?? ??? ????? ?? ??????? ?? ??? ????? ???? ????? ^[?] ( ??????? :Specific orbital energy) ^[?] ${\displaystyle {\epsilon }}$ ?? ??? ?? ???? ??? ???????? ????? ????? ????? ?? ????????? ????? ( ${\displaystyle {\epsilon _{k}}}$) ? ??????? ( ${\displaystyle {\epsilon _{p}}}$) ?? ??? ???? ????? ^[?] ( ${\displaystyle {\mu }}$) ?????? ?? ????? ?? ?????? ????? ???? ????? ????? ^[?] ?? ???? ????? ???????.

${\displaystyle \epsilon =\epsilon _{k}+\epsilon _{p}\!}$

${\displaystyle \epsilon ={v^{2} \over {2}}-{\mu \over {r}}=-{1 \over {2}}{\mu ^{2} \over {h^{2}}}\left(1-e^{2}\right)=-{\frac {\mu }{2a}}}$

??:

• ${\displaystyle v\,\!}$ ???? ???? ??????
• ${\displaystyle r\,\!}$ ????? ?? ?????? ????? ?? ??? ???? ?? ???
• ${\displaystyle \mu ={G}(m_{1}+m_{2})\,\!}$ ????? ??????? ?????? ????????? ^[?] ???? ???? ??? ????
• ${\displaystyle h\,\!}$ ????? ?????? ????? ???????? ???? ???? ^[?] ?? ????? ????? ????????? ???????? ???? ??? ?? ??? ???? ??????????
• ${\displaystyle e\,\!}$ ????? ???? ?? ???? ????? ?
• ${\displaystyle a\,\!}$ ?????? ?? ????? ??? ???? ???? ^[?] ???.

???? ?????? ???? ????? ???? ????? ?? ?????? ?????????? ??????????? ? ????? ?? ?? J/kg ?? ??? ?? m ² ·s ^?2 ? ?????? ?????? ?? ${\displaystyle L^{2}T^{-2}}$ ???. ???? ?? ???? ????? ?? ???? ?? ???? ???? ?? ? ????? ????? ???? ????? ????? ???? ????? ????? ???? ???? ???? ???? ??? ?? ???????? ?? ???? ???? ??? (????? ?? ?? ?? ?? ???? ???? ???? ??????). ???? ?? ???? ?????? ??? ????? ????? ?? ????? ????? ?? ????? ???? ???? ?? ???? ???? ???. ?? ???? ???? ????? ???? ????? ?? ????? ???? ^[?] ????? ???????.

?????? ???? ??????? ????? [ ?????? ]

???? ?? ???? ????? ?????? ?? ??????? ????? ???? ????? ?? ??????? ????? ???????? ???? ????? ??? ? ?? ??? ?? ???? ??? ?? ???? ????? ????? ??? ?? ???? ??? ???? ????? ??:

${\displaystyle \epsilon =-{\mu \over {2a}}\,\!}$

?? ?? ?? ${\displaystyle \mu ={G}(m_{1}+m_{2})\,\!}$ ??????? ?????? ????????? ?? ? ${\displaystyle a}$ ?????? ?? ????? ??? ???? ???? ???. ???? ???? ???? ??? ????? ?? ????? ??????? ????? ???? ??????? ?????? ?? ???? ? ????? ????? ????? ?? ????? ?????? ?? ?????? ??? ??????? ?? ?? ?? ?????? ?????????? ????? ???? ????? ? ????? ???????? ???? ???? ?????:

${\displaystyle \epsilon ={v^{2} \over {2}}-{\mu \over {r}}}$

?? ???? ?? ??? ?????? ???? ????? ???? ????? ??? ??????? ??????? ?? ?? ???? ?? ???? ??? ????? ???? ???? ^[?] ????? ???? ??? ?? ???? ?? ????? ??? ???? ???? ?? ????? ??? ?? ?????? ????? ??? ? ????? ???? ????? ??? ?????? ????? ????? ? ???? ???? ?????? ????? ??? ?? ????? ???? ???? ??? ??????? ?????? ${\displaystyle {h}={v_{p}}{r_{p}}}$ ?? ????? ?? ${\displaystyle {v_{p}}={{h} \over {r_{p}}}}$ ?? ???? ?? ?? ???? ?? ??? ???? ?? ???? ???? ????? ${\displaystyle r_{p}=a(1-e)}$ ?????? ???? ????? ???????:

