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where
R
is the radius of the particle, and
2
AR
π
=
is the crosssectional area. On the other
hand, the gravitational force on the particle is given by Newton’s law of gravitation (Eq.
131):
33
22
2
(4
/3)
4
3
SS
S
g
GM m
GM
R
GM
R
F
rr
r
ρ
ππ
==
=
,
where
3
mR
ρπ
=
is the mass of the particle. When the two forces balance, the
particle travels in a straight path. The condition that
rg
FF
=
implies
23
4
43
PR
GM R
rc
r
=
,
which can be solved to give
26
83
3
1
1
3
2
3
0
7
3
3(3.9 10
W)
16
16 (3 10 m/s)(3.5 10 kg/m )(6.67 10
m /kg s )(1.99 10 kg)
1.7 10 m .
S
S
P
R
cGM
πρ
−
−
×
××
×
⋅
×
=×
(b) Since
g
F
varies with
3
R
and
r
F
varies with
2
,
R
if the radius
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Force, Light, Radiation

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