It’s the Size of Texas

Inspired by five words, or is it six, in the 1998 blockbuster Armageddon, a movie about an asteroid the size of Texas on course to impact Earth in eighteen days and the team of deep core drillers sent to break it up, I wondered whether there were any quantifiable clues to support the statement that the asteroid is the size of Texas, or whether it’s nothing more than a massive metaphor.

Much like the film, this discussion is just a spirited romp. It was written solely for entertainment purposes (mainly this writer’s own) and is not a rigorous analysis. In fact, you might want to give it a miss entirely—much like the Armageddon asteroid ultimately does with Earth.

Let’s face it, asteroid and comet disaster movies aren’t realistic anyway, whether there’s an impact or not. If we want realism, the closest we might get in our lifetime is gate-crashing an IAA Planetary Defense Conference where experts run hypothetical impact scenarios. Or watch a decent documentary about the Chicxulub asteroid impact; there is a good dramatised documentary about what to expect should a similar-sized comet impact near Chicxulub today. Alternatively, there are countless scientific articles interpreting what to expect based on drill core samples, a recent one being The first day of the Cenozoic. Or wait and see whether 99942 Apophis impacts in 2068.

Armageddon provides only sketchy information about the incoming object which, if it is the size of Texas, is about two thousand times the size of Apophis. Still, we can try and determine some of the physical properties of the Armageddon asteroid based on the information in the film.

We might find that this asteroid has as much mass as all the asteroids in the asteroid belt combined, if the Texas-sized statement is to hold up. If so, there would be no asteroid belt from where the rogue comet supposedly knocked the asteroid. And I make no comment on the likelihood of that last bit, other than re-using a line from the 1978 film A Fire in the Sky, that “the odds of it actually impacting are, well, astronomical”.

Many people rant about Armageddon in true Gary Numan style, but not me, because I do like the film—except for the early scenes in the city which always make me wonder how much influence those images had on those out to cause destruction. But I like most asteroid and comet impact movies, and in this one we have an asteroid on steroids.

Armageddon pays great tribute to the 1983 film The Right Stuff, and has some good lines, and one great line. And as we are told by one of the characters in this movie, “it’s deep blue hero stuff”.

Having said that, Armageddon can be a bit of an onslaught on the senses, being so frantically cut and intensely coloured—all to the sound of Aerosmith—making it difficult to take in much of what’s going on with the asteroid.

But the colouring has more depth in its meaning than just the deepness of the blues and greens, for reasons that only become clear if you delve into Disney’s influences for the look of this movie. And I don’t mean the competing 1998 release, Deep Impact. I mean Disney’s own 1954 classic, 20,000 Leagues Under The Sea.

While the script for Armageddon is said to have been written to rival Deep Impact, and the premise for Deep Impact was influenced by the 1951 classic When Worlds Collide, the influence of 20,000 Leagues on Armageddon is very apparent.

If you don’t believe me, click on the link above to watch it.

In Armageddon, there is the deep blue surface of the asteroid with huge jagged spires resembling the underwater structures in Captain Nemo’s water world. And Armageddon‘s monstrous metal asteroid is shaped like a cephalopod on the hunt, in part playing the role of the Nautilus, and in part playing the role of the giant squid that threatens it. The gushing oil rigs and gas-spewing asteroid take the place of the black squid ink, and raging storms on the asteroid replace the raging storms at sea.

There’s a team of deep sea drillers instead of deep sea divers, and while Bruce Willis sacrifices himself on the asteroid for the sake of the planet, in 20,000 Leagues James Mason destroys his island and goes down with his ship to save his secrets from the authorities, again for the sake of the planet.

Although the distance of 20,000 leagues in the 1958 film is measured horizontally, it’s vertically in Armageddon: 20,000 leagues is almost the distance to the zero barrier at which the asteroid must be split apart to save the world.

But getting back to the theme of this post: is this asteroid the size of Texas?

Jump to a section

The size of Texas
The size of asteroids
It’s 97.6 billion—
A huge, craggy mass
The surface conditions
The composition of the asteroid
The compressed iron ferrite
For a Texas-sized asteroid
The shape of the asteroid
The potato radius
What about the 97.6 billion?
If that wasn’t fun, this will be
Further reading

All images in this post are credited to Touchstone/Bruckheimer/Valhalla/Buena Vista, except where shown as Disney. Explanatory graphics are credited to Vissiniti.

The size of Texas

It isn’t only in Armageddon where we hear the Texan size comparison, because the state-sized statement has served as inspiration for at least two other dramas, one lower-budget movie released in 2006 going by three different titles, Force of Impact, Ultimate Limit and Deadly Skies, and the other, a three-minute comedy short from 2011, simply called The Size of Texas.

