# Sans the lone satellite Luna, our planet Earth had cleared debris and other close by space orbiters. How do you find the volume of this cleared neighborhood around the Earth's orbit?

Sep 24, 2016

As of now, the maximum is
$= 4.72 X {10}^{18} k {m}^{3}$

#### Explanation:

Meteoroids that become meteors in the Earth's atmosphere and

meteorites, after hitting Earth's surface, did not have orbits around

the Sun. Yet, their sources , asteroids and comets orbit the Sun. The

elongation of these orbits make their periods long. However, quite

many of them come close to us, near the respective perihelion.

When they are very close, they are included in the list of Near Earth

Objects (NEO). Even here, the Jet Propulsion Laboratory findings

(http://geo.jpl.nasa.gov) showed just one asteroid (2016 RB1) came

as NEO, at about 40000 km from the Earth. Another (2015 TB 145 )

came a little beyond Moon's maximum apogee distance of

405400 km.

In view of all these findings, it is reasonable to admit that the Earth

is yet to clear some NEOs like the asteroid (2016 RB1) that had

come as close as 40000 km to the Earth. For this limit, the

maximum volume of the cleared neighborhood is that of a torus of

This volume is

$2 {\pi}^{2} \left(1 A U\right) {\left(40000\right)}^{2}$

$= 2 {\pi}^{2} R {r}^{2} = 2 {\left(3.14\right)}^{2} \left(1.496 X {10}^{8}\right) {\left(4 X {10}^{4}\right)}^{2} k {m}^{3.}$

$= 4.72 X {10}^{18} k {m}^{3}$

Upon further visits of asteroids to closer than 40000 km, this torus

might become narrower in cross section.

Disambiguation note:

For planets, stars and galactic centers. there is an edge in the form

of a torus within which space bodies that enter into the torus would

be drawn ( attracted ) into the fold of the center of attraction. These

objects might disintegrate before merging into the source of

attraction.

For the star Sun, this torus cross-sectional radius is the distance of

Mercury from the Sun, 0.38 AU, Its central radius is the Milky-Way-

Sun arm that is nearly 27000 light years.long. Here, the

disintegration of comets, like Love Joy C/2011W3 in Dec 2011, is not

included, in view of the weak structure of such comets that loose

mass or disintegrate, at high speeds, near perihelion.

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