Fiction Science: The Surfaces of Halo

 

WELCOME

(The full version of the Fiction Science introduction can be found in Fiction Science #1)

This series looks to take a deep dive into some of the events and places of the Halo franchise and determine how sciencey they are. I make a point to give as much leeway to the fiction, so long as it does not directly contradict with science, since this is, you know, fiction.  Occasionally I will discuss some aspect of Halo is science terms without actually looking at the truthiness of any particular event.  This is one of those times. I always make a point to warn people if there might be spoilers ahead, even if they are incredibly minor, because there are new people getting into the Halo lore every day, and what might be basic and obvious to a lore veteran, it may not for a new recruit.  If nothing else, this article might spur some interest in the extended Halo universe, so if at the end you want to learn more, check out the related media for a good place to start.

RELATED MEDIA

The following article makes reference to and could potentially contain spoilers for Halo: Ghosts of Onyx, Halo: Primordium, and Halo: Glasslands.

 
 

THE QUESTION

HOW MUCH SURFACE AREA DO THE FORERUNNER MEGA-STRUCTURES ACTUALLY HAVE, INCLUDING THE HALOS THEMSELVES, THE LESSER ARK (HALO 3 ARK / INSTALLATION 00), AND THE SARCOPHAGUS (FORMERLY ONYX / LOCATION OF ONIRF TREVELYAN), AND HOW DO THEY COMPARE TO THE EARTH AND OTHER COMMON CELESTIAL BODIES?

 

THE ANSWER

This article was inspired by the recent Lore Stream 343 did a few weeks ago, featuring Jeff Easterling and Kenneth Peters.  It is always hard to imagine the scale of large celestial objects, and the places we visit in the Halo universe are no different.  In many ways they are even harder to comprehend because there is such a wide variety of shapes and sizes of Forerunner mega-structures, and they aren't all the spherical celestial bodies we are used to.  Hopefully this will make it easier for you to grasp the scale of the scene the next time you start up a Halo game or crack open a book.

To start, I am going to briefly go through the equations used to determine surface area.  Once that is out of the way, determining the landmass of each structure or planet will be pretty straightforward, with the exception of the Ark, which is a very complicated surface we will have to simplify considerably to calculate.  Additionally, I don't believe we have ever gotten very specific numbers on the dimensions of the Lesser Ark, so there will have to be some assumptions made.  Its okay. At that size, as long as we get in the ballpark, that will be close enough to get an idea of scale.

While I cover many of the most common locations we see in the Halo universe, I don't cover everywhere.  Namely, I didn't calculate the surface area of the Greater Ark, because while we know it is the foundry for the Senescent Halos, there isn't a whole lot else to go by.  I could just scale up the calculations for the Lesser Ark, but we don't have definitive data the Greater Ark is the exact same shape as the Lesser Ark.  If that information is ever made public, I will be sure to add that in.

I also avoid the shield worlds, with the exception of the Sarcophagus, because there are too many unknowns.  Even Requiem, which is a sphere like the Sarcophagus, has layers of unknown size.  It would be impossible to get a number that I could say with any certainly is anywhere close to accurate. Like the Greater Ark, if that information is ever made public, I'll add that in too.

For the purposes of this article, I am going to stick to calculating surface area and ignore figuring out the volume and density of all the Halo mega-structures.  We have been given bits and pieces of information regarding mass and volume, but it is spread out among several different objects, and trying to correlate between the two would likely result in widely inaccurate information.  I will come back to the topic of the mass of the Forerunner mega-structures when we get some more data on them.

