PENGANTAR MEKANIKA BENDA LANGIT

7
"#$%& '(")*+,,+ ,-./#+#"* !"#$%#&%' )"*%#+*% ,"#-% .%#$+& $0112 $34536317 "8-98 :3453631;<128398=: $=>35?3=@31 ?3:3A '(")*+,,+ #&*"'*,$( -,*+- +,-*#+,& B#-+C -",D", )*$,+E ,-./#+#"* .*+EF,. F#.,DF,)%',.(+ $*+,- '(+$*$*F,+ F#.,",$G, G#EG,F,/., -", "<H3553:=23H ** GIJ23@34K37 LM N OP "0= LPQO

Transcript of PENGANTAR MEKANIKA BENDA LANGIT

Page 1: PENGANTAR MEKANIKA BENDA LANGIT

!"#$%&!'(")*+,,+!,-./#+#"*!

!!!!

!"#$%#&%'()"*%#+*%(,"#-%(.%#$+&(!!!!!!!!!!!!!!!!!

$0112!$34536317!"8-98!!

:3453631;<128398=:!!!!!!!!!!!!!

$=>35?3=@31!?3:3A!!

'(")*+,,+!#&*"'*,$(!-,*+-!+,-*#+,&!B#-+C!-",D",!)*$,+E!,-./#+#"*!.*+EF,.!F#.,DF,)%',.(+!$*+,-!'(+$*$*F,+!F#.,",$G,!G#EG,F,/.,!

!-",!"<H3553:=23H!**!GIJ23@34K37!LM!N!OP!"0=!LPQO!

Page 2: PENGANTAR MEKANIKA BENDA LANGIT

'+#$*%/%#()%&"'+()"*%#+*%(,"#-%(.%#$+&(!!+0(12*2)(*"!."'(&"#&%#$($"'%*(!.%#"&(!R SIH3110>!F0?T04!BQUVQ!R!QWOPC!504<?3@31!3>K4I1I5!K0I4=!:31!53K053K=@3631!:34=!

S045317!501:3?3K! K<J3>! :34=! .29HI! )43H0! BQUXW! N! QWPQC! ?3:3! K3H<1! QWPP! <1K<@!501934=!>0Y<3H!K0I4=!231J!:3?3K!501Z0T3>@31!:3K3!?01J353K31!?T310K!5=T=@!)43H08!

R F0?T04! 50101K<@31! Y01K<@! I4Y=K! ?T310K! 501JJ<13@31! 50KI:0! K4=31J<T3>=! :34=!Y0Y043?3!K=K=@!231J!3:3!:=!I4Y=K!)<5=7!Y<@31!K=K=@!231J!3:3!:=!)<5=!=K<!>01:=4=7!231J!:=?04IT0H!:34=!?01J353K31!?3:3!63@K<!231J!Y04Y0:3RY0:3!5=T=@!)43H0!

R $01J31! 501JJ<13@31! >0Y3J=31! I4Y=K! )<5=! >0Y3J3=! Y3>0T=107! F0?T04! :3?3K!50101K<@31! <@<431! 3456789! I4Y=KRI4Y=K! ?T310K! :31! @0T3Z<31! ?04J043@31! ?T310K!B[!"#$%!" #$$%" &%'" ($)$*" +',&" *-" .$%$/$)&" $%$'" *-" 01$2-%" 1$&223$" %&4$*" 5&#$" 4&'*')"1$26#'267" #-/&266$" /$23$" 4&6'2$*$2" ($)$*" )-1$%&89" :$)&" #&2&1$/",'2;'1" #$%'$2" <=" >"<#%)?2?,&;$1"=2&%9"@"<=">"($)$*")-)$%$"+',&"*-".$%$/$)&C8!

R \<@<5! F0?T04! ?04K353A! ]T=1K3>31! I4Y=K! ?T310K! Y04Y01K<@! 0TT=?>! BY<@31! T=1J@3431C!:01J31!53K3H34=!Y043:3!:=!>3T3H!>3K<!K=K=@!^I@<>_8!