But when the man at Mission Control, or the astronomer at the observatory, declares the approaching asteroid to be “the size of Texas”, what does that size actually mean?

Firstly, we all know the saying that everything about Texas is bigger than anywhere else, so is the statement really just a metaphor for the most devastating impactor we could ever imagine, rather than a measure of the object’s dimensions?

But if the writers did, in fact, mean for their asteroid to have the same physical size as Texas, does the asteroid have a width, length, mean geometric diameter or flat face the size of Texas, or do we wrap Texas around the asteroid?

Texas measures at its N-S and E-W extremes about 1,245 km x 1,290 km, respectively, and covers a surface area of about 695,662 km².

A size announced a split second after the astronomer spots the asteroid for the first time could simply refer to an asteroid that looks as wide as Texas as shown in (i) above — although an asteroid with a diameter of 1,290 km would probably be categorised as a dwarf planet.

If the announced size refers to the flat face of the asteroid as we see it (i.e. its cross-sectional area), then divide the surface area of Texas by π, take the square root and double it and we find that the diameter of the asteroid (modelled as a sphere) is 940 km as shown in (ii) above — about the diameter of the largest body in the asteroid belt, the dwarf planet Ceres.

But if the declared size refers to the surface area of the asteroid (i.e. Texas wrapped around the asteroid) as shown in (iii) above, then the diameter is 470 km (divide the surface area of Texas by 4π, take the square root and double it). A diameter of 470 km would make the asteroid the fourth largest body in the asteroid belt.

So an asteroid the size of Texas could have a diameter of 1,290 km, 940 km or 470 km, depending on the context.

The size of asteroids

About half of the total mass of the asteroid belt is calculated to be contained in just four large asteroidal bodies, which together amount to only about 3% of the mass of the Moon, and just over one third of that mass is contained in dwarf planet Ceres alone.

For comparison purposes, it will be useful to have to hand the diameter, density and surface gravity of those four asteroids for the discussion that follows, as well corresponding details of the largest metal-rich asteroid in the asteroid belt, (16) Psyche, an asteroid that may be the exposed core of a disrupted protoplanet. So keep these in mind:

	Diameter (km)	Density (g/cm3)	Surface Gravity (m/s2)	Mass (x1020kg)	Spectral Type*
1 Ceres	939	2.2	0.28	9.4	C (G)
4 Vesta	525	3.4	0.25	2.6	V
2 Pallas	512	2.9	0.21	2.0	B
10 Hygiea	434	1.9	0.12	0.8	C
16 Psyche	226	3.8	0.06	2.4	X (M)

And the corresponding details for the Moon, Earth and Mercury will be useful as well:

	Diameter (km)	Density (g/cm3)	Surface Gravity (m/s2)	Mass (kg)
Moon	3,474	3.3	1.62	7.3×1022
Mercury	4,880	5.4	3.72	3.3×1023
Earth	12,742	5.5	9.81	6.0×1024

The Chicxulub asteroid that impacted Earth around 66 million years ago in the Yucatán Peninsula, leading to the demise of the non-avian dinosaurs, is thought to have been perhaps 10 km in diameter—that’s the size of Hollywood, measured from Studio City to East Hollywood. However, estimates of the size of the Chicxulub impactor vary greatly, from 6 to 80 km, depending on what you read.

Comparing all this to the size of comets, the largest known comets (meaning cometary nuclei) with trajectories that have taken them inside the orbit of Saturn, are the Comet of 1729 (100 km), Hale-Bopp (60 km) and 109P/Swift-Tuttle (26 km), but most comets may be smaller than 16 km (10 miles). For example, the mean diameter of the nucleus of Halley’s Comet is about 11 km, and that of 67P/Churyumov-Gerasimenko is about 4 km.

At 0:23:54 in Armageddon, we learn that the asteroid has been knocked onto a trajectory towards Earth by a rogue comet on an orbit that took it through the asteroid belt.

Let’s not dwell on the likelihood or mechanics of such a collision (or what happened to the comet which carries on going and is never mentioned again), but the collision launches a cascade of small fragments “the size of basketballs and Volkswagens” towards Earth, with the massive asteroid following in their wake.

It’s 97.6 billion—

We start off hearing about the asteroid’s size at 0:10:35 in the movie, that it’s enormous, and then at 0:10:51 we hear that it’s 97.6 billion—

What? 97.6 billion what?

The NASA Mission Control director interrupts to make it simpler for the politicians being briefed to understand—and that’s when he hear that it’s the size of Texas.

And that is all we are ever told in this film about this asteroid in terms of its size, other than the fact that it will be a global killer. We hear the Texas size comparison only once and never find out any more about the 97.6 billion.

There are endless figures popping up on monitors all around Mission Control, but none of them give us the dimensions of the asteroid (and I’ve scoured the screen).