${\displaystyle {v_{p}^{2}}={h^{2} \over {rp}^{2}}={h^{2} \over {a^{2}(1-e)}^{2}}={\mu a(1-e^{2}) \over {a^{2}(1-e)}^{2}}={\mu (1-e^{2}) \over {a(1-e)}^{2}}\,\!}$

? ?? ???????? ????? ????? ???? ???? ????? ????? ???????:

${\displaystyle \epsilon ={v_{p}^{2} \over {2}}-{\mu \over {r_{p}}}={\mu \over {a}}{\left[{(1-e^{2}) \over {2(1-e)}^{2}}-{1 \over {(1-e)}}\right]}={\mu \over {a}}{\left[{{(1-e)(1+e)} \over {2(1-e)}^{2}}-{1 \over {(1-e)}}\right]}}$

${\displaystyle ={\mu \over {a}}{\left[{(1+e) \over {2(1-e)}}-{2 \over {2(1-e)}}\right]}={\mu \over {a}}{\left[{{e-1} \over {2(1-e)}}\right]}=-{\mu \over {2a}\,\!}}$

???? ?? ???? ???? ??? ?????? ?? ???? ??? ${\displaystyle \epsilon =0\,\!}$ ???? ??????? ? ???? ???? ?????? ???? ?? ????? ${\displaystyle a}$ ?? ????? ???? ??????? ??????? ??? ?? ?? ?? ?? ???? ${\displaystyle \epsilon ={\mu \over {2a}}\,\!}$ ???????? ???? ?? ??? ???? ?? ?? ??? ??? ????? ????? ???? ? ????? ?? ??? ???. ?? ???? ???? ????? ???? ????? ????? ??? ?? ????? ????? ???? ???? ????? ? ?? ????? ???? ( ${\displaystyle {C_{3}}}$) ????? ???. ???? ??? ????? ? ???? ????? ?? ????? ???????? ??? ?? ???? ?????? ????? ??? ?? ?????? ???:

${\displaystyle 2\epsilon =C_{3}=v_{\infty }^{2}\,\!}$

?? ?? ?????????? ??? ???????? ?????? ????.

????? ???? ??? ????? ???? ????? ( ${\displaystyle \mathbf {r} \,\!}$) ? ????? ???? ????? ( ${\displaystyle \mathbf {v} \,\!}$) ?? ?? ????? ????? ????? ?????? ?? ??? ??? ???? ( ${\displaystyle \mu \,\!}$) ????? ??????? ????? ???? ????? ( ${\displaystyle \epsilon \,\!}$) ?? ???? ???? ???? ????? ???.

??? ??????? [ ?????? ]

???? ?? ???? ????? ?? ??????? ??? ???? ???? ?? ?? ${\displaystyle a\,\!}$ ??? ???? ??????? ????? ????? ?? ????? ?? ????? ???? ???? ????? ??? ??:

${\displaystyle {\frac {\mu }{2a^{2}}}\,\!}$

?? ?? ?? ${\displaystyle \mu \,\!}$ ??? ???? ?????????. ?? ????? ?? ??? ??? ???? ?? ???? ????? ${\displaystyle a\,\!}$ ??????? ???? ?? ??? ????? ?? ???? ??? ? ???? ?? ??? ????? ?????? ???.

?? ???? ?? ???? ???? ????????? ??? ???? ????? ??? ?? ??? ???? ????? ???? ???? ???? ???? ???? ???? ?? ???????? ?? ???? ????? ??? ????? ????? ??? ?? ??? ????? ?? ???? ?? ???? ???????? ????? ?? ????? ??? ?? ??? ????? ???????? ?? ??? ???? ?? ????? ????? ??? ????? ?? ????? ?? ??? ????? ??????? ???.