R (TT=?>! K=:3@! T3=1! 504<?3@31! T=1J@3431! 231J! :=?=?=H@317! 1=T3=! 0@>01K4=>=K3>!501<1Z<@@31! >0Y043?3! ?=?=H! ><3K<! 0TT=?>8! B[!"#$%!" -11&0#" 4$0$%" 4&1'*&#" 4-26$2",-26&*$%"#-'%$#" %$1&"0$4$"4'$"0$*'"3$26"4&%$2;$0*$2"*-"*-)%$#7"*-,'4&$2"%$)&*" %$1&"4-26$2" 0-2#&1" 4$2" ,'1$&" ,-1'*&#" *')A$" #$,5&1" ,-26&%$)&" *-4'$" 0$*'9" B?#&#&" 0$*'"4&#-5'%"%&%&*"8?*'#C8!!

!$6:;63(<8!`343!50T<@=>!0TT=?>!

!R -<5Y<! ?31Z31J! :34=! 0TT=?>! 231J! 50T063K=! @0:<3! K=K=@! ^I@<>! 0TT=?>! :=>0Y<K! ><5Y<!

532I48!-0?34I!:34=!><5Y<!532I4!:=>0Y<K!><5Y<!>05=532I48!R &=1J@3431!K=:3@!T3=1!3:3T3H!@3><>!@H<><>!0TT=?>!231J!@0:<3!K=K=@!^I@<>123!Y04=5?=K7!

>0H=1JJ3!><5Y<!>05=532I4!501Z3:=!Z0Z34=!T=1J@34318!

Page 3: PENGANTAR MEKANIKA BENDA LANGIT

R -09343!53K053K=>7! 0@>01K4=>=K3>! 3:3T3H! 43>=I! Z343@! @0:<3! K=K=@! ^I@<>! 0TT=?>! :01J31!?31Z31J! ><5Y<! 532I48! F0K=@3! 0@>01K4=>=K3>! Y041=T3=! 1IT7! Y0434K=! @0:<3! K=K=@! ^I@<>!Y04=5?=K7!53@3!:=?04IT0H!T=1J@3431!>05?<4138!

R \3123!?04T<!:3K3!><5Y<!>05=532I4!:31!0@>01K4=>=K3>!<1K<@!:3?3K!501JJ35Y34@31!<@<431!:31!Y01K<@!T=1K3>31!I4Y=K!?T310K8!

R $34=! :3K3! ><5Y<! 532I4! B$C! :31! 0@>01K4=>=K3>! B-C7! :3?3K! :=K01K<@31! K=K=@! K04:0@3K!?T310K! @0! "3K3H34=! B0-)&/-1&?2C! :31! K=K=@! K04Z3<H! ?T310K! :34=! "3K3H34=! B$0/-1&?2C8!S343@! ?04=H0T=I1123! 3:3T3H! $BQ! N! -C! :31! Z343@! 3?H0T=I1123! 3:3T3H! $BQ! a! -C! :34=!"3K3H34=8!

R )3H63! T=1K3>31! I4Y=K! ?T310K! Y04Y01K<@! 0T=?>! >31J3K! Y04Y0:3! :01J31! @0?04932331!,4=>KIK0T0>7! `I?041=9<>! H=1JJ3! E3T=T0I! Y3H63! T31J=K! 501J35Y=T! Y01K<@! J0I50K4=!b>05?<413c! 23=K<! T=1J@34318! +35<1! @34013! 1=T3=! 0@>01K4=>=K3>! ?T310K! 231J! >31J3K!@09=T7!@09<3T=!"04@<4=<>7!T=1K3>31!I4Y=K!?T310K!H35?=4!505Y01K<@!T=1J@34318!