So, what information is there in the movie about this monstrous asteroid that’s heading for Earth at 22,000 miles per hour?

A huge, craggy mass

We don’t get our first proper visual of the asteroid until 1:23:43 when the astronauts on the two shuttles spot it for the first time after their slingshot around the Moon, and the asteroid is anything but spherical, not even potato-shaped, but elongate with a ragged tail.

It’s nothing like any of the images of asteroids we’ve ever seen from real space missions. Like a monstrous metal kraken from Hollywood movies of old, this asteroid was given an evil attitude; we even hear its sinister tone when the crew first descends to the asteroid’s surface.

We see a shape model early on, at about 0:45:00, that gives us the outline of the asteroid. In a draft script it’s described as “a huge, craggy mass surrounded on all sides by a debris cluster of rock and ice“.

The fact that it’s so craggy and icy and shrouded in a coma is somewhat perplexing, as if the writers couldn’t decide whether they wanted it to be an asteroid or a comet, but we know there are small bodies that blur the lines between asteroids and comets, so-called active asteroids, so let’s assume it’s something like that.

Being so irregular in shape, and the size of Texas, does help a lot in determining its composition, but more on that later.

Its ragged shape made me rethink the three earlier ideas about what the diameter of this asteroid might be if modelled as a sphere. My earlier graphic shows: (i) 1,290 km, (ii) 940 km, and (iii) 470 km, depending on the context.

Some people think we should wrap Texas around a spherical asteroid, making its surface area equal to the size of Texas, giving the diameter in (iii) above. But I don’t think that’s what the statement means in this film: when the man at Mission Control says it’s the size of Texas, he’s not expecting us, and the politicians being briefed, to mentally unwrap the asteroid’s surface to visualise how big it would look laid out flat. It needs to be simpler than that, that’s why he interrupted the 97.6 billion to make the Texas analogy.

I appreciate you may be thinking that I’m taking this way too seriously, after all it’s only a movie, but it is very interesting. And the “size of Texas” comparator has now crossed over into the real scientific community and is being used in real asteroid missions to give us a way of visualising how big a particular asteroid is. But there needs to be a consensus on how the size of the particular landmass being used is being interpreted (i.e. is it (i), (ii) or (iii) above).

Initially, I thought I would set the cross-sectional area of a spherical Armageddon asteroid to the size of Texas, as shown in (ii) above (cross-sectional area being a much more meaningful comparison than surface area). But I think we can do better than that for this bizarrely-shaped rock.

So instead, I model the asteroid as a cylinder with a length of 1,290 km (the E-W dimension of Texas) and a diameter of 540 km.

When viewed side-on lengthways, this 1,290 x 540 km cylinder has a flat face area the size of Texas (695,662 km²) as shown in (v) above, as does our irregularly shaped asteroid when viewed in the same manner, shown in (iv) above.

The cylinder has a volume of 2.95 x 10⁸ km³ and if we rejig that into a sphere, we get a spherical asteroid with a diameter of 826 km, as shown in (vi) above. This is about 88% of the diameter of dwarf planet Ceres, making the Armageddon asteroid the second largest object in the asteroid belt.

So an asteroid with a diameter of 826 km is what I will base my discussion on from here onwards.

The surface conditions

We hear at 0:41:48, during the drill team’s training session for their new generation space suits that come with “directional accelerant thrusters” to cope with low gravity environments, that in terms of the low surface gravity of the Moon, “this will be similar to the asteroid”. We are also told at 0:44:40 that “this asteroid is big, it’s dense, it’s got some gravity, you can walk around, but use your thrusters so you can work easier“.

The Moon has a surface gravity of 1.62 m/s², but the asteroid is much smaller than the Moon, so we can safely assume the surface gravity of the asteroid is lower too. We can work it out once we’ve established more about the asteroid’s composition.

For an asteroid, or any planetary body, with a fixed mean density ρ, the surface gravity g is proportional to its radius r. Using Newton’s Universal Law of Gravitation, we can calculate g, as follows:

where M is the mass of the body and G is the universal gravitational constant.

We don’t know the mass M of the asteroid, but we can model the density ρ and substitute for mass using M = ρV (density x volume), then rearrange to find r.

Parking that formula for a moment, let’s think about the Moon’s size and density first.

The Moon has a diameter of 3,474 km and a density of 3.34 g/cm³ compared to Earth’s density of 5.51 g/cm³ and diameter of 12,742 km. The Moon has a lower density than the Earth because of its smaller core to total volume ratio compared to Earth, the theory being that the Moon was formed largely from mantle material in the impact between Earth and a Mars-sized body.

So what assumptions can we make about the composition of the asteroid?

