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1. Space Environment
Lecture 36 – Space Debris (Vol. 3)
A systems model
Professor Hugh Lewis
SESA3038 Space Environment

2. Overview of lecture 36
• In this lecture we introduce systems thinking – an approach that will
ultimately allow us to view the space debris environment as a system
• We develop the thinking, starting with a very simple example (a bath tub)
and ending with a simple model that allows us to make predictions of, and
understand, the growth of the space debris population
• As with some of the most recent lectures, many of the slides here are
highlighted with red borders, indicating their importance to the space
debris modelling topic
Space Environment – Space Debris (Vol. 3)

3. Systems thinking Space Environment – Space Debris (Vol. 3)
1. A simple bath system
Water level
Water
inflow
Water
outflow
• The water level is a STOCK
• The water inflow and water outflow are FLOWS
Water level
Water
inflow
Water
outflow
This is shown as a
“tap” here because
it controls the flow
rate. It doesn’t
represent a tap in
the real world
I’ve used a thick arrow here
because it represents a flow
of something that adds to (or
takes away) from the stock.
In this case: water
The clouds represent other
parts of the system that we
are not including (it’s the
rest of the world…)

4. Systems thinking Space Environment – Space Debris (Vol. 3)
1. A simple bath system
Water level
Water
inflow
Water
outflow
Water
level
Time
Turn on tap,
close drain:
water level rises
Turn on tap, open
drain: water level is in
dynamic equilibrium Close tap, open
drain: water
level falls

5. Systems thinking Space Environment – Space Debris (Vol. 3)
2. A more complex bath system
Water level
Water
inflow
Water
outflow
Water level
Water
inflow
Water
outflow
We add a feedback (we pass
information, not water so it
is a thin arrow). Now, the
rate of water outflow is a
function of the water level.
The greater the water level,
the faster the outflow.

6. Systems thinking Space Environment – Space Debris (Vol. 3)
2. A more complex bath system
Water
level
Time
Turn on tap,
close drain:
water level rises
Turn on tap, open
drain: water level
reaches dynamic
equilibrium (given
enough time)
Close tap, open
drain: water level
falls following an
exponential decay
Water level
Water
inflow
Water
outflow

7. Systems thinking Space Environment – Space Debris (Vol. 3)
3. Human population system
Fertility
Number of
people
Births Deaths
Mortality
This is a “balancing”
feedback: it leads to
exponential decay
This is a
“reinforcing”
feedback: it leads to
exponential growth
There are really only three types of behaviour of this system:
• Birth rate > death rate (fertility > mortality)  exponential growth
• Death rate > birth rate (mortality > fertility)  exponential decay
• Birth rate = death rate (fertility = mortality)  dynamic equilibrium
The birth rate (flow) and death rate (flow)
both depend on the number of people

8. Systems thinking Space Environment – Space Debris (Vol. 3)
4. Space debris system
Number of
orbital
objects
Collisions
Re-entries
This is a “balancing”
feedback: it leads to
exponential decay
This is a
“reinforcing”
feedback: it leads to
exponential growth
The launch rate (so there is no feedback) does
not depend on the number of objects in orbit.
However, the collision rate and the re-entry rate
both depend on the number of objects
Launches This is a combination of the bath system
and the human population system

9. Systems thinking Space Environment – Space Debris (Vol. 3)
4. Space debris system
Number of
orbital
objects (N)
Collisions Re-entries
Launches
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
= 𝐴𝐴
The inflow due to launches
does not depend on the
number of objects already
in the system
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
= 𝐶𝐶𝑁𝑁2
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
= −𝐵𝐵𝐵𝐵
The collision rate is proportional to
the square of the number of objects
(c.f. the number of football matches
in a round-robin tournament)
A, B and C are parameters
that affect the flows in this
system.

10. Systems thinking Space Environment – Space Debris (Vol. 3)
4. Space debris system
If we assume that A, B and C do not change over time then there are only three
broad behaviours for this system (same as the human population system):
• Launch rate + Collision rate > Re-entry rate  exponential growth
• Re-entry rate > Launch rate + Collision rate  exponential decay
• Launch rate + Collision rate = Re-entry rate  dynamic equilibrium
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
= 𝐴𝐴 − 𝐵𝐵𝐵𝐵 + 𝐶𝐶𝑁𝑁2

11. Overview of lecture 36
• In this lecture we introduced systems thinking – an approach that enables
us to view the space debris environment as a system and to develop a
systems model
• We developed the thinking, starting with a very simple example (a bath
tub) and ending with a simple model that would allow us to make
predictions of, and understand, the growth of the space debris population
• A final reminder that many of the slides here were highlighted with red
borders, indicating their importance to the space debris modelling topic
• There are activities associated with this lecture that used to form the basis
for computer labs for this module – more on the next slide
Space Environment – Space Debris (Vol. 3)

12. Activities
• Microsoft Excel activities available on Blackboard
– Develop your own systems model of space debris
– These are not compulsory and you can take the activities as far as you’d like
– I would allow up to an hour for each activity to ensure a good understanding
although you might complete them faster than that
Space Environment – Space Debris (Vol. 3)