# 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?

Sep 21, 2016

$120100000$ 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