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31. (a) Let
r
be the radius and
ρ
be the density of the particle. Since its volume is (4
π/
3)
r
3
, its mass is
m
=(4
π/
3)
ρr
3
.L
e
t
R
be the distance from the Sun to the particle and let
M
be the mass of the
Sun. Then, the gravitational force of attraction of the Sun on the particle has magnitude
F
g
=
GMm
R
2
=
4
πGMρr
3
3
R
2
.
If
P
is the power output of the Sun, then at the position of the particle, the radiation intensity is
I
=
P/
4
πR
2
, and since the particle is perfectly absorbing, the radiation pressure on it is
p
r
=
I
c
=
P
4
πR
2
c
.
All of the radiation that passes through a circle of radius
r
and area
A
=
πr
2
, perpendicular to the
direction of propagation, is absorbed by the particle, so the force of the radiation on the particle
has magnitude
F
r
=
p
r
A
=
πPr
2
4
πR
2
c
=
Pr
2
4
R
2
c
.
The force is radially outward from the Sun. Notice that both the force of gravity and the force
of the radiation are inversely proportional to
R
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Force, Mass

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