Sphere Equations

SURFACE AREA OF SPHERES

This, of course, is what we want to know when determining the surface area of a planet like the Earth.  This equation also works equally well for any sphere, including the Sarcophagus, a.k.a. Shield World 006 a.k.a. the Station Formerly Known as Onyx. If you remember from way back in middle and high school (or maybe not that way back depending on how old you are), there are some basic equations for determining the dimensions of a circle. These are:

  • CIRCUMFERENCE = 2 · π · radius

  • AREA = π · radius²

That's a two-dimensional object, so for a sphere, the equations are:

  • SURFACE AREA = 4 · π · radius²

  • VOLUME = 1.33 · π · radius³

I won't get into the details here, but if you are wondering why these equations seem similar, the answer is calculus.  Knowing one of these equations, you can determine the others.  Same goes for acceleration, velocity, and distance.  Calculus.  So I don't lose my audience, I will leave it at that for now.

The only one we are particularly interested in right now is the surface area of a sphere, but we are going to need that circumference equation in just a minute.  So keep those in the back of your head.  Or just scroll up.
 

Cylinder Equations

SURFACE AREA OF A CYLINDER

A Halo is just a very short cylinder, so to figure out its surface area, we will need the equation for a circle's circumference, and multiply by the height, or in this case width, of the cylinder.  The equations are:

  • CIRCUMFERENCE = 2 · π · radius

  • SURFACE AREA = 2 · π · radius · width

Remember π is pi, or 3.141592654...  Now we have the equations for a sphere and a cylinder, so before we dive into the mess that is the Lesser Ark, lets get the easy ones out of the way.
 

SURFACE AREA OF EARTH

So lets use the equations above to figure out how much land area there is on different Forerunner mega-structures as well as Earth.  That will provide some concept of scale.

Using Wikipedia, the diameter and radius of Earth is:

  • EARTH DIAMETER = 12,742 kilometers

  • EARTH RADIUS = 6,371 kilometers

Assuming the Earth is a perfect sphere, which it isn't, but close enough, the surface area of the Earth is:

  • EARTH SURFACE AREA = 4 · π · radius² = 510,064,472 km²

So the Earth is just over 510 million square kilometers of area.  That is water and land together, but since we don't know the ratios of water to land on the Halos or any other Forerunner structure, it is impossible to do a good comparison of just land area, so I am going to ignore that question until further information is provided.

SURFACE AREA OF A NEOTERIC HALO (ALPHA HALO)

If you are unaware, 343 recently did a Lore Stream where they revealed some more details regarding the Halos, which included the names of the Halo array types.  The Neoteric Array are the ones most people are familiar with, including all the Halos we have seen in the games (Think Alpha Halo).  These are the smaller of the two, so I figured I would start there.  I strongly recommend you watch the recording of the lore stream, as there is some interesting information there that really helps solidify a lot of the math in this article.

 
 

To shorten this up a little bit, I'll just continue with showing the equation, the constants, and the results.  If there are any questions about any of this math, you can refer above, or if that doesn't help, comment below and I will get back to you.

The dimensions of a Neoteric Halo, as shown in the second Halo Lore Stream.

To figure out the surface area of a halo, you need the diameter and the width of the band.  In the case of the Neoteric Array, the diameter is exactly 10,000 kilometers. Boy, either the metric system is an imprinted geas onto humanity, or it is just one hell of a coincidence. Anyway, the width is 318 kilometers.  Both of these numbers were provided directly from the lore stream I just mentioned.

As you can see, 343 already did the math to determine the interior surface area, which is the livable surface on a Halo.  But since it is always good to double check, here is the math:

  • NEOTERIC HALO RADIUS = 5,000 km

  • NEOTERIC HALO WIDTH = 318 km

  • NEOTERIC HALO SURFACE AREA = 2 · π · radius · width = 9,990,265 km²

So that is just under 10 million square kilometers of total surface area.  Compared to Earth, that is about 2% of the total surface area.  Seems kind of small when you look at it that way.  But wait, our calculation is about 5,000 square kilometers larger than the official 343 numbers.  Do they have a more exact number for the dimensions of the Halo they haven't provided us?  It turns out no.  It looks like they just rounded pi to '3.14' rather than something more accurate like '3.1415' or '3.141592654' which I like to use.  There number isn't technically wrong, but it is less accurate than the number we calculated.  So go tell Jeff that 343 needs to update the Halo Bible.
 