R \<@<5!F0?T04! @0:<3A! ]J34=>! @H323T! 231J!501JH<Y<1J@31!53K3H34=! :01J31!?T310K!50123?<! T<3>31! 231J! >353! ?3:3! =1K04d3T! 63@K<! 231J! >353_!B4-26$2" *$%$" 1$&2!" 01$2-%" 5-)6-)$*" 1-5&/" ;-0$%" 4&" 0-)&/-1&?2" 4$2" 1-5&/" 1$,5$%" 4&"$0/-1&?2C8!

R F0:<3! H<@<5! F0?T04! :3?3K! 501Z0T3>@31! ^01I5013! Y04d34=3>=123! @0904T31J31!B5)&6/%2-##C!?T310K!:31!J043@!<1=@!:34=!?T310K!?3:3!I4Y=K123!B0)?6)$4-C)-%)?6)$4-C8!

R \<@<5! F0?T04! K=:3@! H3123! Y04T3@<! <1K<@! ?T310K7! K3?=! <1K<@! >05<3! Y01:3! 231J!501JI4Y=K!Y01:3!T3=18!

R F0:<3!H<@<5!F0?T04!:=K04Y=K@31!K3H<1!QWPe!:31!50120Y<K@31!H3123!Y04T3@<!<1K<@!?T310K!"34>8!

R QP! K3H<1! Y04=@<K1237! F0?T04! 50T<3>@31! H<@<5123! @0! >05<3! ?T310K! B"04@<4=<>!H=1JJ3! -3K<41<>7! 231J! K04353K=! >33K! =K<C! :31! 50135Y3H! H<@<5! @0K=J3A!]@<3:43K! ?04=I:0! >=:04=>! I4Y=K! ?T310K! >0Y31:=1J! :01J31! ?31J@3K! K=J3! ><5Y<!>05=532I4_!#-4-)/$2$23$A!0L!B:3T35!K3H<1!)<5=C!f!$O!B:3T35!>3K<31!,%C7!>053@=1!Z3<H!?T310K!:34=!53K3H34=7!63@K<!<1K<@!50120T0>3=@31!>3K<!?<K3431!>053@=1!T3538!!

&6;45(<8!$=501>=!.3K3!-<423!'T310K! -<5Y<!

-05=532I4!B$C!:3T35!,%!

'04=I:0!#4Y=K!B0C!:3T35!K3H<1!)<5=!

(@>01>K4=>=K3>!#4Y=K!B-C!

0LD$O!!

"04@<4=<>! P7OMV! P7LXQ! P7LPW! Q7PPL!g01<>! P7VLO! P7WQU! P7PPV! Q7PPQ!)<5=! Q7PPP! Q7PPP! P7PQV! Q7PPP!"34>! Q7ULX! Q7MMQ! P7PeO! Q7PPP!S<?=K04! U7LPO! QQ7MW! P7PXM! P7eee!-3K<41<>! e7UOV! Le7XL! P7PUX! P7eeM!%431<>! Qe7Qe! MO7VU! P7PXV! P7eeO!+0?K<1<>! OP7PV! QWO7V! P7PPe! P7eMW!'04H3K=@31! ?3:3! K3Y0TA! @09<3T=! "04@<4=<>7! I4Y=K! ?T310K! H35?=4! T=1J@3431! B1=T3=!0@>01K4=>=K3>! 501:0@3K=! 1ITCh! :31! >053@=1! Z3<H! :34=! "3K3H34=7! ?04=I:0! ?T310K!>053@=1!Y0>348!!

R \<@<5! F0?T04! :3?3K! :=J<13@31! <1K<@! 501JJ35Y34@31! 5I:0T! K3K3! ><423! :01J31!Y01K<@! :31!&'&($") (*+$%!,! 231J! K0?3K! :34=! I4Y=K! ?T310K7! 135<1! K=:3@!50123K3@31!<@<431! I4Y=K! 231J! >0Y0134123! B<@<431! K=:3@! :3T35!@=TI50K047! 135<1!:3T35! Z343@!