Here’s the first full image we see, a long way into the movie at 1:23:43:

We know that the asteroid is much smaller than the Moon (24% of the diameter, assuming the asteroid has a diameter of 826 km) and a bit smaller than Ceres (88% of the diameter).

But because of its craggy appearance for its size, the Armageddon asteroid is probably a substantial collisional chunk of a much larger body than Ceres. It may well, therefore, contain a much higher proportion of metal than the Moon, and be very different to Ceres which is composed of much lighter material and ice. It is probably more like asteroid (16) Psyche, only much, much larger.

The Armageddon asteroid is depicted as an extremely dark, highly irregular, semi-cavernous body with canyons of razor-sharp rock. In the first few scenes on the asteroid, we see an overall metallic lustre and we soon find out that a not insignificant amount of this asteroid is composed of compressed iron ferrite.

The two space shuttle teams sent to the asteroid, on Freedom and Independence, were aiming to land in Grid 8 which is an area of the softest rock that NASA could determine from thermographics, and into which the team could drill more easily to plant a nuclear bomb 800 feet (0.25 km) down.

Shuttle Freedom overshoots its target by 26 miles (40 km) and we are told (at 1:30:20) that they land by mistake in Grid 9 (part of Segment 202, at site 15H/32). The shuttle touches down on the floor of a canyon in a region of exposed iron ferrite, with all the onboard instruments disrupted by the strong magnetism of the rock.

I suppose we can say they landed on a rock in a hard place (and that’s the only Aerosmith reference I’ll make). Shuttle Independence crash lands elsewhere on the asteroid.

We know the drill-busting ferrite was once deeply buried because it’s in a compressed phase. In the drill team’s astronaut training, NASA simulated reaching a layer of iron ferrite at 635 feet (0.19 km). How it became exposed on the surface is an interesting question.

One explanation is, of course, by collision and this is particularly important when deriving a density estimate for the Armageddon asteroid (more on that later).

Alternatively, was the ferrite exposed, or exhumed, as a consequence of the formation of the canyons that we see on the surface? Although how the canyons formed, or what carved them, we don’t know — was it erosion by ice or lava, or withdrawal of subsurface magma, or rifting, or something else entirely?

We know the asteroid has at least one large fault that runs all the way through it, because the idea is that the bomb the team will deploy will split the asteroid in two along this fault, and each piece of asteroid will pass safely by Earth.

The canyons look perplexingly like something we would find on Earth or Mars, both of which are differentiated planets with a core, mantle and crust.

So it seems we are on a huge metal asteroid that has vast canyons of sedimentary rock and buttes on the surface. Curiouser and curiouser.

It all looks rather like the Badlands of South Dakota — but of course it is just that, being the film set and inspiration for these particular rock formations on the asteroid.

We know that this asteroid is active, being told at 0:44:47 that it will have “unexpected eruptions”. The asteroid is certainly active enough expelling enough material to have a “comet-like” coma of gas and dust. We see a series of violent eruptions partway through the drilling, at 02:05:00, that send rocks flying horizontally across the surface and are told these are gas eruptions. I don’t recall any volcanic eruptions.

But would we even recognise volcanic eruptions on this asteroid? Instead of the typical lava, or molten mantle, we are familiar with on Earth, a massive differentiated asteroid might be spewing molten core in a way not seen on Earth. This asteroid is big enough for its interior heat not to have been completely lost and still be partly molten.

So could all the metal on the surface of this asteroid be the result of ferrovolcanism — volcanic eruptions of iron solidifying into monstrous metal spires and pooling into vast metal plates. And this is where Freedom happened to land.

Seeing as much of Armageddon depicts the drama of drilling through the compressed iron ferrite in Grid 9 that ultimately destroys every drill bit the team has, we must assume that this iron deposit is so extensive over the whole surface of the asteroid that the Freedom team cannot simply drive their Armadillo over to a softer patch of rock in the eight hour time limit they have.

On what type of surface Independence crash lands we are not told, but the surviving crew drives an Armadillo rover to site 15H/32 on the other side of another vast canyon, taking a few hours to do so. If they drive at, say, 10 miles an hour, they would cover about 50 miles (80 km), across one massive canyon, along the floor of another, over soft rock and dodging their share of huge jagged spires. The circumference of an asteroid with a diameter of 826 km is 2,595 km (1,622 miles), so this drive would be about 3% of the way round the asteroid.

The Freedom team has eight hours to drill, plant the bomb, take off and detonate before the asteroid passes the so-called zero barrier that we hear about (at 0:45:14).

