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_ ( t ) = t 0 l n [ t / t 0 + "( t / t o ) 2 + 1 ] ( t ?@8 t / t 0 ë 1
_ ( t ) = t 0 l n [ t / t 0 + "( t / t o ) 2 + 1 ] ( t 0 l n 2 ( t / t 0 ) ?@8 t / t 0 » 1 ,
345 <K 2K45;8;8 ?@545;L=>5 ?>2545=85 7028A8<>AB8 _ >B t 2 A0<>< =0G0;5 @073>=0 8 ?>A;5 53> 7025@H5=8O. !>>B25BAB25==>, CA:>@5=85, A:>@>ABL ?>;5B0 8 B@05:B>@8O :>@01;O 2K3;O4OB 4;O 75<=>3> =01;N40B5;O A;54CNI8< >1@07><: a ( t ) = a 0 / [ 1 + ( t / t 0 ) 2 ] 3 / 2 = a 0 ( 1 v 2 / c 2 ) 3 / 2 ( a 0 ?@8 t / t 0 ë 1 ,
a ( t ) = a 0 / [ 1 + ( t / t 0 ) 2 ] 3 / 2 = a 0 ( 1 - v 2 / c 2 ) 3 / 2 ( 0 ?@8 t / t 0 » 1 ;
v ( t ) = a 0 t / [ 1 + ( t / t 0 ) 2 ] 1 / 2 ( a 0 t ?@8 t / t 0 ë 1 ,
v ( t ) = a 0 t / [ 1 + ( t / t 0 ) 2 ] 1 / 2 ( c ?@8 t / t 0 » 1 ;
r ( t ) = r 0 { [ 1 + ( t / t 0 ) 2 ] 1 / 2 - 1 } = r 0 { 1 / ( 1 - v 2 / c 2 ) 1 / 2 - 1 } ( a 0 t 2 / 2 ?@8 t / t 0 ë 1 ,
r ( t ) = r 0 { [ 1 + ( t / t 0 ) 2 ] 1 / 2 - 1 } = r 0 { 1 / ( 1 - v 2 / c 2 ) 1 / 2 - 1 } ( c t ?@8 t / t 0 » 1 ,
345 22545=0 ?>AB>O==0O r 0 = c t 0 = c 2 / a 0 E0@0:B5@=0O 4;8=0 @073>=0 ( ?@8 r » r 0 :>@01;L ?@0:B8G5A:8 845B A> A:>@>ABLN A25B0* ) .
* -B> ;53:> C2845BL, 8A?>;L7CO 2K@065=85 A:>@>AB8 G5@57 ?CBL: v = A[ 1 - 1 / ( 1 + r / r 0 ) 2 ] 1 / 2 ( "2 a 0 r r / r 0 ë 1
v = A[ 1 - 1 / ( 1 + r / r 0 ) 2 ] 1 / 2 ( c [ 1 - 1 / 2 . ( r 0 / r ) 2 ] r / r 0 » 1
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