SURFACE AREA OF A SENESCENT HALO (ORIGINAL ZETA HALO)

The exact same math applies for the larger, 30,000 kilometer diameter Halos in the Senescent Array.  Based on the events of Primordium where Zeta Halo is forced to shed some sections and becomes a Neoteric Halo, it is a safe assumption that the other dimensions of the Senescent Halos, including the width, are the same.  So using those numbers, we get:

  • SENESCENT HALO RADIUS = 15,000 km

  • SENESCENT HALO WIDTH = 318 km

  • SENESCENT HALO SURFACE AREA = 2 · π · radius · width = 29,970,794 km²

So that is quite a bit bigger, in fact, it is three times larger.  This makes sense since the Senescent Halos are three times the diameter.  And being three times larger means the Senescent Halos have about 6% the surface area of Earth
 

A BRIEF DETOUR THROUGH THE CENTER OF THE HALOS

As a quick aside, since the Halos are, well, halo-shaped, you can play the game of Throw the Planet Through the Halo.  For the Neoteric Halos, which are 10,000 km in diameter, the Earth (12,756 km diameter) and Venus (12,104 km) are just a bit too large, but Mars (6,794 km) and Mercury (4,878 km) would fit through no problem.

For the Senescent Halos, which are 30,000 km in diameter, both the Earth and Venus would fit through (along with Mars and Mercury), but that is it, at least for our solar system.  The next largest is Neptune, but at 49,532 km, is way too big, even for the larger Halos.  You could, however, put the first three planets, Earth, Venus, and Mercury, side-by-side-by-side, and juuuust fit them through (29,738 km).
 

SURFACE AREA OF THE SARCOPHAGUS

The Sarcophagus, the mega-mega-mega-structure that used to by the diminutive planet Onyx, is, by far, the largest Forerunner structure, or largest anything, the Halo universe has seen to date.  The scale is almost impossible to grasp.  It has been described as the size of the Earth's orbit around the Sun, meaning it has a radius of 1 astronomical unit, or  92.96 million miles (149.6 million kilometers). If you are having trouble picturing it, that's because it is nearly impossible to fully grasp how enormous this thing is.  Watch the video below, and pause when you get to the point where they show the solar system out to Earth (2:42).

 

Watch This Guy Build a Massive Solar System in the Desert | Short Film Showcase

 

That tiny blue dot, that you can't even see from that view, is Earth.  That other yellow dot at the center is the sun.  That is the unimaginable large ball of gas that is 1.3 million times larger than Earth.  And the circle representing the Earth's orbit around the sun?  That's the circumference of the Sarcophagus.  This thing isn't a Halo either.  This is a full sphere, with its own planets orbiting within its structure.  Compared to a Halo, or even the Ark, this thing dwarfs them.  And since as far as we know the entire inside of the sphere is a habitable surface, we can use the full diameter to calculate the surface area.  How much does it dwarf everything else?  Lets see:

  • SARCOPHAGUS RADIUS = 149,598,000 km

  • SARCOPHAGUS SURFACE AREA = 4 · π · radius² = 281,230 Gm² (gigameter²)

That is unfathomably huge.  Like, I couldn't possibly try to conceive that number.  So lets put it in terms of the surface area of Earth.  At 510,064,472 square kilometers, you would need 551,361,408 ENTIRE EARTHS to match the surface area of the Sarcophagus.  I'm not sure that speaks to the tiny size of Earth or the massive size of the Sarcophagus, but either way, its mind boggling.  

Before we continue, lets review the sizes we have covered so far, since the next section covers the Lesser Ark, and the Lesser Ark is a much harder nut to crack.  I've included the sizes of a couple countries for comparison.

