Geoscience Reference
In-Depth Information
Fig. 9.8
An imaginary planet
and the solar system
m
1
m
2
m
3
r
3
r
2
r
1
m
o
r
o
m
i
r
i
r
s
CMI
m
s
The equations to find relevant parameters are given as
m
s
r
s
2
D
m
1
r
1
2
C
m
2
r
2
2
CC
m
i
r
i
2
(9.20)
m
o
r
o
2
D
m
1
r
1
2
C
m
2
r
2
2
CC
m
i
r
i
2
(9.21)
m
o
D
m
1
C
m
2
CC
m
i
:
(9.22)
d
i
D
r
i
C
r
s
(9.23)
Some manipulations of the above equations provide the distance
r
s
:
.m
s
m
o
/r
s
2
C
2C
1
r
s
C
2
D
0;
(9.24)
where
C
1
,
C
2
are constants consisting of observed quantities:
C
1
D
m
1
d
1
C
m
2
d
2
CC
m
i
d
i
(9.25)
C
2
D
m
1
d
1
2
C
m
2
d
2
2
CC
m
i
d
i
2
(9.26)
Using the numbers in Table
9.1
, the distance
r
s
is calculated,
r
s
D
4.921
10
10
m,
and using Eqs.
9.21
,
9.22
,and
9.23
, the distance
r
o
is calculated,
r
o
D
1.344
10
12
m.
The imaginary planet has a mass
m
o
D
2.668
10
27
kg from Eq.
9.22
.Tofindthe
radius of the imaginary planet, weighted mass densities are considered as
D
1
m
1
m
o
C
2
m
2
m
o
CC
i
m
i
o
m
o
:
(9.27)
From the mass and the density given by Eqs.
9.22
and
9.27
, the radius of the
imaginary planet is calculated,
R
o
D
8.057
10
7
m with
0
D
1.218 g/cm
3
,where
the imaginary planet is assumed to be a sphere having an average mass density
given by Eq.
9.27
.
Now calculate the spin period of the Sun using Eq.
9.12
. As the numbers are put
into the appropriate variables in Eq.
9.12
,
T
s
D
T
o
/232.528. To find the spin period
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