Page 4: PENGANTAR MEKANIKA BENDA LANGIT

40T3K=^! )<5=R"3K3H34=C7! @34013! F0?T04! 501J<@<4! :01J31! 50KI:0! K4=31J<T3>=! 231J!501JJ<13@31!I4Y=K!)<5=!>0Y3J3=!Y3>=>!K31?3!501J0K3H<=!<@<431!I4Y=K!)<5=8!

R '01J<@<431!Z343@!)<5=R"3K3H34=!:01J31!50KI:0!K4=31J<T3>=!>09343!T31J><1J!:3?3K!:=T3@<@31! Z=@3! :3?3K! :=<@<4! ><:<K! ?343T3@>!"3K3H34=7! 135<1! @34013! K04T3T<! Y0>34!:31!K04T3T<!K0431J7!H3T!=1=!><T=K!:=T3@<@318!

R -0Y0T<5! ?04K01J3H31! 3Y3:! LP7! ?01J<@<431! 1=T3=! ,%! :=T3@<@31! :01J31! 50KI:0!K4=31J<T3>=! ?3:3! ?T310K!"04@<4=<>! :31! g01<>! @0K=@3!501J3T35=! K431>=K! B[%)$2#&%" >"8-2?,-2$"*-%&*$"01$2-%"&28-)&?)"5-)$4$"4&"$2%$)$".$%$/$)&"4$2"+',&9":$)&"0-),'*$$2"+',&7"01$2-%"$*$2"2$,0$*"#-5$6$&"%&%&*"/&%$,"3$26",-1&2%$#&"1&26*$)$2".$%$/$)&C8!

R F34013!T353123!K431>=K!K04Z3:=!:3?3K!:=<@<4!>09343!3@<43K7!53@3!?I>=>=!?T310K!:3?3K!:=K01K<@31! :01J31! K0?3K8! F05<:=31! :01J31! J0I50K4=! >0:04H313! :3?3K! :=K01K<@31!Z343@!?T310K!:01J31!501JJ3Y<1J@31!?01J353K31!:34=!Y0Y043?3!TI@3>=!:=!)<5=8!

R "0KI:0! 5I:041! <1K<@! 50101K<@31! 1=T3=! ,%! Y<@31! :01J31! 50KI:0! K4=31J<T3>=7!135<1!501JJ<13@31!K0@1ITIJ=!43:34!B231J!504<?3@31!J0TI5Y31J!0T0@K4I53J10K=@!?3:3!^40@<01>=!43:=IC7!:=!5313!>=123T!43:34!231J!:=K05Y3@@31!@0!><3K<!?T310K!3@31!:=?31K<T@31! @05Y3T=! @0! )<5=! BK=:3@! :3?3K! :=K05Y3@@31! @0!"3K3H34=! @34013! 3@31!:=>043?!:31!K=:3@!:=?31K<T@31C8!!

R $01J31! ?31K<T31! 43:34! :34=! g01<>! @0K=@3! Y043:3! ?3:3! Z343@! K04:0@3K! @0! )<5=7!:=?04IT0H!1=T3=!Q!,%!f!QXe8UeV8MVP!@5!3K3<!:=Y<T3K@31!>0Y3J3=!QUP!Z<K3!@58!!!

++0()"*%#+*%(#"=&>#(!

R F0K=J3! H<@<5! F0?T04! :=?04IT0H! >09343! 05?=4=>7! 23=K<! H3123! Y04:3>34@31! 313T=>=>!:3K3!?01J353K317!K31?3!50T=Y3K@31!K0I4=!3K3<!5I:0T!53K053K=>8!

R [*>339!+06KI1!BQWXL!N!QVLVC!:01J31!@0K=J3!H<@<5!J043@123!:31!H<@<5!J43d=K3>=7!505Y04=@31! T31:3>31! K0I40K=>! 3K3>! J043@! ?T310K! 501J0T=T=1J=! "3K3H34=7! :31!501Z363Y!?04K312331!:4?@6A6!?T310K!Y04J043@!501J=@<K=!\<@<5!F0?T048!