The Zero Barrier:
If the two shuttles encounter the asteroid as they swing around the Moon, landing on the surface when it’s at the Earth-Moon distance of 384,000 km, and spend 8 hours on the asteroid, mostly drilling, with the asteroid travelling towards Earth at 22,000 miles (35,400 km) per hour, allowing some time at the end to take off (it’s just a movie), then the zero barrier is roughly 101,000 km (63,000 miles, or 18,150 leagues) from Earth’s surface, in order to allow for the two parts of the asteroid created in the explosion to pass safely by either side of Earth.

The composition of the asteroid

Either the asteroid is differentiated, meaning it is segregated into some kind of core, mantle and crust, or it isn’t differentiated and is homogenous, like a chondrite or achondrite meteorite, which we know it’s not. If it were homogenous, the onboard geologist Rockhound wouldn’t be describing their landing site as the “massive iron plate” that we hear at 1:30:20.

The likely explanation is this asteroid is part of the collisional remains of an even more massive body that was differentiated, leaving behind this ragged mass of metal core with varying amounts of sedimentary crust, and maybe a bit of mantle, or not.

We know that the team drills through 800 feet (0.25 km) of compressed iron ferrite, the minimum depth required to plant the bomb in the fault line. But the ferrite goes deeper, they just don’t need to drill any deeper.

The extensive amount of iron is one of the reasons for the “unpredictable gravitational conditions” we are told about at 0:44:40 during the crew’s briefing, conditions made worse by the asteroid’s highly irregular shape.

The main point is, this asteroid is probably a great deal more metal than rock, in which case the asteroid’s density is far greater than that of the Moon (3.3 g/cm³) which has a metal core of only 4% of its total volume. Greater even than Earth’s density (5.5 g/cm³) which has a metal core of 15% of its total volume, or Mercury’s density (5.4 g/cm³) which has a metal core of nearly 55% of its total volume.

The reason Mercury’s density is lower than Earth’s, even though its metal core is proportionally larger, is due to gravitational compression; if uncompressed, Earth’s density would be lower than Mercury’s.

To put these densities in more context with other interior planetary materials:

The density of Earth’s mantle ranges from about 3.4 to 4.4 g/cm³ depending on how deep you go.

The density of stony-iron meteorites, which are samples of differentiated or partly differentiated protoplanets, ranges from 4.2 to 4.8 g/cm³, depending on whether they sample the core-mantle boundary (pallasite meteorites) or whether they are a core-crust mix (mesosiderite meteorites).

The density of iron meteorites, which are thought to be from the iron-nickel cores of protoplanets, ranges from 7 to 8 g/cm³. The density of Earth’s core is estimated to range from about 10 g/cm³ in the liquid outer region, to about 13 g/cm³ in the solid centre due to the ultra-high pressure.

The compressed iron ferrite

Ferrite is one of the allotropes of iron (one of half a dozen or so known structural forms). Ferrite is the low pressure, or alpha iron (α-Fe), phase and has the body-centred cubic structure. At high pressure, it transforms to the more compact hexagonal close-packed form of epsilon iron (ε-Fe), known as hexaferrum.

The low pressure ferrite has a density of 5.2 g/cm³ and the high pressure (compressed) hexaferrum has a density of 10.2 g/cm³, so let’s consider the compressed iron ferrite on the asteroid to be something like hexaferrum.

Hexaferrum is rare on Earth’s surface because it requires the type of high pressure regime found deep within the Earth. The ferrite to hexaferrum transition occurs at a pressure of around 13 GPa, which is the level found at around 410 km at the start of the Transition Zone in Earth’s mantle. Hexaferrum may be metastable at lower pressures at the bottom of the lithosphere (or even nearer the surface depending on the other element in the alloy with iron) but will ultimately slowly revert back to the low pressure α-phase ferrite as the pressure drops.

So unless you happen to come across some grains of hexaferrum in a chromitite vein in an exposed mantle peridotite in, say, the Koryak Highland of far eastern Russia, or in the Cordillera Central of the Dominican Republic, or you have the equipment to produce it in a laboratory by squeezing tiny pellets of α-phase ferrite between diamond anvils, the only place you are possibly likely to find hexaferrum stable in any great abundance is at the ultra-high pressures of planetary cores. It’s one of the ultra-high-pressure forms that theoretically could dominate Earth’s solid inner core as an iron-nickel alloy.

We must assume that the internal pressure of the Armageddon asteroid is (or was when it was part of the much larger body) sufficiently high for compressed iron ferrite, or hexaferrum, to be stable in the core, or otherwise, whether alloyed with nickel or iridium or something else.

But for compressed iron ferrite to be metastable on the surface of the asteroid now, the collision that exposed it must have been recent. And since nothing in movieland is impossible, maybe this was the collision with the rogue comet that knocked the asteroid out of the asteroid belt?

If the compressed iron ferrite (hexaferrum) was exposed in an earlier collision, some may have reverted back to the low pressure α-phase ferrite as the pressure dropped.