RELATIVE SURFACE AREA (COMPARED TO EARTH)

CELESTIAL BODY SURFACE AREA % EARTH
Earth 510,064,472 km² 100%
Neoteric Halo 9,990,265 km² 1.96%
Senescent Halo 29,970,794 km² 5.88%
Sarcophagus 281,230 Gm² 55.1 billion%

RELATIVE SURFACE AREA (COMPARED TO NEOTERIC HALO)

LAND MASS SURFACE AREA % HALO
Neoteric Halo 9,990,265 km² 100%
Canada 9,984,670 km² 99.94%
United States 9,833,517 km² 99.43%
Europe 10,180,000 km² 101.9%

RELATIVE SURFACE AREA (COMPARED TO SENESCENT HALO)

LAND MASS SURFACE AREA % HALO
Senescent Halo 29,970,794 km² 100%
Moon 37,930,000 km² 126.6%
Africa 30,370,000 km² 101.3%
North America 24,709,000 km² 82.4%

RELATIVE SURFACE AREA (COMPARED TO THE SARCOPHAGUS)

LAND MASS SURFACE AREA % SARCOPH.
Sarcophagus 281,230 Gm² 100%
Rigel 80,000 Gm² 28.6%
Sun + Planets 6.2 trillion km² 0.0022%
Earth 510 million km² 0.00000018%

*Sun + Planets not visible on graph because it is so small it doesn't even take up a single pixel of the chart.

Hopefully this helps grasp the surface area of the Halos.  As for the Sarcophagus, there really isn't much else I can think of to help imagine the sheer scale of this thing.  Even when I looked at the sun AND all the planets, I couldn't even get close to one hundredth of one percent.  Maybe if you included all the smaller objects like asteroids and dwarf planets you would get close to 0.0025%. It really is just unfathomably large. 

 

Relative sizes of some common celestial objects. The Sarcophagus falls between Rigel and Antares.

 

SURFACE AREA OF THE LESSER ARK

So now for the hard part.  Everything up until now was a pretty simple geometry problem.  The Lesser Ark is not a simple shape.  It is sort of like a flower petal, but not really.  If we want to come up with a model that would at least generally represent the shape of the Ark, we will have to break it up into smaller chunks and then add them together.

Based on the Halo Essential Visual Guide and the Lore Stream 343 put out a few weeks ago, we know the Lesser Ark is 127,530 km in diameter, or exactly ten Earth diameters.  But it certainly isn't a circle.  Or a triangle, or a cylinder, or anything close to a simple shape.  So for the purposes of estimation, I am going to assume the Ark consists of the following:

The Ark, with a Neoteric Halo and Earth to scale.

  • 1 large circle (center)

  • 1 smaller circle hole (foundry)

  • 4 large triangles (large spires)

  • 4 small triangles (small spires)

We know the foundry is about 10,000 km in diameter since this is where the new Halos are constructed.  Based on the scale to the right, the large center area is about two Earth diameters, or 25,500 km.

The ends of the spires are about one Earth diameter, or 12,750 km, leaving three Earth diameters, 38,250 km, as the length of each large spire. As for the width of the base of the large spires, it appears to be about one Earth diameter, or 12,750 km across. 

The small spires are slightly harder to get good numbers for since we don't know the smaller diameter of these spires.  Still, based on the scale, I estimate an entire small spire to be about 2.25 Earth diameters long, or 28,700 km, with the spire ends spanning about half an Earth diameter, or 6,350 km.  That leaves a habitable length on the small spires of 22,350 km. From above, the base of each large spire is 12,750 km across. Using the equation for calculating circumference, the entire large circle is 80,110 km around.  Four large spire bases equals 51,000 km, leaving 29,110 km, or about 7,250 km per small spire base.

So now that we established some basic dimensions, we will model the ark as follows:

  • +1 large circle, 25,500 km diameter (12,750 km radius)

  • -1 small circle, 10,000 km diameter (5,000 km radius)

  • +4 large isosceles triangles, 38,250 km height, 12,750 km width

  • +4 small isosceles triangles, 22,350 km height, 7,250 km width

From here we can calculate the surface area of each section then add (or subtract) each part together to get our answer.

