Average distance among pieces of space debris in low earth orbit?

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Discussion Overview

The discussion centers around estimating the average distance between pieces of space debris in low Earth orbit, considering the large number of debris pieces and their distribution in a specified altitude range. Participants explore various methods of calculation and assumptions regarding the distribution of debris.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant notes that there are over 170 million pieces of space debris larger than 1mm in low Earth orbit and questions the average distance between them.
  • Another participant suggests a naive model assuming uniform distribution of debris, calculating the volume of a hollow sphere from 160 km to 2000 km altitude, leading to an estimated density of debris and an average distance of approximately 8.27 km.
  • A later post corrects the volume calculation using the Earth's radius, resulting in a different volume estimate of about 1.3 x 10^12 km³, which leads to a recalculated average distance of approximately 19.7 km between pieces of debris.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the average distance between debris, as different methods and assumptions lead to varying results. The discussion remains unresolved with multiple competing calculations presented.

Contextual Notes

The calculations depend on assumptions about the uniform distribution of debris and the specific altitude range considered. There are also potential discrepancies in volume calculations that could affect the final estimates.

Kevin Le
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Hello all,

I have a question about space debris.

The number of space debris in the low Earth orbit is huge.There are more than 170 million pieces of space debris which is greater than 1mm. So in the orbit of the Earth, what is the average distance between 2 pieces of space debris?
 
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Hello
A very naive way of thinking about it is to consider they're uniformly distributed in the low Earth orbit. Considering the altitude to be between 160 km and 2000 km (from wikipedia), the volume of a hollow sphere with radii equal to those numbers is 3.35 \times 10^{10} km^3. So the density is n=\frac {17 \times 10^7}{3.35 \times 10^{10}} \approx 5 \times 10^{-3} km^{-3}. Which means there is 1 debris in every 200 km^3 of the llow Earth orbit volume. Assuming those are almost in the middle of a cube with that volume, the distance between them becomes \sqrt 2 \times 5.84 km=8.27 km. Assuming other shapes and places will give different numbers but at least it tells us that distance is of the order of several kilometers.
This is very crude but is a good starting point for further work.
 
Last edited:
Latex is driving me insane - sorry.
Volume recalculation --
with r(Earth)=6371km
r1 = r(Earth) + 160 == 6531
r2 = r(Earth) + 2000 == 8371

V = ( 8371^3 - 6531^3) * 4.188 ~~ 1289960242829 ( 1.3 x 10^12) km^3
 
Last edited:
jim mcnamara said:
Latex is driving me insane - sorry.
Volume recalculation --
with r(Earth)=6371km
r1 = r(Earth) + 160 == 6531
r2 = r(Earth) + 2000 == 8371

V = ( 8371^3 - 6531^3) * 4.188 ~~ 1289960242829 ( 1.3 x 10^12) km^3
For 170 million pieces of debris, that would mean one piece for every 7647 km^3. To get a linear distance between pieces, we may take the cubic root, and that results in 19,7 km of distance between any two pieces. Quite close...
 

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