Geoscience Reference
In-Depth Information
Circular disk
Let the thickness b of the cylinder go to zero such that the product
κ = b
(3-17)
remains finite. The quantity κ may then be considered as the surface density
with which matter is concentrated on the surface of a circle of radius a .We
need potential and attraction for an exterior point. By setting
= κ
b
(3-18)
in (3-9) and (3-11) and then letting b
0, we get by well-known methods
of the calculus
U e =2 πGκ a 2 + c 2
c ,
A e =2 πGκ 1
.
(3-19)
c
a 2 + c 2
Sectors and compartments
For a sector of radius a and angle
α = 2 π
n
,
(3-20)
we must divide the above formulas by n . For a compartment subtending the
same angle and bounded by the radii a 1 and a 2 (Fig. 3.4), we get, in an
obvious notation,
n U ( a 2 ) − U ( a 1 ) ,
A = 1
U = 1
(3-21)
n A ( a 2 )
A ( a 1 ) .
P
®
a= 1
a= 2
Fig. 3.4. Template compartment
Search WWH ::




Custom Search