LESSER ARK CENTRAL SECTION SURFACE AREA

To get the area for the central section, we just need to figure out the area of the entire area (large circle), and subtract the area of the foundry (small circle).

  • LARGE SURFACE AREA = π · radius² = 510,705,156 km²

  • SMALL SURFACE AREA = π · radius² = 78,539,816 km²

  • CENTER SURFACE AREA = LARGE CIRCLE - SMALL CIRCLE = 432,165,340 km²

LESSER ARK SPIRES SURFACE AREA

To get the large spire surface area, approximating it as an isosceles triangle, we need the equation for the area of an isosceles triangle.

  • ISOSCELES TRIANGLE AREA = (width · height) / 2

  • LARGE SPIRE AREA = (12,750 · 38,250) / 2 = 243,843,750 km²

  • SMALL SPIRE AREA = (7,250 · 22,350) / 2 = 81,018,750 km²

LESSER ARK TOTAL SURFACE AREA

Now that we have all the sections calculated, all we have to do is add them all together to get the total surface area.

  • CENTRAL SURFACE AREA = 432,165,340 km²

  • LARGE SPIRES SURFACE AREA = 243,843,750 km² · 4 spires = 975,375,999 km²

  • SMALL SPIRES SURFACE AREA = 81,018,750 km² · 4 spires = 324,075,000 km²

  • LESSER ARK SURFACE AREA = CENTER + LARGE SPIRES + SMALL SPIRES = 1,731,615,340 km²

There you have it.  A pretty good approximation of the surface area of the Ark, or more accurately the Lesser Ark, or Installation 00.  It isn't a perfect calculation as we had to estimate some dimensions and shapes, but if 343 has an official number for the Lesser Ark's surface area, I bet it is pretty darn close.  So how does that compare to some other celestial bodies?

RELATIVE SURFACE AREA (COMPARED TO THE LESSER ARK)

CELESTIAL BODY SURFACE AREA % ARK
Lesser Ark 1,731,614,340 km² 100%
Earth 510,064,472 km² 29.5%
Neptune 7.6 billion km² 441.3%
Jupiter 62 billion km² 3,590.8%

 

CONCLUSION

We did it!  We figured out the surface areas of some of the most iconic Forerunner mega-structures.  Hopefully this helps to provide some idea of the scale of these things.  The Halos, both the Neoteric and the Senescent Arrays, are fairly modest in scale.  Even the Lesser Ark's size, which dwarfs the Halos, is fairly easy to grasp I think.  But it is just put to shame by the Sarcophagus, which is simply unimaginably large.  Hopefully the diagrams and videos above help you make some sense of the grandiosity of that thing, but to be honest, I'm still not sure I can grasp it.  Just for one last comparison, here are all the structures we calculated, as compared to the Earth, minus the Sarcophagus due do it making the other objects impossibly small.

CELESTIAL BODY SURFACE AREA % ARK
Lesser Ark 1,731,614,340 km² 100%
Earth 510,064,472 km² 29.5%
Senescent Halo 29,970,794 km² 1.7%
Neoteric Halo 9,990,265 km² 0.6%

Thinking about the Forerunners and the political battle that the Didact had with the Master Builder, I can now see why the Master Builder ultimately won that battle.  The Halo Arrays, including both the Greater and Lesser Arks, the twelve Senescent Halos, and the six Neoteric Halos, were, at least physically, nothing compared to the Sarcophagus alone.  That says nothing for the hundreds or thousands of other shield worlds scattered throughout the galaxy.  The Didact may have been a superior warrior, but he has no concept of balancing a checkbook.  He was bankrupting the Ecumene with his shield world strategy, and the Master Builder knew it.  Turns out, for as big of a douchebag as he was, the Master Builder was right.  All hail the Master Builder!

 

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