Unformatted text preview: ar toRasra rcll
dV dM
M
=V ( # )( # )( + l! # + l! # ) #
+ l! + l! + l! rel
(All doLtid .x6 dtrrc to thtuth
tt .mtd hf
th. oN's dr do 'tN.)
v
v=
a= dt dt 2 v
a=
R
uniform circular motion: C9.6 Now we arein a pGition to answertheq
is th€total kinetic eneBy of an obiecttha
as t r t i o n
I
l r a n s l a t i o nn d R oa aclling obiect)?t tu.ns out tlEt the o
i dv
v2
ˆ
ˆ
a=
Now we arein a pGition to answertv −questionraisedin s€ctionC9.li w
he r
dt
R
ntonuniforminetic eneBy of an obiectthat is both moving ard rctating (s
circular motion:
is h€total k asa rclling obiect)?t tu.ns out tlEt the obicrt's total kineticenergyis ius
I 1
v x (t ) = ax t + v0 x x (t ) = ax t 2 + v0 x t + x0
2
Ffriction = µ Fnormal
1
Fdrag = C ρ Av 2
2 v!(t ) = v (t ) − β (t ) Galilean velocity transformation a!(t ) = a (t ) − A(t ) Galilean acceleration transformation ma! = −mA + F1 + F2 + … Fictitious forces
dA L
Kepler’s second law: dt = 2m = constant
4π 2
GM
2
TP roblems a 3 also V =
=
Nepler’s tS olvino rbit
13.4
O
K
hird law:
GM
R 233 TsbleN 13.1 T ableo i u seful uations for solvin orbit Item
Definitions of E and L 2E
:Dm Calculation o f e ccentricity e2:,+#GlG) Item Elliptical ase
C Hvperbolicc ase 2E GM 2E GM m a m a Connection b etween a a nd E
Location o f e xtremes 2GM , and L : r asin
m rr:a(le)
rg llJ :?J) rr:a(e\) E:
L:
Gt?t:
M:
r:
?:
d:
a:
/c: rl:a(l+e) r/:
Other useful relations ,':Hot
(Kepler'st hird l aw) tang: J V :*,(il,r
T:
0: t otal s ysteme nergy
system angular momentum
gravitational constant
satellitemass
p rimary m ass
distancefrom primary
satellitespeedat that point
angle between i and6
semimaioraxis for ellipse,
analogousfor hyperbola
f
d istance rom p rimary t o
closestpoint on the orbit
distancefrom primary to
farthest point on the orbit
o rbital p eriod
angle of asymptotes N13.4 Solving rbit Problems
O
The point of the last sectionis that knowing the values of 2E/m andL/m for
a system involving a satellite orbiting a massiveprimary allows us to calculate a and e, which in turn completely specify the shapeof the satellite'sorbit.
Table N13.1 summari...
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 Spring '08
 cramer
 Magnetism, Trigraph, dt, IMR, vide dle disk

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