R \<@<5!?04K353!+06KI1!K01K31J!J043@!50123K3@31A!]>0K=3?!Y01:3!231J!:=35!3@31!K0K3?!:=357!:31!Y01:3!231J!Y04J043@!:01J31!@090?3K31!@I1>K31!3@31!K0K3?!Y04J043@!:01J31! @090?3K31! @I1>K31! @09<3T=! Z=@3! :=<Y3H! IT0H! J323! 231J! Y0@04Z3! ?3:3! Y01:3!K04>0Y<K_!

R \<@<5!@0:<3!+06KI1!K01K31J!J043@!50123K3@31A!]S=@3!40><TK31!J323!D!Y0@04Z3!?3:3!Y01:3!Y0453>>3!,7!53@3!Y01:3! K04>0Y<K!3@31!:=?0490?3K!>0Y31:=1J!:01J31!D!:31!Y04Y31:=1J!K04Y3T=@!:01J31!,8!,K3<!$!f!DD,_8!

R \<@<5!@0K=J3!+06KI1! K01K31J!J043@!50123K3@31A! ]-0K=3?!3@>=! 3@31!505<19<T@31!403@>=!231J!Y0>34123!>353!135<1!?3:3!343H!231J!Y04T363131_8!

R \<@<5!J43d=K3>=!+06KI1!50123K3@31A!]-0K=3?!Y01:3!3@31!>0T3T<!50134=@!Y01:3!T3=1!:01J31! J323! 231J! Y0>34123! >0Y31:=1J! :01J31! ?04@3T=31! 53>>3! @0:<3! Y01:3! :31!Y04Y31:=1J!K04Y3T=@!:01J31!@<3:43K!Z343@!@0:<3!Y01:38!,K3<!DJ!f!E,Q,LD)L!:01J31!E!f!W7WV!i!QPRQQ!+5L@JRL!3:3T3H!%-%$0$2"6)$A&%$#&_8!

R [E323! K34=@!J43d=K3>=!31K343!"3K3H34=!:31!?T310K!231J!1=T3=123!Y04Y31:=1J! K04Y3T=@!:01J31!@<3:43K! Z343@!50120Y3Y@31!?T310K!Y04J043@!:3T35!I4Y=K! 0T=?>7! :31!@34013!53>>3!"3K3H34=! T0Y=H! Y0>34! :34=!53>>3! ?T310K7!53@3!"3K3H34=! T0Y=H!501:I5=13>=!:3T35!=1K043@>=!J43d=K3>=8!

R $3T35! J043@123!501J0T=T=1J=! "3K3H34=7! ?T310K! Y<@31!501J0T=T=1J=! ?<>3K! "3K3H34=7!50T3=1@31! Y04>353R>353! "3K3H34=! @0:<3123! 501J0T=T=1J=! ABC67( :6CC6! >=>K05!"3K3H34=R?T310K8!+35<1!@34013!53>>3!"3K3H34=! 231J! Z3<H! T0Y=H!Y0>34!:34=! ?T310K7!53@3!?<>3K!53>>3!@0:<3!Y01:3!Y043:3!:0@3K!:01J31!?<>3K!"3K3H34=8!

Page 5: PENGANTAR MEKANIKA BENDA LANGIT

!$6:;63(D8!'I>=>=!?<>3K!53>>3!B901K04!I^!53>>C!5=4=?!:01J31!?I>=>=!K=K=@!K<5?<!3J34!Z<1J@3KR!(((((((((((((((((((((((((Z<1J@=K!>0K=5Y31J!B3C!Z=@3!53>>3!@0:<3!Y01:3!>353h!BYC!Z=@3!53>>3!Y01:3!:=!@3131!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!T0Y=H!Y0>34!:34=!231J!:=!@=4=!!

