Good morning, Interweb.
Good morning, Interweb.

Let's worldbuild.
Let's worldbuild.

Today, let's embark on bit of terrestrial planet moonbuilding.
Today, let's embark on bit of terrestrial planet moonbuilding.

For the purposes of this build, I'm going to classify moons by size and composition.
For the purposes of this build, I'm going to classify moons by size and composition.

Size:
Size:

All natural satellites can either be major moons or minor moons.
All natural satellites can either be major moons or minor moons.

Minor moons are small satellites that lack the necessary gravity to force them into a
Minor moons are small satellites that lack the necessary gravity to force them into a

spherical shape.
spherical shape.

These potato shaped bodies, like the moons of Mars, will be no greater than about 200-300km
These potato shaped bodies, like the moons of Mars, will be no greater than about 200-300km

in size.
in size.

Major moons, on the other hand, like our own Moon, are gravitationally rounded, as such
Major moons, on the other hand, like our own Moon, are gravitationally rounded, as such

they must have radii larger than 200-300 km.
they must have radii larger than 200-300 km.

Composition:
Composition:

Moons can be either predominantly rocky, again like our Moon, or predominantly icy like Mimas.
Moons can be either predominantly rocky, again like our Moon, or predominantly icy like Mimas.

A grid like this, although simplistic, is very useful tool when it comes to moonbuilding.
A grid like this, although simplistic, is very useful tool when it comes to moonbuilding.

So, here's a system comprised solely of terrestrial planets – three inner worlds (one in the
So, here's a system comprised solely of terrestrial planets – three inner worlds (one in the

habitable zone) and one outer planet.
habitable zone) and one outer planet.

Before we plot the location of any moons it's worth going over some general guidelines.
Before we plot the location of any moons it's worth going over some general guidelines.

1) Amount!
1) Amount!

For the most part, terrestrial planets will have very few satellites if any They may occasionally
For the most part, terrestrial planets will have very few satellites if any They may occasionally

capture a few asteroid minor moons but are unlikely to have major moons.
capture a few asteroid minor moons but are unlikely to have major moons.

2) Habitability!
2) Habitability!

Terrestrial planets intended to be habitable must have at least one major moon.
Terrestrial planets intended to be habitable must have at least one major moon.

Major moons are pretty much a prerequisite for habitability – they help moderate a
Major moons are pretty much a prerequisite for habitability – they help moderate a

planets climate by stabilizing it's axial tilt.
planets climate by stabilizing it's axial tilt.

Without a moon, Earth would look less like this and more like this.
Without a moon, Earth would look less like this and more like this.

3) Distance!
3) Distance!

Close in planets will have less moons than distant planets.
Close in planets will have less moons than distant planets.

Compare moonless Mercury with Pluto's veritable orgy of moons.
Compare moonless Mercury with Pluto's veritable orgy of moons.

Aaaand...
Aaaand...

4) Composition!
4) Composition!

Inner system moons will be predominantly rocky and outer system moons will be predominantly
Inner system moons will be predominantly rocky and outer system moons will be predominantly

icy.
icy.

So with all this in mind, I'll elect to give this guy no moons, this guy one captured asteroid
So with all this in mind, I'll elect to give this guy no moons, this guy one captured asteroid

minor moon.
minor moon.

My habitable world must get a rocky major moon (which probably formed as result of a
My habitable world must get a rocky major moon (which probably formed as result of a

collision similar to that which formed our moon) and I'll less give this distant guy...oh,
collision similar to that which formed our moon) and I'll less give this distant guy...oh,

i dunno...4 icy minor moons.
i dunno...4 icy minor moons.

Just 'cause I can.
Just 'cause I can.

Alrighty then, Moon-building engage!
Alrighty then, Moon-building engage!

As the habitable world will likely be the most important locale in the system, let's
As the habitable world will likely be the most important locale in the system, let's

begin by constructing it's moon.
begin by constructing it's moon.

First up, let's figure out what it's made of.
First up, let's figure out what it's made of.

We know it needs to be predominantly rocky so let's say it's comprised of 90% silicate
We know it needs to be predominantly rocky so let's say it's comprised of 90% silicate

rock, 9% iron and 1% water ice.
rock, 9% iron and 1% water ice.