But as the team attempt to drill into the asteroid, the geology genius Rockhound admits to seeing some stuff that he has never seen before. We might therefore assume that a not insignificant amount of the metal could still be in the high pressure phase. Or maybe he’s looking at the remnants of some weird form of ferrovolcanic rock that he would certainly never have come across on Earth.

For a Texas-sized asteroid

To arrive at a density for the asteroid, I will assume that it is the remains of a differentiated protoplanet and that some of the mantle was stripped away in a collision, so that it is now composed of negligible crustal material, 25% mantle material and semi-exposed metal from the core, or otherwise, making up the remaining 75% of the volume.

The stripped off material could be the basketball- and Volkswagen-sized rocks that already battered the Earth (if the recent encounter with the rogue comet was the event that exposed the core). Alternatively, that material could be lurking elsewhere in the asteroid belt.

Initially, I’ll assume an average density of 3.9 g/cm³ for the mantle material (between the 3.4 to 4.4 g/cm³ upper to lower mantle range on Earth), as well as 10.2 g/cm³ for hexaferrum in the core, 5.2 g/cm³ for any ferrite that has reverted to the low pressure alpha-phase, and 2.5 g/cm³ for any soft crustal rocks (canyon walls, for example).

Starting with 1% crust, 29% mantle, 25% ferrite and 45% hexaferrum, this gives a mean density for the asteroid of 7.05 g/cm³ [= (0.1 x 2.5) + (0.29 x 3.9)+ (0.25 x 5.2)+ (0.45 x 10.2)]. Now to model the characteristics of the asteroid.

Using the formula for surface gravity, and substituting for mass (which we don’t know) using M = ρV (density x volume), we have:

and rearranging for the radius r, we have:

Plugging in the initial assumptions for the asteroid, i.e., g = 1.62 m/s², ρ = 7.05 g/cm³ (7,046 kg/m³) and G = 6.674×10⁻¹¹ m³/kg/s², we get a value of r = 822 km, or a diameter of 1,645 km.

This diameter is almost double the 826 km that I assumed based on modelling the asteroid as a cylinder in the second of my earlier graphics. The cross-sectional area (flat face) of a spherical asteroid with a diameter of 1,645 km is equivalent to just over 3x the surface area of Texas. What might we consider changing for the asteroid to be 1x the size of Texas?

We could reduce the density or the surface gravity, or maybe account for porosity effects due to the assumed collision that caused this asteroid’s ragged shape:

(1) Reduce the density:

Reducing the density of the asteroid simply increases its (sphere-derived) diameter, which is no good as we want to get the diameter down by half, so I’ll keep density as is, 7.05 g/cm³.

(2) Reduce the surface gravity:

Reducing the surface gravity of the asteroid, reduces the diameter by the same factor (for example, halving the surface gravity, halves the diameter). We know the asteroid is much smaller than the Moon, so we can reduce the surface gravity by half.

Assuming 50% of the Moon’s surface gravity, i.e. 0.81 m/s², gives a diameter for the asteroid of 826 km, which is what we need for this asteroid to be the size of Texas. Although the diameter of this asteroid is 88% of the size of Ceres, it has a mass 2.2x Ceres, or 87x Psyche, 3% of the Moon, 1% of Mercury (which itself is composed of 55% by volume metal core), or 87% of the entire asteroid belt. (I summarise all of this in the tables below.)

(3) Account for porosity:

The violent collision that left behind this craggy lump of metal, probably left many wounds and fractures and it may harbour a not insignificant amount of porosity. We know this asteroid has a coma (whether we like it or not) so may be spewing some type of volatile gases from these pores.

Assuming a conservative estimate of 10% porosity, more in the mantle and low pressure ferrite than in the core, this reduces the mean density of the asteroid to 6.63 g/cm³, and for a 826 km diameter asteroid, the surface gravity now reduces to 0.77 m/s² and the mass to 82% of the entire asteroid belt.

(4) Reduce the metal and change the porosity:

(a) Assuming 50% ferrite (25% core + 25% low pressure ferrite), 50% mantle, little or no crust and 0% porosity, gives a mean density of 6.05 g/cm³, surface gravity of 0.70 m/s² and an asteroid with a mass 75% of the entire asteroid belt.

(b) Assuming 35% porosity, gives a mean density of 3.93 g/cm³, surface gravity of 0.45 m/s² and an asteroid with a mass 48% of the entire asteroid belt.

(5) Increase the metal and change the porosity:

(a) Assuming 75% ferrite (60% core + 15% low pressure ferrite), 25% mantle, little or no crust and 20% porosity, gives a mean density of 6.40 g/cm³, surface gravity of 0.74 m/s² and an asteroid with a mass 79% of the entire asteroid belt.

