Документ взят из кэша поисковой машины. Адрес оригинального документа : http://lnfm1.sai.msu.ru/~olympiad/1997/files/sol1997teor.pdf Дата изменения: Wed Nov 15 19:40:04 2006 Дата индексирования: Mon Oct 1 23:28:22 2012 Кодировка: Поисковые слова: http astrokuban.info astrokuban

Euro-Asian Astronomical Society

IV
. , 7-11

5. , , :
h = - (90° - ) 0° ,



90° - .
, ,

8-9 1. 2. . , . A a (1 + e ) 1 + e = = 1.6 P a (1 - e ) 1 - e
b = a 2 - 2 = a 1 - e 2 0.97 a

34°30' .
, 3 18 .
6. , :
h = - (90° - ) 0° ,

, , ( ) . , - , . 3. , : . ( ­ ); . (); . , . , . 4. , . , u 360є/29.5 0,51 ../. , , . ( : , , .) ( )

, . , - 25 ( = 45°50'). ­ . , ( = 00h39m) , 04m, = 00h16m. , t* = - = 00h23m ( 12h31m + 00h23m = 12h54m ). hmax = 45°50' + 90° - 55°30' = 80°20' , () , .

= 2( - o ) = 68" .


=


u

=

68" 134 0.51" /

: , . ( , ).


Euro-Asian Astronomical Society

IV
. , 7-11

3. 8, , (2\) , ­ , \.

(

M + m) T 2 = const , a3

10 1. ( ), , 0 = - 90° . , ( 44°24' ) 0 -45°36'. -46°36', = -47°30' . , . , H

, ".. ­ ­ \". (2 + 1) \ 177 , , 50 .. 50 .. 2,5", 1 .. 0,05", 20 .
4. , . ,

u 360є/29.5 0,51 ../. , , . ( : , , .) ( )

l = arctg , R
R 6400 ­ , l

l 2 = (R + H

)2

- R 2 = H (2 R + H ) .

= 2( - o ) = 68" .

H << l << R , l 2 RH
l 2H ( ). R R

=


u

=

68" 134 0.51" /

( -, m = 44°36', H = 1545 ) 0,022 1°16'. , ,

m = 44°36'-90° - 1° - 1°16' -47°40'
, .
2. , , , , , , : mv 2 mc T + m + mc T + mr , 2

m ­ , T ­ , , 50° 100°.
v 2 (c T + + c T + r ) ,
v
max

, . , , , ( , ). , , . -. : ­ v1 = 2R/ 950 /, v2 = 2r-cos/t 315 /. ( R = 384000 ­ , = 6380 ­ , = 29,5 ­ , t ­ , = 52° ­ ). , v2 v1. , 01h, 0lh + 113°/(15°/h) 08h32m, 3 28 , 52° ­ . , v* = vt - v2cos52° 780 /. , 134 ·(950/780) 163 . .
5. , : = 0,9951 : = 0,914 .. ,

2(2100 50 + 330000 + 4200 100 + 2300000 ) 6310000 ,

vmax 2,5 /. , (), , , , , . , " " .

a=

p 186,5 .., 1- e

, III ( )


T = T a

3/ 2

2550 .

6. , :
h = - (90° - ) 0° ,

, . , - 25 ( = 45°50'). ­ . , ( = 00h39m) , 04m, = 00h16m. , t* = - = 00h23m ( 12h31m + 00h23m = 12h54m ). hmax = 45°50' + 90° - 55°30' = 80°20' , () , .


Euro-Asian Astronomical Society

IV
. , 7-11

, , , : mv 2 mc T + m + mc T + mr , 2 m ­ , T ­ , , 50° 100°. v 2 (c T + + c T + r ) ,
v
max

11 1. , . , , , . , Ro Rg, , , A( Ro , Rg ) =

2(2100 50 + 330000 + 4200 100 + 2300000 ) 6310000 ,

(R

g

- Ro ) (Fg - Fo 2

)

,

vmax 2,5 /. , (), , , , , . , " " .
3. 8, , (2\) , ­ , \.

Fg Fo ­ Rg Ro . ,
Fg m = V
2 g g

R

,

Fo Vo2 = , m Ro

(

m ­ . , Rg Rmax ( ), 1/2, GMm GMm , A(Rg , Rmax ) = - Rg Rmax G ­ , M ­ , , , GM = Rg Vg2 . Rmax

M + m) T 2 = const , a3

, ".. ­ ­ \". (2 + 1) \ 177 , , 50 .. 50 .. 2,5", 1 .. 0,05", 20 .
4. , . ,

u 360є/29.5 0,51 ../. , , . ( : , , .) ( )

1 mV*2 (Rg - Ro )(Fg - Fo ) 1 = + GMm - R 2 2 Rmax g

;

Vg2 Vo2 + 2V + V*2 = (Rg - Ro ) R g Ro

2 g

R 1 - g R max



= 2( - o ) = 68" .


( , ), : R
max

43,7
2 g 2 o

=


u

=

68" 134 0.51" /

, V, V V + 2V + V 2 (Rg - Ro ) R g Ro , : v2 483 /.
2.
2 g

, , ,

, . , , , ( , ). , , . -. : ­ v1 = 2R/ 950 /, v2 = 2r-cos/t 315 /. ( R = 384000 ­ , = 6380 ­ , = 29,5 ­


, t ­ , = 52° ­ ). , v2 v1. , 01h, 0lh + 113°/(15°/h) 08h32m, 3 28 , 52° ­ . , v* = vt - v2cos52° 780 /. , 134 ·(950/780) 163 . .
5. , : = 0,9951 : = 0,914 .. ,

a=

p 186,5 .., 1- e
3/ 2

, III ( )

T = T a

2550 .

6. , Ab v ( ), :

(

B -V

)0

= B0 - V0 = (B - Ab ) - (V - Av ) =

= (B - 2.5 lg b ) - (V - 2.5 lg v ) = (B - V ) - 2.5(lg b - lg v )
0.22 - 2.5 (0.4 - 0.3) 0.22 - 0.25 -0.03

10000 .