Simply multiply the density of each material by the percentage you chose to get the overall
Simply multiply the density of each material by the percentage you chose to get the overall

density of your moon.
density of your moon.

In this case we're looking at a density of about 3.62 g/cm^3 aka 0.66 times the density
In this case we're looking at a density of about 3.62 g/cm^3 aka 0.66 times the density

of Earth.
of Earth.

Next we can use this equation to find our moon's mass and radius: M, the mass of our
Next we can use this equation to find our moon's mass and radius: M, the mass of our

moon in earth masses is equal to it's radius, in earth radii, cubed, multiplied by it's
moon in earth masses is equal to it's radius, in earth radii, cubed, multiplied by it's

density, in earth densities – which we already have.
density, in earth densities – which we already have.

Because we're building a major moon, we want to selected a radius greater than 200-300km
Because we're building a major moon, we want to selected a radius greater than 200-300km

aka 0.03 to about 0.05 Earth radii.
aka 0.03 to about 0.05 Earth radii.

Let's say our moon will be just under a third the size of earth which gives us a mass of
Let's say our moon will be just under a third the size of earth which gives us a mass of

0.018 earth masses.
0.018 earth masses.

This makes it slightly more massive than Earth's moon.
This makes it slightly more massive than Earth's moon.

Which is perfect; in order to ensure that our moon will stabilize our habitable world
Which is perfect; in order to ensure that our moon will stabilize our habitable world

we need to design it in such a way so as to be physically comparable to Earth's moon.
we need to design it in such a way so as to be physically comparable to Earth's moon.

As a quick aside, a satellites mass must always be less than or equal to the mass of the planet
As a quick aside, a satellites mass must always be less than or equal to the mass of the planet

it orbits.
it orbits.

However, the closer the two objects are in mass the more the system begins to resemble
However, the closer the two objects are in mass the more the system begins to resemble

a double planet system ala Pluto and Charon.
a double planet system ala Pluto and Charon.

A useful point for those wishing to construct double habitable planets.
A useful point for those wishing to construct double habitable planets.

Now, let's plug our mass and radius into this equation to get our moons surface gravity
Now, let's plug our mass and radius into this equation to get our moons surface gravity

relative to Earths.
relative to Earths.

In this case, it's surface gravity is 0.2 – about 23% higher than that of Earth's
In this case, it's surface gravity is 0.2 – about 23% higher than that of Earth's

moon.
moon.

So, that's the essential physical parameters take care of...let's put the moon into orbit.
So, that's the essential physical parameters take care of...let's put the moon into orbit.

To do this we're going to need the know the physical characteristics of our star and our
To do this we're going to need the know the physical characteristics of our star and our

planet.
planet.

I've covered the construction of stars and planets in previous videos so click the links
I've covered the construction of stars and planets in previous videos so click the links

on screen, or in the doobly-doo, if you need a bit of a refresher.
on screen, or in the doobly-doo, if you need a bit of a refresher.

Tl;dr my star here is identical to our sun and the planet is a slightly larger version
Tl;dr my star here is identical to our sun and the planet is a slightly larger version

of earth.
of earth.

Anyways!
Anyways!

Planets, like all astronomical objects, are encased in a sort of gravitational bubble
Planets, like all astronomical objects, are encased in a sort of gravitational bubble

we call a Hill Sphere.
we call a Hill Sphere.

Any object inside a planet's Hill Sphere will be gravitationally bound to that planet.
Any object inside a planet's Hill Sphere will be gravitationally bound to that planet.

So, by definition, satellites must be placed inside this bubble the outer limit of which
So, by definition, satellites must be placed inside this bubble the outer limit of which

is given by the equation: “a” the semi major axis of the planets orbit in AU, times
is given by the equation: “a” the semi major axis of the planets orbit in AU, times

the cubed root of the mass of the planet in Earth masses, divided by the mass of the star
the cubed root of the mass of the planet in Earth masses, divided by the mass of the star

in solar masses multiplied 235.
in solar masses multiplied 235.

Plugging the relevant numbers in gets me a value of roughly 269.
Plugging the relevant numbers in gets me a value of roughly 269.

That is, this planets Hill sphere extends out roughly 269 earth radii from the centre
That is, this planets Hill sphere extends out roughly 269 earth radii from the centre

of the planet.
of the planet.