(b) Assuming the collision stripped away most of the rock surrounding the metal core, leaving a composition of 90% ferrite (65% core + 25% low pressure ferrite) and 10% mantle, and that the body now has 10% porosity, gives a mean density of 7.53 g/cm³, a surface gravity of 0.87 m/s² and a chunk of metal with a mass 93% of the entire asteroid belt.

Summarising all that:

For the Armageddon asteroid to be the size of Texas, the physical characteristics could be as follows — or whatever else you choose (I could carry on forever). It’s a big, dense asteroid:

	(2)	(3)	(4a)	(4b)	(5a)	(5b)
Structure: Core Ferrite Mantle Crust	45% 25% 29% 1%	45% 25% 29% 1%	25% 25% 50% –	25% 25% 50% –	60% 15% 25% –	65% 25% 10% –
Surface: Ferrite Silicates	65% 35%	65% 35%	50% 50%	50% 50%	70% 30%	80% 20%
Porosity	0%	10%	0%	35%	20%	10%
Density (g/cm3)	7.05	6.63	6.05	3.93	6.40	7.53
S. Gravity (m/s2) (Moon%)	0.81 (50%)	0.77 (48%)	0.70 (43%)	0.45 (28%)	0.74 (46%)	0.87 (54%)
Mass (x1021kg)	2.1	2.0	1.8	1.2	1.9	2.2
Mass compared to: Asteroid Belt Ceres Psyche	87% 2.2x 87x	82% 2.1x 82x	75% 1.9x 75x	48% 1.2x 48x	79% 2.0x 79x	93% 2.4x 93x
Diameter (km)	826	826	826	826	826	826

Scenarios (2) and (5b) give a density similar to the range for iron meteorites (7 to 8 g/cm³), so the Armageddon asteroid would most likely be an exposed core. Scenario (4b) with 50% volume of iron ferrite and 35% porosity, gives a density similar to, for example, asteroid Psyche (3.8 g/cm³), slightly lower than mesosiderite meteorites (4.2 to 4.8 g/cm³). Scenarios (3), (4a) and (5a) with 50 to 75% iron and 0 to 20% porosity, respectively, lie somewhere in between.

It is, however, generally thought that the largest asteroids have very low porosity due to self-gravity closing up the voids. If that’s the case with this asteroid, then being so big and so metallic and with little porosity, we are probably looking at a density greater than 6 g/cm³. This would make it the densest body in the Solar System, about 10% more dense than Earth.

The shape of the asteroid

At 0:43:08, we see the crew watch a demonstration of the mission with models of Earth, the asteroid and two space shuttles. We know the models are not to scale!

We see enough images and representations of the asteroid throughout the film to know that it is anything but spherical. We see irregular, elongate, craggy and other oddly-shaped masses on the monitors in Mission Control.

The first significant image that the scientists see of the asteroid, from the Hubble Space Telescope, is a glowing amoebic blob, but when they land, after dodging a seemingly endless storm of debris, it resembles a sinister Fortress of Solitude. In the scenes when the crew first sees the asteroid emerge from behind the Moon, it has the uncanny appearance of tentacled sea creature, but when Rockhound probes the surface with his spectrometer-on-a-stick, the device shows two views of a spherical body.

The training scene above shows the asteroid as a diamond shape, much like the shape of asteroid 2867 Šteins (although Šteins is very small in comparison, only about 5 km).

I’m not implying any other similarity of asteroid Šteins to our fictitious asteroid. Unlike the Armageddon asteroid, Šteins is a Tholen E-type asteroid, quite bright, with an iron-poor surface and thought to be part of the mantle of a now disrupted differentiated body. In contrast, the Armageddon asteroid would be classified as a Tholen M-type asteroid: it’s dark with an iron-rich surface and may be an exposed metal core, or exhumed parts thereof.

While the dwarf planet Ceres is closest in size to the Armageddon asteroid, there is no asteroid with the composition of the Armageddon asteroid. Psyche may be the closest in composition, being an asteroid with an M-type surface, but they are not similar in size or mass. Similarly, it is thought that Psyche underwent some type of disruption, leaving little or no mantle material.

Some estimates for Psyche suggest it contains 30 to 60% metal by volume, but its estimated 3.8 g/cm³ density is less than that of mesosiderite meteorites because it contains much less iron-rich silicate minerals and it may harbour up to 20% porosity. Psyche is the twelfth largest asteroid in the asteroid belt, comprising about 1% of the mass of the asteroid belt, but if it is an exposed core, it would be the largest exposed core in the Solar System.

With a sphere-modelled diameter of 226 km, Psyche’s cross-sectional area is less than 6% the size of Texas (more like two thirds of just the panhandle) or in terms of other U.S. states, just smaller than Massachusetts+Connecticut combined, or the size of Switzerland. Its spherical surface area is about 23% the size of Texas, a bit smaller than Wisconsin and a bit bigger than Georgia.

