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6.17
From
Example 6.10.1 …
()
1
2
2
2
2
1s
i
qq
d
d
ε
=+ −
n
φ
where
e
v
v
q
=
and
e
r
d
a
=
are dimensionless ratios of the comet’s speed and distance from the Sun in terms of the
Earth’s orbital speed and radius, respectively (
q
and
d
are the same as the factors
V
and
R
in Example 6.10.1).
is the angle between the comet’s orbital velocity and direction
vector towards the Sun (see Figure 6.10.1).
The orbit is hyperbolic, parabolic, or elliptic as
ε
is > , = , or < 1 …
i.e., as
2
2
q
R
−
is > , = , or < 0.
2
2
q
R
−
v
v
is > , = , or < 0 as
is > , = , or < 2.
2
qd
6.18
Since
l
is constant,
v
occurs at
r
and
v
occurs at
, i.e.
and
and form the constancy of
l
…
max
D
min
11
vr
1
r
max
v
=
D
min
1
v
=
=
DD
2
min
max
1
1
r
vv
v
v
v
r
==
D
2
1
k
rv
m
=+
(See Example 6.5.4)
From equation 6.6.5 …
2
2
ka
GM
a
m
π
τ
:
2
min
max
1
1
2
a
a
r
+
=⋅
From equation 6.5.21a&b …
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
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