Those who watched my “rings” video, will know that a moon cannot orbit arbitrarily
Those who watched my “rings” video, will know that a moon cannot orbit arbitrarily

close to a planet so the inner limit here is given by the Roche limit: 2.44 times the
close to a planet so the inner limit here is given by the Roche limit: 2.44 times the

radius of our planet in Earth radii, times the density of the planet divided by the density
radius of our planet in Earth radii, times the density of the planet divided by the density

of the moon to the 1/3 power.
of the moon to the 1/3 power.

Again, whack in the relevant numbers and out pops 2.65.
Again, whack in the relevant numbers and out pops 2.65.

So, the inner limit lies 2.65 earth radii from the centre of our planet.
So, the inner limit lies 2.65 earth radii from the centre of our planet.

Bit of bonus info here is that moons also have Hill Spheres and Roche limits meaning
Bit of bonus info here is that moons also have Hill Spheres and Roche limits meaning

it's theoretically possible for to construct moons of moons.
it's theoretically possible for to construct moons of moons.

Regardless...this right here is moon territory!
Regardless...this right here is moon territory!

In general, terrestrial planet moons will be what's known as regular satellites.
In general, terrestrial planet moons will be what's known as regular satellites.

That is, they will orbit relatively close to the planet on prograde, uninclined, nearly
That is, they will orbit relatively close to the planet on prograde, uninclined, nearly

circular orbits.
circular orbits.

“Close to the planet” generally means within 1/2 of the maximum value here.
“Close to the planet” generally means within 1/2 of the maximum value here.

So, I'll put my moon into orbit about 80 earth radii out.
So, I'll put my moon into orbit about 80 earth radii out.

I'll give it a prograde orbit, a very low orbital inclination, say 2 degrees, and very
I'll give it a prograde orbit, a very low orbital inclination, say 2 degrees, and very

low eccentricity - about 0.01.
low eccentricity - about 0.01.

Oh, and for those wishing to construct two separate major moons ensure that they never
Oh, and for those wishing to construct two separate major moons ensure that they never

come within 10 planetary radii of each other.
come within 10 planetary radii of each other.

Now, our moons orbital period, which will play an important role in future calendar
Now, our moons orbital period, which will play an important role in future calendar

building, will be given by: 0.0588 times the square root of the radius of the moon's orbit
building, will be given by: 0.0588 times the square root of the radius of the moon's orbit

in earth radii cubed, divided by the sum of the masses of the planet and the moon in earth
in earth radii cubed, divided by the sum of the masses of the planet and the moon in earth

masses.
masses.

After another bout of intense number vomit we get an orbital period of 34.15 earth days.
After another bout of intense number vomit we get an orbital period of 34.15 earth days.

So, lunar months on this world will be roughly 34 earth days long.
So, lunar months on this world will be roughly 34 earth days long.

And that right there is how one goes about constructing moons for habitable earth-like
And that right there is how one goes about constructing moons for habitable earth-like

planets!
planets!

Now...on to the other terrestrial planets!
Now...on to the other terrestrial planets!

Uninhabitable terrestrial planets require a very different moon building technique.
Uninhabitable terrestrial planets require a very different moon building technique.

Why?
Why?

Because...
Because...

1) Terrestrial planets shouldn't really be given any major moons.
1) Terrestrial planets shouldn't really be given any major moons.

Earth is anomalous in this regard.
Earth is anomalous in this regard.

Instead we have to deal with minor moons.
Instead we have to deal with minor moons.

Minor moons aren't spheres so there's less we can/need say about them.
Minor moons aren't spheres so there's less we can/need say about them.

And 2) The stabilization effect of minor moons
And 2) The stabilization effect of minor moons

is minimal so we can be more liberal when choosing their orbits.
is minimal so we can be more liberal when choosing their orbits.

Let's start with this guy.
Let's start with this guy.

It's rocky so, by definition, it's density should be in the ball park of 3 g/cm^3 – the
It's rocky so, by definition, it's density should be in the ball park of 3 g/cm^3 – the

higher the value here to more iron content the minor moon will have.
higher the value here to more iron content the minor moon will have.

Useful for those wishing to construct potential mining locations.
Useful for those wishing to construct potential mining locations.

I'll go with a density of 4 g/cm^3 aka about 3/4s the density of earth.
I'll go with a density of 4 g/cm^3 aka about 3/4s the density of earth.