R \<@<5!F0?T04!?04K353!K01K31J!J043@!?T310K!K04@I40@>=!>0Y3J3=A!]?T310K!501J0T=T=1J=!"3K3H34=!:3T35!I4Y=K!Y04Y01K<@!0TT=?>7!:=!5313!?<>3K!53>>3!>=>K05!?T310KR"3K3H34=!Y043:3!:=!>3T3H!>3K<!K=K=@!^I@<>_8!

R S=@3!:<3!Y01:3!T31J=K!231J!>3T=1J!501JI4Y=K!Y0453>>3!>3537!53@3!I4Y=K!@0:<3!Y01:3!Y04Y01K<@! 0TT=?>! =:01K=@! :31! ?<>3K! 53>>3! Y043:3! :=! K=K=@! ^I@<>! 231J! K04T0K3@! :=!K01J3HRK01J3H!Z343@!@0:<3!Y01:38!

R S=@3!:<3!Y01:3!T31J=K!231J!>3T=1J!501JI4Y=K!Y0453>>3!Y0:37!53@3!I4Y=K!@0:<3!Y01:3!K0K3?!Y04Y01K<@!0TT=?>!:01J31!0@>01K4=>=K3>!>353!:31!Y04Y3J=! >3K<! K=K=@! ^I@<>!231J!>3537!135<1!Y01:3!Y0453>>3! T0Y=H!Y0>34!505=T=@=! >05=!532I4!231J! T0Y=H!?01:0@!:31!Y04J043@!T0Y=H!T35Y3K8!

!$6:;63(E8!)01K<@!T=1K3>31!I4Y=K!:<3!Y01:3!231J!>3T=1J!501JI4Y=K!:31!?I>=>=!?<>3K!53>>3!B3C!@0:<3!!!!!!!!!!!!!!!!!!!!!!!!!Y01:3!Y0453>>3!>353h!BYC!Y01:3!:=!@3131!:<3!@3T=!T0Y=H!Y0>34!:34=!Y01:3!:=!@=4=!!

R [FI40@>=! +06KI1! ?3:3! H<@<5!F0?T04! ?04K353! >0K343! :01J31! @I40@>=! F0?T04! ?3:3!5I:0T!`I?041=9<>8!

Page 6: PENGANTAR MEKANIKA BENDA LANGIT

R $34=! H<@<5!@0:<3!+06KI1! K01K31J! J043@! :31! H<@<5! J43d=K3>=7! >04K3!501J31JJ3?!Y3H63! I4Y=K! ?T310K! Y04Y01K<@! T=1J@3431! >05?<413! B=1J3KA! Y01:3! 231J! Y04J043@!50T=1J@34! 501J3T35=! ?0490?3K31! >01K4=?0K3T! $>! f! ALD)C! 53@3! D>! f! DJ! >0H=1JJ3!:=?04IT0HA!

0L!B:3T35!K3H<1!)<5=C!f!$O!B:3T35!,%C!D!.KIK3T!B:3T35!53>>3!"3K3H34=C!:01J31!.KIK3T!3:3T3H!Z<5T3H31!53>>3!@0:<3!Y01:3!T31J=K8!

R '04>35331! K04>0Y<K! 504<?3@31! @I40@>=! +06KI1! K04H3:3?! H<@<5! F0?T04! @0K=J3!K01K31J! J043@! ?T310K7! 135<1! @34013! 53>>3! "3K3H34=! Z3<H! T0Y=H! Y0>34! :34=! 53>>3!?T310K7!53@3!.KIK3T! Y041=T3=! H35?=4! >353!:01J31!53>>3!"3K3H34=7! >0H=1JJ3! Y01K<@!363T!H<@<5!F0?T04!@0K=J3!K0K3?!9I9I@!:01J31!H3>=T!IY>04d3>=!.29HI!)43H08!

