Star-Lord Peter Quill and the gang are back as Guardians of the Galaxy, Volume 2 opens in cinemas from today in another outing of the galactic blockbuster.

It’s one of the most fun films I’ve seen in years, combining hilarity with characters you care about, and spectacular visuals that trump the first instalment, Guardians of the Galaxy in 2014.

With the awesome music of “Awesome Mixtape #2”, the team unravel the mystery parentage of Quill (played by Chris Pratt) and meet several new characters (watch the credits carefully). Old foes become new allies and there are treats in store for fans of the comics.

But what about the actual science in the film, how does that stack up?

I’m going to start by giving the film a very generous allowance for being a blockbuster made for entertainment, not an educational documentary. That being said, it’s always fun to get stuck into some of the maths- and science-filled scenarios in the film.

Be warned though, there are some mild spoilers ahead.

## Maths fail as humour

It was fantastic to see the film uses explicit maths fails as an integral part of the humour.

Not surprisingly, some of the villain characters in the film aren’t particularly bright, and one memorable scene has them screwing up (in several different ways) elementary maths – basic fractions and percentages – when arguing about a juicy cash bounty.

Maths fails have been used as humour in other films and television shows; William Shatner’s tongue in cheek maths in Star Trek being one good example:

These were pretty simple maths fails though and there was a lot of other maths and science in the rest of the film.

## Escaping a quantum asteroid field

In one of the many starship chase scenes in the film, the ships have to navigate through what is called a quantum asteroid field.

#### Asteroids come and go. 123rf.com/Tom De Spiegelaere/Michael Milford

Asteroids randomly appear and disappear as the ships navigate through the field, making it a very dangerous way to escape (a nice twist on traditional asteroid fields where you can see all the asteroids).

So what are the chances of a ship making it through the quantum asteroid field?

The field looks to be mostly empty space. So let’s say that each second the ship spends in the field, there’s a 1 in 100 chance that an asteroid will suddenly materialise on top of the ship, destroying it.

If a ship spends 3 minutes navigating the length of the field, we can calculate the chances of any one ship making it through:

= (survival chance per second)

^{number of seconds}= (1 – destruction chance per second)

^{number of seconds}= (1 – 0.01)

^{3 × 60}= (0.99)

^{180}= 16.38%

That’s pretty high actually, a 1 in 6 chance. From watching the film, it looks like not many make it through (apart from the heroes of course).

If we know how many of the ships actually make it through, we can work out the survival rate per second. Let’s say 1 (just the heroes’ ship) out of 100 ships make it through, then the chance of surviving the field per second becomes:

= (Chance of surviving field)

^{1/number of seconds}= (Chance of surviving field)

^{1/180}= (0.01)

^{1/180}= 0.9747

= 97.47%

Which would suggest a higher danger from the asteroids – a 2.53% chance of being destroyed by a quantum asteroid in any second.

## Elevation grenades

Rocket Raccoon (again voiced somewhat unrecognisably by Bradley Cooper) gets to kick some butt in this film too.

Yet another unique weapon is some sort of electrical effect mine, which chucks aliens high up into the air only for them to fall back to earth again (see the trailer):

#### Elevating the aliens. 123rf.com/Beata Kraus, Chastity/Michael Milford

To chuck aliens so they reach the top of the pine trees (say 30m), we can work out the velocity of the blast:

2 × gravity × height-change = v-final

^{2}– v-initial^{2}

At the top, the alien’s velocity (v-final) is zero, so:

2 × -9.81 × 30 = 0

^{2}– v-initial^{2}v-initial

^{2}= 2 × 9.81 × 30v-initial = square root (2 × 9.81 × 30)

v-initial = 24.26 m/s

So to knock the aliens up to the treetops, the mine would have to propel them upwards at an initial speed of about 24m/s.

This is actually a very low blast velocity (possibly to reduce harm), compared to typical conventional explosives that can travel faster than the speed of sound (although objects hit by the blast don’t necessarily travel as fast).

## Visiting every planet

One of the characters, the awesomely named Ego (Kurt Russell), has spent many years visiting many, if not all of the planets in the galaxy.

#### Visiting every planet. 123rf.com/Viktar Malyshchyts, Vadim Sadovski/Michael Milford

This, one can imagine, is not a trivial feat.

According to a recent study, there might be approximately 100 billion planets in our Milky Way galaxy.

To work out how long it normally takes to visit all these planets, you’d have to solve the infamous travelling salesman problem. This problem is about calculating the fastest way to visit a number of locations.

Luckily for us, this particular character regularly has to return to home base. We can simplify the calculation a little by assuming they only visit one planet per trip away from their base.

We also need to know how big the Milky Way is. Best estimates are that it’s between 100,000 and 180,000 light years in diameter. We can simplify this by saying it’s a circle of uniform diameter 140,000 light years.

We can also simplify matters by assuming that the home base is optimally positioned at the centre of the galaxy.

Our traveller is going to need to make 100 billion trips out to a planet and back.

Stars (and associated planets) are generally more densely distributed near the centre of the galaxy, and more sparse further out. A rough approximation we can use is that the average distance from home base to a planet is one quarter of the galaxy diameter – 35,000 light years. That’s a return trip of 70,000 light years, so the total trip distance is:

= average trip distance × number of trips

= 70,000 light years × 100,000,000,000

= 7,000,000,000,000,000 light years

That’s 7 quadrillion (7×10^{15}) light years. The universe is estimated to be only about 14 billion years old, which is nowhere near enough time to visit all those planets one by one.

With some more calculations, it turns out even visiting all the planets in one go takes longer than the age of the universe.

So, even with speed of light transportation, this is stretching what might be possible for Ego.

## Yondu kicks butt

Yondu Udonta (Michael Rooker) is the morally ambiguous rogue and leader of a group of outlaw mercenaries called the Ravagers. He kidnapped Peter as a boy in the original Guardians film, and raised him into adulthood, resulting in a complex relationship to say the least.

Yondu is armed with one of the most unique of weapons in recent film history, a lethal arrow that he can control by whistling. He uses it to great effect in the first film, but steps up his game even further in Volume 2.

#### Shooting the enemy, one arrow at a time. 123rf.com/mik38, Chastity/Michael Milford

In one scene, he clears out an entire ship of bad guys. It’s not clear how fast Yondu’s arrow can go, but let’s say it can go faster than a car but slower than a plane, say maybe 275kmh, like a conventional arrow.

A large spacecraft might have a couple of kilometres of corridors and various rooms spread out within it, so the time to clear out the baddies is:

= total distance / speed

= 2km / 275kmh

= 0.0073 hours

= 26.3 seconds

Most fight scenes involving Yondu don’t last more than a few seconds, so that sounds about right.

## The verdict

Guardians of the Galaxy, Volume 2 is a lot of fun. Hats off to the scriptwriters and director for the explicit maths fail jokes, and for all the other science- and math-filled content.

Some of the fantastical situations in the film could happen mathematically, but at least one of them would be tough.

Still, films are made to be entertaining, and Guardians of the Galaxy, Volume 2 delivers in an epic way.

*Michael Milford is a Chief Investigator at the Australian Centre for Robotic Vision, an Australian Research Council Future Fellow, Microsoft Research Faculty Fellow and Founding Director of the education startup Math Thrills Pty Ltd. He receives funding from the Australian Research Council, the Queensland Government, Caterpillar Corporation, Mining3, Microsoft, the Asian Office of Aerospace Research and Development and AMP.*