GNU Free Documentation License . .

: ,

, .

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, . , , , , . 90° . , . , , , .

a\,\! b\,\! e\,\! l\,\!, :

b = a \sqrt{1-e^2},\,
\ell=a(1-e^2),\,
a\ell=b^2.\,

. , () , ( ):

r(1-e\cos\theta)=\ell.\,

r={\ell\over{1+e}}\,\! r={\ell\over{1-e}}\,\! a={\ell\over 1-e^2}.\,

[]

y = x2

, , , l\,\! . a\,\! b\,\! , a\,\! , b\,\!.

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, x\,\! ( ). , :

\frac{\left( x-h \right)^2}{a^2} - \frac{\left( y-k \right)^2}{b^2} = 1.

, :

a={\ell \over e^2-1 }.

, , .[1]

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T\,\! :

T = 2\pi\sqrt{a^3 \over \mu}

:

a\,\!
\mu (en:standard gravitational parameter)

, , .

, , .

.

\frac{T_1^2}{T_2^2} = \frac{a_1^3}{a_2^3}

:

T\,\! ;
a\,\! .

:

T^2= \frac{4\pi^2}{G(M+m)}a^3\,

:

G\,\!
M\,\!
m\,\! . , , . , , , .

(), . , , . -. 81,30059. 384400 . - 379700 , - , 4700  . 1,010 /, 0,012 /. 1,022 /; , , .

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  • .

, . , , :

a \left(1 + \frac{e^2}{2}\right).\,
  • , :
\sqrt{ab} = a\sqrt[4]{1-e^2}.\,


[] ;

a\,\! :

a = { - \mu \over {2\varepsilon}}\,

a = {\mu \over {2\varepsilon}}\,

\varepsilon = { v^2 \over {2} } - {\mu \over \left | \mathbf{r} \right |}

(en:specific orbital energy)

\mu = G(M+m ) \,

( ), :

v\,\! , ,
r\,\! , (, , ),
G\,\! ,
M\,\! m\,\! .

, .

[] .

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  1. 7.1 Alternative Characterization

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