????? ????? ^[??] (??????) [ ?????? ]

??? ??? ????? ????? ???? ${\displaystyle R\,\!}$ ????? ?? ??????? ????? ????? ???? ???? ???? ????? ?? ???? ????? ???? ?? ???? ???? ????? ?? ??? ??? ?? ???? ??? ????? ???:

${\displaystyle \ -{\frac {\mu }{2a}}-{({-}{\frac {\mu }{R}})}={-}{\frac {\mu }{2a}}+{\frac {\mu }{R}}={\frac {\mu (2a-R)}{2aR}}}$

• ??? ????? ???? ????? ????? ???? ?? ????? ?? ??? ${\displaystyle R/2}$ ?????? ?????? ???? ?? ???? ??????? ${\displaystyle (2a-R)g}$ ?? ??????? ????? ???? ${\displaystyle 2a-R}$ ???? ????? ?????? ???? ????? ????? ??? ?? ??? ?? ????? ????? ????? ^[??] (????? ????? ??? ???? ???? ?? ???? ???? ?? ???? ?????)? ?? ????? ???? ????? ???? ????? ????? ?? ????? ????? ????? ???? ???? ????? ???.

?????? [ ?????? ]

??????? ????? ?????????? (ISS) [ ?????? ]

??????? ????? ?????????? ???? ???? ????? ????? ????? ????? ?? ??????? ???? ????? ???? ???????? ??? ???? ???? ????? ????? ?? ???? ??? ????. ????? ???? ????? ${\displaystyle MJ/kg}$ ????? ? ????? ??????? ${\displaystyle MJ/kg}$ ????? ? ????? ????? ${\displaystyle MJ/kg}$ ???? ???. ???? ?????? ????? ??????? ??? ??? ${\displaystyle MJ/kg}$ ????? ??? ?? ????? ??????? ?????? ???? ?? ${\displaystyle MJ/kg}$ ??? ?? ????? ??????? ?? ????? ????? ${\displaystyle MJ/kg}$ ?? ???. ???? ????? ${\displaystyle km/s}$ ??? ??? ? ????? ???? ???? ^[??] ???? ????? ?? ??? ???? ???? ${\displaystyle km/s}$ ??? ??? (????? ???? ????? ?? ???? ?????? ??? ^[??] ? ?????? ????? ^[??] ?????? ????? ??? ??? ?? ???????? ?? ????? ????? ???).

?? ????? ${\displaystyle km}$ ??? ?? ???? (???? ????? ?? ${\displaystyle km}$ ????):

????? ${\displaystyle MJ/kg}$ ????? ???? ????? ??????? ${\displaystyle MJ/kg}$ ????? ? ????? ????? ${\displaystyle MJ/kg}$ ????? ?? ???? ?? ????? ??????? ??? ??? ?? ????? ${\displaystyle MJ/kg}$ ?????. ????? ????? ??????? ?? ${\displaystyle MJ/kg}$ ??? ? ??????? ????? ????? ?? ${\displaystyle MJ/kg}$ ???? ???.

??? ?????? ????? ${\displaystyle J/kg}$ ??? ?? ???? ?? ??? ???? ??? ??? ????? ?? ??? ????? ???? ?? ????? ${\displaystyle m/s^{2}}$ ??? ??????. ???? ${\displaystyle km/s}$ ??? ? ????? ???? ???? ${\displaystyle km/s}$ ??? ???.

?? ?????? ???? ???? ???? ???? ?? ????? ????? ????? ???? ???? ???? ${\displaystyle km/s}$ ???? ???? (?? ???? ????? ?? ???? ?? ??? ???) ?? ????? (????? ?? ???? ?? ???) ???.

????? ? ^[??] [ ?????? ]

???? ????? ?? ???? ?? ?????? ?? ??????? ?????? ?????????: km ³ s ^?2 ??????????????? = ${\displaystyle \mu =GM\,\!}$

? ???? r = ?? ??????? ??????? ? ???? v = ???? km/s

${\displaystyle \epsilon =\epsilon _{k}+\epsilon _{p}={v^{2} \over {2}}-{\mu \over {r}}}$

${\displaystyle ={146{km^{2}s^{-2}}-8{km^{2}s^{-2}}=138{km^{2}s^{-2}}}}$

???? ??? ??? ??????? ?? ??? ???? (???? ???? ?? ???????? ???) ?? ????? ?? ???? ??? ???:

${\displaystyle v_{\infty }={\sqrt {2\times 138km^{2}s^{-2}}}=16.6{km/s}\,\!}$

????? ?????? [ ?????? ]

??? ????:

• a ???? ????? ?? ????? ??????
• g ???? ??????
• v ???? ????

