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F?G 15=55@14=55 A0+BC J%9+ EEEEEEEEEE
>:
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R 65C5 9K .8#&O
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b/c
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R L#0- #< 65C5 .) &+$KC M* 8%< O-$
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bOc
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A newly discovered comet (Balley’s Comet) is in an elliptical orbit around the Sun(which has mass 1.99 x 1030 kg) with orbital period 162 years. Its distance of closest
approach to the Sun is 8.98 x 1010
m where its speed is observed to be 54.1 km/s. F8-
)%
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R /&+.9 L#*8 )%
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7+8
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!024567 ) 89* !2%./$:
R /&+.9 +B L++O L#*8 )%
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b/c
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!024567 > 8(* !2%./$:
R ;$#B+0) O#
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@20715A B"66/3 !"#$%&$ (,* A.C ()* @%.A5 DEA7
1, >+*#+$ L#*8 .+$+*#+$ L#*8 .+$+*#+$=
a x = 0 a
y = !g g = 9.80m/s
2
P$#B+0) 7#0.;&%0 >+*#+$
arad
=
v2
R=
4! 2 R
T 2
v =2! R
T
G-&%*#N- i-&+.#*:!
vP/ A
=
!
vP/ B
+
!
v B/ A
S-L*+$g< H%L<!
F =m!
a!!
F A"on" B = "
!
F B"on" A
j;%O0%*#. B+0);&%
ax2+bx+ c = 0 ! x =
"b± b2" 4ac
2a"0#.*#+$%& "+0.-< f K = µ K n
f S ! µ S n
?+093 '$-0K:3 %$O A+L-0
W =!
F •!
s = Fs cos! !W =!
F •d !
l "
K =1
2mv
2W
tot = #K
P =dW
dt =
!
F •!
v
W = !"U
K i +
U i +
W other =
K f +
U f
F grav = mg U grav = mgy
F spring = !kx U spring =
1
2kx2
F x = !
#U
# x
>+)-$*;) %$O M)I;&
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G+*%*#+$%& >+*#+$
! =d "
dt # =
d !
dt
vtan
= r! atan
= r#
arad
= r! 2=v2
r
I = miri
2 I P = I
CM + Md
2!
K =1
2 I
cm! 2+1
2 Mv
cm
2
I thin!rod !end =
ML2
3 I
thin!rod !middle = ML
2
12
I hoop = MR2
I disk = MR2
2 I sphere =
2 MR2
5
!
"
=
!
r #!
F = d
"
Ldt
" = rF sin$ = r%F = rF %
" & = I '
P = "( "
L =!
r # !
p = I "
( L = rpsin$
Gravity :
F g =
Gm1m2
r2
G = 6.67 "10#11 N m2 /kg2
vorbital =GM
r
Kepler's 3rd Law : T =2$ a3 / 2
GM
a = semimajor axis
U = #Gm1m2
r RSchwartzchild =
2GM
c2
Astronomical Data
MEarth = 5.97 "1024 kg
R Earth = 6.37 "106
m
MSun =1.99 "1030
kg
RSun = 6.96 "108 m
Mean Earth #Sun Distance =1.50 "1011 m
k