4R/yDHDXLoetB46gP776SyrY43sNHteHJCLhipCcaH40CehEOVRA0a4n55HH1+yIvCgB5Eh1kjp0hq5+PJmzHAhPUhn6XWM433I/Sv6J8tD+ID/iHeG5oYeD32MsRjhO4yhGTSP2mgd3UyPYFVfoBfpb+xbbgLnGekleYN8MXQ3ZJtFVRj7NHDPQts7sEpBGkB4E7OMZk7MYgybymayJayH7WUD7B32Dle4C0fl5yIgXhXvSaNkOTQWLSVoN3loyVxqxQr8CNK+G/N9nF6iV1g8y2IFmNGbqP81v47XIDzKz/D3xVbRI12Sfzw0OPSnoW9D3Xh7qoHeNUCaT0IKf2UJGEMuW8Y62EcY+W7+tIgSNuEWZaJSzBaNYrvYI34pfiOtlg5J78qT5Gb5kKF56Kah10N1odshC4a7Wjo0KZ9KaTT0ZzG0aTnG146wmjbSZuqmO6Evd1Mv/N0BOkWv0O/pD/RnrAAxF8a8FL2vhNZtZXci3M8Os+fZS+wV9gH7Wgs8AyGHj+IVvJqP50v4VoQ9/Cx/k38qUsUC3L+7EPbhKegdWGlJCsnFCBPlHfJjyquGHMNEQ4vxtUsXLuddbrz8/hANJQ/9cGjv0PNDn4TmhNZj/B4qoBEY6TaM8n7o4AGEJ6GJx+hleo3e0sf6BeNMhsYnMTe0IR+rVsEmwNWYxKawGQjXI8xl8xCaWQtrRehkXWwLu43dznaxe/RwH+Z2gD3BjiE8w04g/J6dY39kn7MvOJSYC2izh2fzQl6OmVbzCXwan4mwhLchtPPVfB1W6DHez4/zN0Ws8MDaNotV4n7xc/GC+J34RuJSvlQo+aQ50hLpNumM9Lr0tvSt7JBr5VZ5n/yCkqKUKtcry5T7lCPKp8olg2KYDnd1o+F3hpDRA4v1C8z7KNb0u1+hcoZ1yHHSLfwc9kWSaJe3seshMYXPFivEneK38mJ2UTjZu6xbLBXLQ4+K8fyfoo3N4adYhnDIY/GUs5NC7BD/gH/JP5Hi2Wz+GcuR7mLP8DZRzfHGAJv6hhQv3SZ/iteAt2gs38RO85fwcnVb6L9orLyPnZP38dfJKQ3yWDqHXb2N34tKv+FL+Q5qkErlb2kp5P6EfAvkPY5vZ3nid9I++li4+d9xu9oLq/FrNlnK5DfycnYIFvcyS6cLbBW1s3tIZSfZH9gAfOLHxWOsnkditQLcwkbjseXXwsV+JyKoURsjy+LxbDq/yK8XzypnRRmuPWfpt7SBCVYE3bnyG6KbsAP28GzYtFpYkzdYMSXRvbD3Xw49q1ls+W15B/TsYZFPM6mI5vNXaSz2xscIDfRjvNGdgA5upyJ+H20MdbGFsPtTYD854d5GhcwMa5mIsXXivEjgGbCFTej6n7D/v4LVr2N/oZuZEzvrNOVIGmWnVAvL5If93YGwkOYj9yDdrRyV36BpLJFIcg7tg5a/RzfizPkI/SfjhfouWLaHpXyM2gnLvAo1HhyaSCrCj+lVxmkTxjwO+3y6NBGWd29oGWa4FGdUPc7EV2hp6F6qxtrNDN0W2kFNoYdDN+CGOyv0OOzvulCQRtE2uZHPkb1SKWzsK+xFnEf/w3bAbk+kd2GPPCyJPkf4OcY/Tj5J3dJbsJ0VoZ2h3+OVNQcvr/fDzkyG9VpJf4HcJorTVDI0lfeFxot2nFDnaEbosZCDRVBraAUs77N0wCDD9nRRunwAurtDWsyLMN5cSmCFKL1B3k+kVl0/W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