Assuming that the Earth is a sphere and its orbit around the Sun is a circle, how do you find the volume of the torus that is just sufficient to accommodate the Earth?
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Answer:
120100000
billion cubic lm
Explanation:
The volume of the torus is
#2pi^2(orbit radius)(Earth radius)^2 cubic units
#=2pi^2(1495987871)(6378)^2 cubic km
=
1.201
X
10
17
cubic km
=
120100000# billion cubic lm
To accommodate Luna also in this this torus tunnel, its cross
sectional radius has to be increased by the apogee distance +radius of the Moon of
Luna from the Earth.
The volume of this wider tunnel
#= =2pi^2(1495987871)(6378+405400+1737)^2 cubic km
=
5.049
X
10
20
cubic km
=
504900000
trillion cubic km.
As [the Earth]
earth)'s and Moon's radii are 4-sd approximations, these related
approximations are restricted to 4-sd
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