ecuacion de velocidad radial
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Ecuaciones de Velocidad RadialTRANSCRIPT
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a detailed derivation ofThe Radial Velocity Equation
Kelsey I. Clubb
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Kelsey I. Clubb
Department of Physics & AstronomySan Francisco State UniversitySan Francisco, CA USA
August 2008
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$0, %!()!* +,*-&)$. ,23!$)-4 77
APPENDIX B: THE EXPRESSION FOR z
F$ 63;%$ 9& - 93$ 23##34:/$ $' :12&).$-12 >%&)& $%& &B:-$3'1 #') z 4'6&. #)'65 .' FC(& 314/:2&2 - 6')&
2&$-3/&2 3//:.$)-$3'1 '# $%& -1;/&. -12 /&1;$%. 31 B:&.$3'1 <.%'>1 31 6CIVB; TX?@
l-)$ '# $%& 0/-1&$C. ')93$ -)':12 3$. %'.$ .$-) %-. 9&&1 6-2& 9<:D 31 $%& 23-;)-6@ P& >3// -..:6& $%3.
$' 9& - .$)-3;%$ /&1;$% -12 )&#&) $' 3$ -. (bold length) 31 $%& #'//'>31; &B:-$3'1.@ U'$& $%-$ $%& -4$:-/
(-/:& #') $%& /&1;$% 3. 1'$ 1&&2&2@
# 3. $%& -1;/& 9&$>&&1 $%& /31&D'#D1'2&. <8D-,3. 31 K3;:)& Zc? -12 0&)3-.$)'1@ ! 3. $%& -1;/& 9&$>&&1
0&)3-.$)'1 -12 $%& 0/-1&$C. 0'.3$3'1 (&4$')5!
r <$%& 6-;13$:2& '# >%34% 3. )5 $%& 23.$-14& 9&$>&&1 $%&
0/-1&$ -12 3$. %'.$ .$-)?@ A%& -1;/& 9&$>&&1 $%& 8D-,3. -12 $%& 0/-1&$C. 0'.3$3'1 (&4$') 3. " +# <FC//
/&-(& 3$ $' $%& )&-2&) $' 6-=& 4&)$-31 %&Y.%& :12&).$-12. >%8 $%3. 3. $%& 4-.&L 9:$ 3# 8': -)&1C$ 4&)$-315
68 %31$ 3. $' $)8 6-=31; :0 1:69&). #') ! -12 # ') 6'(31; $%& 0/-1&$ $' -1'$%&) 0'.3$3'1 31 3$. ')93$?@
P& 1'> %-(& $%& 1&4&..-)8 31#')6-$3'1 -125 >3$% $%& -32 '# $)3;'1'6&$)85 >& #312]
sin " +# ( ) =bold length( )
r$ bold length( ) = r sin " +# ( )
sin i = z
bold length( ) " z = bold length( ) sin i # z = r sin $ +% ( ) sin i
6CIVB; TX E O 23-;)-6 .0&43#34-//8 4)&-$&2 $' .%'> $%& 360')$-1$
/&1;$%. -12 -1;/&. 1&&2&2 #') 2&$&)63131; -1 &,0)&..3'1 #') z@
7/17/2019 Ecuacion de Velocidad Radial
http://slidepdf.com/reader/full/ecuacion-de-velocidad-radial 34/34
REFERENCE FOR CALCULATING RV SEMI-AMPLITUDE
F# 8': =1'> $%& 1:6&)34-/ (-/:& #') &-4% '# $%& #'//'>31; 0-)-6&$&). #') - 0/-1&$ -12 3$. %'.$ .$-)5
! P <$%& 0/-1&$ ') %'.$ .$-)C. ')93$-/ 0&)3'2 31 2-8. ') 8&-).?
! M planet sin i <$%& 0/-1&$C. 63136:6 6-.. 31 $&)6. '# $%& 6-.. '# J-)$% ') m:03$&)?
! M
star <$%& 6-.. '# $%& %'.$ .$-) 31 $&)6. '# $%& 6-.. '# $%& V:1?
! e <$%& &44&1$)343$8 '# $%& 0/-1&$C. ')93$ -)':12 3$. %'.$ .$-) E )-1;&. #)'6 +DZ?
$%&1 &1$&)31; $%& -00)'0)3-$& (-/:& 31$' '1& '# $%& #'//'>31; #':) &B:-$3'1. >3// ;3(& 8': $%&
1:6&)34-/ (-/:& '# $%& .$-)C. )-23-/ (&/'43$8 .&63D-60/3$:2&]
K star = 0.6395 m s"1 1 day
P
#
$ %
&
' (
1
3 M planet sin i
M Earth
#
$ %
&
' (
M Sun
M star
#
$ %
&
' (
2 / 3
1
1" e2
K star = 0.0895 m s"1 1 yr
P
#
$ %
&
' (
1
3 M planet sin i
M Earth
#
$ %
&
' (
M Sun
M star
#
$ %
&
' (
2 / 3
1
1" e2
K star = 203.255 m s"1 1 day
P
#
$ %
&
' (
1
3 M planet sin i
M Jupiter
#
$ % %
&
' ( (
M Sun
M star
#
$ %
&
' (
2 / 3
1
1" e2
K star = 28.435 m s"1 1 yr
P
#
$ %
&
' (
1
3 M planet sin i
M Jupiter
#
$ % %
&
' ( (
M Sun
M star
#
$ %
&
' (
2 / 3
1
1" e2