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?

1 Answer
Sep 21, 2016

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](https://socratic.org/astronomy/our-solar-system/the-

earth)'s and Moon's radii are 4-sd approximations, these related

approximations are restricted to 4-sd