R \<@<5! @0K=J3! F0?T04! 231J! :=@I40@>=! +06KI1! =1=! Y04T3@<! <1K<@! >05Y3431J! >=>K05!231J!Y043:3!:=!K3K3!><423!3K3<!:=!T<34!K3K3!><4238!

R $34=! ?04>35331! :=! 3K3>! :3?3K! ?<T3! :=?04IT0H! 1=T3=! @090?3K31! ?T310K! Y04J043@!501J0T=T=1J=! "3K3H34=! v = GM / r 7! :01J31!.! 3:3T3H!53>>3! Y01:3! 231J! :=@0T=T=1J=!B"3K3H34=C8!%1K<@!)<5=!53@3!:=?04IT0H!1=T3=!OP!@5D>8!

R S=@3! @090?3K31! =1=! 505Y0>34! 2 @3T=123! BQ7XQXj! @3T=123C7! 23=K<! vmin = 2GM / r 7!53@3!?T310K!:3?3K!50TITI>@31!:=4=!:34=!K34=@31!J43d=K3>=!"3K3H34=7!>0H=1JJ3!:=>0Y<K!>0Y3J3=!F4G4A676?( 5H5HC7! 23=K<! @090?3K31!5=1=5<5! 3J34! Y01:3! :3?3K!50TITI>@31!:=4=!:34=!K34=@31!J43d=K3>=!Y01:3!T3=1123!231J!T0Y=H!53>>=d08!'04>35331!=1=!Y04T3@<!Z<J3!<1K<@!>=>K05!:<3!Y01:3!T3=11238!!

!!+++0(/>%.I/>%.(.%&+1%#(!F04Z3@31!>I3TR>I3T!Y04=@<Kk!Q8 '01J353K31!.29HI!)43H0!K04H3:3?!Y=1K31J!:31!?T310K!3@<43K!H=1JJ3!Q!501=K!Y<><4!

BQcC8!)043?3!Y0>34! Z343@!231J!:=H3>=T@31!><:<K! =1=!:=Y31:=1J@31! Z343@!B3C!)<T31!BYC!"3K3H34=7!B9C!-3K<41<>!BM7U!,%Cl!

L8 .04H3:3?!?01J353K!:=!)<5=7!Y043?3!><:<K!231J!:=Y01K<@!"34>!231J!Y04J043@!40T3K=^!K04H3:3?! Y=1K31J! LX! Z35! >0K0T3H! @0:<3! ?T310K! Y043:3! ?3:3! Z343@! K04:0@3K123l!,1JJ3?!I4Y=K!)<5=!:31!"34>!Y04<?3! T=1J@3431!:01J31! Z0Z34=! Q!,%!:31!Q7U!,%!:31!Y043:3!?3:3!Y=:31J!231J!>3538!,?3@3H!J043@123!0)?6)$4-!3K3<!)-%)?6)$4-l!

O8 -0Y<3H!3>K04I=:!505=T=@=! Z343@!?04=H0T=I1!L!,%!:31! Z343@!3?H0T=I1!X!,%8!.01K<@31!><5Y<!>05=532I4!I4Y=K1237!0@>01K4=>=K3>!:31!?04=I:0123k!

X8 -0Y<3H! 63H313! 4<31JR31J@3>3! 505=T=@=! I4Y=K! 231J! 50120405?0K! I4Y=K! )<5=! :=!3?H0T=I1!:31!50120405?0K!!I4Y=K!g01<>!:=!?04=H0T=I18!"=>3T!)<5=!:31!g01<>!Y043:3!:=! ?I>=>=! 231J! K0?3K! :31! >33K! 231J! K0?3K7! Y043?3! 63@K<! 231J! :=Y<K<H@31! 63H313!K04>0Y<K!<1K<@!Y04J043@!:34=!)<5=!@0!g01<>l!