?? ??? ????? ???? ????? ????? ???? ???? ${\displaystyle \mathbf {v} \cdot \mathbf {a} }$ ??? ?? ??? ????? ????? ?? ?? ${\displaystyle \mathbf {v} \cdot (\mathbf {a} -\mathbf {g} )}$ ? ??? ????? ??????? ?? ?? ${\displaystyle \mathbf {v} \cdot \mathbf {g} }$ ???.

????? ????? ???? ???? ???? ???? ????? ?? ????? ???? ^[??] ????? ??? ??:

${\displaystyle {\frac {\mathbf {v\cdot a} }{|\mathbf {a} |}}}$

?? ?? ??? ??? ?? ??????? ??????? ????? ???? v ? ?????? ???????? ?? ?? ??? ????? ???? a ???????.

???????? ?????? ?? ???? ? ???? ?? ??? ????? ? ?????? ?? ????? ???? ?????? ???? ???? ????? ??? ????? ????? ???? ????? ???? ?? ?????? ??????. ?????? ?? ????? ??? ???? ? ???? ??? ???? ?? ????? ???? ???? ????? ?? ???? ?????? ?? ???? ??????? ??? ?? ???? ????? ???? ??????? ?? ???? ?? ????????? ???? ? ?? ????? ????? ???? ???. ?? ????? ?? ???? ?? ??? ??? ???????? ?? ???? ?????? ????? ?????? ?? ?????? ?? ???. ?? ????? ???? ?????? ?? ?? ???? ?????? ?? ???? ?????? ????? ?????? ?? ????? ????? ???? ???????.

????? ????? ????? ???? ???? ???? ????? ???? ????? ??????? ????? ????? ?? ????? ??? ?? ???? ? ???? ?? ???? ????? ????? ? ????? ??? ???? ??? ?????? ???? ???? ????. ?????? ?? ?????? ??? ???? ? ???? ??? ???? ????? ???? (??? ?? ??? ??? ???????? ???? ???? ?????? ) ?? ?? ?????? ?? ?? ???? ???????? ?? ??? ?? ??? ??? ????? ??? ???? ???? ?? ?????? ?? ???? ????? ????? ???? ?? ???????? ???? ???? ???. ?? ??? ??? ?? ???? ?? ????? ?? ???? ????? ????? ?????? ?? ?????? ?? ???? ? ????? ???? ?? ???? ???? ???????? ?? ???? ????? ????? ?????? ?? ??? ?? ?????? ???? ???? ???????.

?????? ?? ???? ? ???? ?? ?? ??? ??? ????? ????? ????:

${\displaystyle \Delta \epsilon =\int v\,d(\Delta v)=\int v\,adt}$

???? ??????? ( ????? ) ????? ? ????? ????? ???? [ ?????? ]

??????? ????? ? ????? ????

???? ?????	????? ???? ?? ???? (km)	????? ?? ??? ???? ?? ?????? (km)	???? ????? (km/s)	???? ???? (h min sec)	????? ???? ?????(MJ/kg)
??????? ???? ??? ????? (???? ??????)	?????	?	??????	?? (? ???)	?????
???? ??? ????? ?? ?????	?????	?	???	? ´?? ´´??	?????
???? ????? ????	????? ?? ?????	??? ?? ?????	???? ????????: ??? ?? ??? ???? ?????: ??? ?? ???	? ´?? ?? ? ´?	?????
???? ?????? [??]	????? ?? ??????	??? ?? ??????	??? ?? ????	?? ´??	????
???? ???? ????	??????	??????	???	?? ´??	????
???? ???? ???	??????? ?? ???????	??????? ?? ???????	???? ?? ????	??? ´?? (???? ???)	????

?????? [ ?????? ]

????? [ ?????? ]

• ?????????????? ?????????. ≪ Specific orbital energy ≫. ?? ????????? ?????????? ??????? ? ??????????? ?? ?? ?? ????.