There’s a fantastic scene in the recent film The Martian, where Matt Damon’s character, stranded on Mars, does a series of calculations to evaluate his chances of survival. Rarely is long division in a movie as gripping as it appears here, and it illustrates how mathematics underpins every single aspect of aerospace, from flight trajectories to the calorie intake of an astronaut.
As teachers, we’re constantly striving to make our subject relevant to pupils, and unpicking some of the mathematics jam-packed in aerospace is an exciting and engaging way to do so. Sixty years on from the first space flights, people of all ages continue to be amazed by them and it’s an area that’s increasingly relevant with the expansion of private aerospace companies.
Equations govern every aspect of astrophysics and most of these are well beyond any school curriculum. However, presenting some of these to our pupils – omitting the need to understand every principle or theory behind them – provides them with an exciting and engaging context within which to practise their algebraic manipulation. Two such areas are orbits and extra-terrestrial life.
The Drake equation is supposed to model the likelihood of finding intelligent life elsewhere in the universe. Most of the variables are currently unquantifiable, but by directing pupils to make suitable assumptions and substitute in values, they’ll consolidate their ability to manipulate algebra. They can then research the variables further and evaluate their assumptions in light of known data, or they can create their own version of such an equation. A topic often perceived as quite uninspiring comes alive when it allows pupils to examine the possibility of an alien invasion.
The idea of an orbit is explored relatively early on in a pupil’s schooling through looking at Earth’s orbit around the Sun. Aspects of this that can be related to their experience, such as longer days in summer and shorter in winter. But exploring our orbit around the Sun through an equation is an approach that allows pupils to combine sophisticated areas of maths with their prior knowledge. Orbital equations can be unpicked to find out why they’re elliptical as opposed to circular, and what the critical values represent. Younger pupils can plot tables of values or simply experiment with the algebra. Older pupils could derive these equations themselves or investigate other planets. The subject also dovetails nicely into gravity, an incredibly rich area of astrophysics.
Similar to orbits, pupils have a grounding in certain features of gravity. Most know there’s a weaker force of gravity on the Moon than the Earth, some even that a Weight Watchers weigh-in at the top of a mountain provides favourable results. However, these aren’t often linked with Newton’s laws at younger ages, and there’s no reason why they shouldn’t be.
Again, pupils can explore the algebra involved by playing around with the related equations: just how different is their weight on the top or bottom of a mountain? Then they can go further and explore the escape velocity needed for an object to leave the Earth’s atmosphere. There are numerous real-world examples that enrich the maths: a Star Trek actor’s ashes were once unsuccessfully launched into space, whereas Pizza Hut managed to send a Russian astronaut a pizza. More able mathematicians could model these scenarios using differential equations – I find that pupils are always impressed to learn that among an astronaut’s varied skillset is a command of calculus.
Rockets’ trajectories could also be explored: how do astrophysicists calculate the path a rocket takes? What if the shuttle needs to be launched into an orbital path? Airbus’ Mission to the Moon series of activities takes pupils through these ideas and more, with engaging visuals and the opportunity for them to design and build their own rockets.
Journeys into space
Often thought of as the necessary but boring feature of any holiday – I just want to get to the beach, not think about the amount of petrol needed – the logistical considerations within travel are immediately more interesting in terms of space travel because of the wondrous and dangerous nature of it. Rocket fuel, supplies, the length of the journey are all attributes that are very carefully determined for any space journey. Examining these in a lesson can capture pupils’ attention and get them to practise estimation, numeracy and problem solving with something more interesting than the typical "Which bank account is better value?" problem.
They can calculate how much of each variable is needed for a particular space journey and be prompted to consider contingencies: what’s an appropriate extra amount to store in the payload that covers different eventualities? This is also an ideal scenario to explore the future of space exploration and focus on forthcoming projects, such as deep space. Sending manned missions to deep space is an exciting prospect and one that most pupils relish investigating. How far could we travel with our current fuel and technology? How long would it take to travel to Mars? What impact would advances in harnessing solar energy in space have?
The class could even be plunged into an emergency space situation, akin to The Martian, where they have to calculate their own chances of survival and how best to ration. In the book and film, the character colonised Mars with potatoes. Were he able to sow another vegetable, could he have produced a sustainable amount of calories in a more efficient way?
Mathematics is a conduit to understand the world better, as it supports and furthers developments in Stem (science, technology, engineering and maths) subjects. Aerospace is a diverse treasure trove of mathematical applications, whether it’s the physics of a rocket launch or the biology of why astronauts are taller in microgravity. By studying maths through this fascinating field, pupils gain an appreciation of why it’s a core subject, and it potentially sparks an interest in aerospace that goes beyond school. If only Matt Damon did a film about fractions.
Miren Jayapal is deputy head of mathematics at Fortismere School in London
For more ideas on how to incorporate aerospace into your maths lessons, check out this collection of Airbus resources.