U8 FI50K!\3TT02!505=T=@=! Z343@!?04=H0T=I1!P7W!,%!:31!?04=I:0!I4Y=K!VW! K3H<18!)043?3!Z343@!3?H0T=I1!@I50K!\3TT02!:34=!53K3H34=l!

W8 )043?3! Y0>34! ?343T3@>! 53@>=5<5! 231J! 5<1J@=1! :34=! "04@<4=<>! @0K=@3! K04Z3:=!K431>=K!53K3H34=!:=T=H3K!:34=!@0:<3!<Z<1J!J34=>!:3>34!B5$#-1&2-C!>0?31Z31J!OPPP!@5!231J!3:3!:=!)<5=l!

V8 )043?3! T353! >0Y<3H! >=123T! 43:34!50120T0>3=@31! T=1K3>31! YIT3@RY3T=@! 31K343! )<5=!:31!"34>!@0K=@3!@0:<3!?T310K!K04?=>3H!>0Z3<H!P7V!,%l!

M8 `3TT=>KI!501JI4Y=K!S<?=K04!?3:3!Z343@!Q7MM!Z<K3!@58!'04=I:0!I4Y=K!501J0T=T=1J=!S<?=K04!3:3T3H! QW7V! H34=8! )043?3! 53>>3! S<?=K04l! B31JJ3?! 53>>3! `3TT=>KI! :3?3K! :=3Y3=@31!K04H3:3?!53>>3!S<?=K04C!

Page 7: PENGANTAR MEKANIKA BENDA LANGIT

e8 "3K3H34=!Y04J043@!501J0T=T=1J=!?<>3K!J3T3@>=!)=53>3@K=!231J!Y04Z343@!LW!4=Y<!K3H<1!93H323! :3T35! I4Y=K! 231J! H35?=4! T=1J@34318! S=@3! @0T3Z<31! I4Y=K! >0@=K34! LLP! @5D>7!K01K<@31!?04=I:0!I4Y=K!"3K3H34=!:31!Y0>34123!?0490?3K31!>01K4=?0K3T!:31!J<13@31!H3>=T123!<1K<@!505?04@=43@31!53>>3!J3T3@>=!@=K38!

QP8 '3:3!Z343@!Y043?3!:34=!"3K3H34=!>0Y<3H!?T310K!505=T=@=!?04=I:0!I4Y=K!>0Y0>34!Q!Z<K3!K3H<1l!)043?3!Y0>34!?04=I:0123!Z=@3!Z343@123!Q!K3H<1!93H323l!

QQ8 '0490?3K31!J43d=K3>=!:=!?045<@331!)<5=!:=@0K3H<=! >0Y0>34!e7M!5D>L8!)043?3!Y0>34!?0490?3K31! J43d=K3>=! ?3:3! @0K=1JJ=31! B3C! QPP! @5! BYC! QPPP! @5! B9C! QPPPP! @5l!B,1JJ3?!Z0Z34=!)<5=!>0Y0>34!WXPP!@5C!

QL8 )043?3! @0T3Z<31!63H313! 4<31JR31J@3>3! 231J!501JI4Y=K! :3T35! T=1K3>31!50T=1J@34!?3:3! >0K=3?!@0K=1JJ=31! 231J!:=>0Y<K!:=! >I3T! >0Y0T<5123l!)043?3!Y0>34!?0490?3K31!>01K4=?0K3T!:=Y31:=1J@31!?0490?3K31!J43d=K3>=123l!

QO8 S=@3! 53>>3! )<T31! >0Y0>34! V7X! i! QPLL! @J! :31! Z0Z34=123! QVPP! @57! Y043?3! @0T3Z<31!63H313! 4<31JR31J@3>3! 231J! Y04J043@! :3T35! I4Y=K! 50T=1J@34! K0?3K! :=! 3K3>!?045<@331!Y<T31l!)043?3!Y0>34!@0T3Z<31!TITI>!:34=!)<T31l!

!!!

!