Current assumptions on the composition of Psyche are discussed at length in Elkins-Tanton et al (2020).

We will know much more about Psyche by the end of the decade because the asteroid is the target of a future space mission that will launch in 2023 or 2024 (delayed from 2022). It will be the closest we will get to seeing what might be a planetary core and the excitement I feel is almost uncontainable.

However, I will never know more about the Armageddon asteroid than I do now, nor do I wish to.

The potato radius

A final discussion on why the Armageddon asteroid must be a chunk of something larger — much larger than Texas.

At a radius of around 200 km to 300 km, known as the potato radius, an irregular, lumpy planetary body will have enough self-gravity to pull itself into a near-spherical shape. This transition (to what is called hydrostatic equilibrium) is partly what is used by the International Astronomical Union (IAU) in its official definition of a dwarf planet.

The potato radius is 200 km (400 km diameter) for icy bodies and 300 km (600 km diameter) for rocky bodies. Psyche has a sphere-derived radius of 113 km and is somewhat irregular and flattened (actually a tri-axial ellipsoid). Ceres has a radius of 473 km and is near-spherical. Vesta has a radius in between the two (263 km) and is described as an oblate spheroid.

If the Armageddon asteroid has a diameter of 826 km (413 km radius), and if it were an undisrupted asteroid (or disrupted long ago, early in the history of the Solar System), physics says it should be near-spherical. Being anything but spherical, it must be a residual chunk of something much larger that was once spherical, something the size of—

I’ll leave that for someone else to figure out.

What about the 97.6 billion?

I tried to work out how the “97.6 billion” mentioned at the start of the film might fit in (ignoring the fact that it is something that one of the writers plucked out of the air one day to bolster the “big as Texas” metaphor) and I came across an obscure unit of measure called ‘squares’.

A square is an Imperial unit for measuring area in the US and Canadian construction industry, where one square equals 100 sq feet, or approximately 9.3 sq metres.

From that we can calculate that 97.6 billion squares is about 1.3x the size of Texas.

If that wasn’t fun, this will be

A year or so after first writing about asteroids and the size of Texas, I came across a three minute comedy on the website Funny or Die, written by Scott Gairdner and entitled The Size of Texas with Clint Howard, which aired in 2011. It’s a must-see for anyone with an interest in asteroids. But you need to have watched Armageddon to appreciate the subtleties.

Further Reading:

For those who haven’t quite had enough of densities, metal-rich asteroids, exposed cores, compressed iron ferrite, the size of U.S. states and impact disaster movies, here is a list of the main reference material that I mentioned or accessed when writing this article:

Psyche and other asteroids:

Elkins‐Tanton, L. T., et al. (2020) “Observations, meteorites, and models: a preflight assessment of the composition and formation of (16) Psyche.” Journal of Geophysical Research: Planets 125.3: e2019JE006296. doi.org/10.1029/2019JE006296

Hanuš, J., et al. (2017) “Volumes and bulk densities of forty asteroids from ADAM shape modeling.” Astronomy & Astrophysics, 601: A114. doi.org/10.1051/0004-6361/201629956

Hexaferrum:

Cabri, L., & Aiglsperger, T. (2018). “A review of hexaferrum based on new mineralogical data.” Mineralogical Magazine, 82(3): 531-538. doi.org/10.1180/mgm.2018.86

Mochalov, A. G., et al. (1998) “Hexaferrum (Fe, Ru),(Fe, Os),(Fe, Ir)–a new mineral.” Zapiski Vserossiiskogo Mineralogicheskogo Obshchestva, 127.5: 41-51. Link

Earth’s density by layer:

Robertson, E.C. (2001) “The interior of the Earth.” USGS, Washington: Government Printing Office, 2001. USGS, accessed 2020-12-10.

U.S. states:

List of US states and territories by area. Wikipedia., accessed 2020-12-10.
Map of USA with names of states. Wikipedia., accessed 2020-12-10.

Films:

A Fire in the Sky (1978)
Armageddon (1998)
Deep Impact (1998)
Force of Impact (2006)
The Right Stuff (1983)
Funny or Die – The Size of Texas (2011)
20,000 Leagues Under The Sea (1954)
When Worlds Collide (1951)

Fair Use Notice: All images from Armageddon shown in this article are credited to Touchstone Pictures / Jerry Bruckheimer Films / Valhalla Motion Pictures / Buena Vista Pictures. The poster for 20,000 Leagues Under The Sea is credited to The Walt Disney Company. The images have been carefully chosen to support the commentary. I believe this constitutes a ‘fair use’ of any such copyrighted material, but if you would prefer me to take them down, just ask.