The moon is non spherical so it's shape can be whatever we wan't it to be but, for ease
The moon is non spherical so it's shape can be whatever we wan't it to be but, for ease

of construction, I'd advocate modeling minor moons as ellipsoids.
of construction, I'd advocate modeling minor moons as ellipsoids.

Which means we're gonna need to specify three axes: a, b and c.
Which means we're gonna need to specify three axes: a, b and c.

Let's say this guy is very roughly 80 km x 50km x 30km.
Let's say this guy is very roughly 80 km x 50km x 30km.

Like this!
Like this!

'Cause, ya know, who doesn't like fibonacci inspired minor moons.
'Cause, ya know, who doesn't like fibonacci inspired minor moons.

FYI ellipsoids come in three distinct flavors: tri-axial ellipsoids (where a is greater than
FYI ellipsoids come in three distinct flavors: tri-axial ellipsoids (where a is greater than

b which in turn is than c), oblate spheroids (where a and b are equal and greater than
b which in turn is than c), oblate spheroids (where a and b are equal and greater than

c) and prolate spheroids (where a and b are equal but less than c).
c) and prolate spheroids (where a and b are equal but less than c).

Choose at will.
Choose at will.

With density, size and shape done, let's talk mass.
With density, size and shape done, let's talk mass.

The mass of an ellipsoid is given by P the density times 4/3 pi, times the three axes
The mass of an ellipsoid is given by P the density times 4/3 pi, times the three axes

a,b and c.
a,b and c.

To make sure the units work out we have to multiply each of our inputs by 1000.
To make sure the units work out we have to multiply each of our inputs by 1000.

In this case my moon ends up with a mass of about 2x10^18 kg which seems like a lot but
In this case my moon ends up with a mass of about 2x10^18 kg which seems like a lot but

really it's just 0.00000033 Earth masses.
really it's just 0.00000033 Earth masses.

Now, we could try and set surface gravity but given the irregularity of minor minors,
Now, we could try and set surface gravity but given the irregularity of minor minors,

even I think that'd be overkill.
even I think that'd be overkill.

I mean determining their mass is already sorta overkill...surface gravity would be a total
I mean determining their mass is already sorta overkill...surface gravity would be a total

fatality.
fatality.

Simply knowing a minor moons composition, size and shape is more than enough really.
Simply knowing a minor moons composition, size and shape is more than enough really.

That said, let's put this guy into orbit.
That said, let's put this guy into orbit.

Same method applies as before.
Same method applies as before.

Find the Hill sphere, like so, and the Roche limit, like so, and place your moon within
Find the Hill sphere, like so, and the Roche limit, like so, and place your moon within

this zone.
this zone.

Because the minor moons of terrestrial planets will likely be captured asteroids, they can
Because the minor moons of terrestrial planets will likely be captured asteroids, they can

pretty much orbit anywhere in the zone no restrictions.
pretty much orbit anywhere in the zone no restrictions.

So, I'll place this guy at about 30 earth radii out.
So, I'll place this guy at about 30 earth radii out.

Giving him a orbital period of just over 11 earth days.
Giving him a orbital period of just over 11 earth days.

Minor moon done!
Minor moon done!

Same stick with our distant terrestrial planet.
Same stick with our distant terrestrial planet.

I selected 4 densities that indicate an icy composition, i.e., in and around the 1-2 g/cm^3
I selected 4 densities that indicate an icy composition, i.e., in and around the 1-2 g/cm^3

mark.
mark.

The higher density values here indicate a mixture of rock and ice – dirty snowballs
The higher density values here indicate a mixture of rock and ice – dirty snowballs

if you will.
if you will.

I made 3 of them oblate spheroids and one a tri-axial ellipsoid.
I made 3 of them oblate spheroids and one a tri-axial ellipsoid.

And placed each of them in the moon zone whilst ensuring that no two moons came within 10
And placed each of them in the moon zone whilst ensuring that no two moons came within 10

planetary radii of each other.
planetary radii of each other.

And there you have it one terrestrial planetary system all decked out in moons.
And there you have it one terrestrial planetary system all decked out in moons.

Next time, we'll have a look at gas giant moon systems AND the possibility of habitable
Next time, we'll have a look at gas giant moon systems AND the possibility of habitable

moons!!
moons!!

Stay tuned!
Stay tuned!