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!"#$%&$ ()*+(,* 

"#$%& '(%)#$%*#+$

,-.-)/-0 123 4516

78-.9 :+;0 ?" 15=55@11=55 A0+BC D-#$-: EEEEEEEEEE

FG 14=55@1=65 A0+BC H#; EEEEEEEEEE

FG 15=65@14=55 A0+BC F8+)?" 14=55@1=55 A0+BC H#I-&-< EEEEEEEEEE

>?" 11=55@14=55 A0+BC H#I-&-< EEEEEEEEEE

F?G 15=55@14=55 A0+BC J%9+ EEEEEEEEEE

>:

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!024567 ( 89* !2%./$:

R 65C5 9K .8#&O

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b/c 

8(9 !2%./$: RB*-0 *8- /%&& #< .%;K8*3 L8%* #< *8- %$K;&%0

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!024567 9 89* !2%./$:

R L#0- #< 65C5 .) &+$KC M* 8%< O-$

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bOc 

8) !2%./$: R* *#)- ! ̀ 5 *8- L#0- #< $+* )+N#$KC F8- *+I K0%I8

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!024567 < 89* !2%./$:

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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b.c 

8) =2%./$: d%&&-: #< +/

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!024567 , 89* !2%./$:

R /&+.9 L#*8 )%

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7+8 

8; !2%./$: MB *8- /&+.9 0-

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!024567 ) 89* !2%./$:

R /&+.9 +B L++O L#*8 )%

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b/c 

8> !2%./$: D+L );.8 *#)- O+-< #* *%9- B+0 *8- /&+.9 *+ 0-*;0$ *+ #*<

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!024567 > 8(* !2%./$:

R ;$#B+0) O#

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!024567 ? 8(* !2%./$:

T+; %0- *0:#$K *+ 0%#

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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