# How maths could save the world - really!

Do you want to learn how to save the earth from an asteroid using maths? Read on to find out how it’s done from former NASA scientist, Colin Beveridge.

Asteroids are lumps of space rock which orbit the sun along with all the planets and moons in our solar system.

Once in a while, they crash into a planet - depending on how big the asteroid is, this can be extremely bad news.

For example, you’ve probably heard of the ten-kilometre wide asteroid that burst through the Earth’s atmosphere and exploded, kicking up dust, blocking out the sun… and causing the end of the dinosaurs 66 million years ago.

So how do we make sure it doesn’t happen again?

## Watching the skies

Around the world, astronomers are continually scanning the skies.

To find an asteroid, they study photographs of the same section of the sky, taken through a telescope. They look for changes in the pictures where a dark spot becomes brighter in the next picture, or a bright spot becomes darker. If these changing spots lie roughly in a straight line, the pictures may be showing an asteroid.

By looking at the brightness of the spots, where they are in the sky, and how fast they seem to be moving, we can make a good guess at how big they are, how far away they are, and what direction they’re going.

Once we know that, we can start to predict their orbit and figure out the chance – the probability – of a collision with the Earth.

## So, what are the chances?

Because asteroids are a long way away, it’s difficult to measure exactly where they are and where they’re heading. So we say, ‘It could be anywhere in this patch of sky’.

Then we ask our computers, ‘If it’s here and going this way, does it hit the Earth?’ Then we do the same with lots of different guesses.

To work out the probability of the asteroid hitting the Earth, we divide the number of times we answered “yes” by how many guesses we had altogether. This way of calculating probability works for everything, not just asteroids, so it’s a good lesson!

Calculating probability:

If we tried 10,000 guesses and 100 of them ended up with a collision, that would be a probability of 100 ÷ 10,000 = 0.01 (or 1%). If there were 2,000 collisions, that would be 2,000 ÷ 10,000 = 0.2, or 20%. The bigger the probability, the more likely a collision.

Calculating the odds:

We can also write probabilities as odds – which you get by dividing the number of guesses by the number of hits. In the first case above, we’d get odds of 10,000 ÷ 100 = 100, which means that in every hundred computer simulations, roughly one asteroid hit the earth. In the second we get the answer of 5, which means that one in every five ended up with a collision.

As we get more pictures of an asteroid, we can make better guesses about where it is. Then we ask the computer to work with our new guesses and do the whole probability calculation again.

## How do we save the world from asteroids?

So, if we’ve done the maths and it looks like there’s an asteroid headed this way - what could we do?

As long as we spot it when it’s far away, we only need to change a typical asteroid’s flight path by a tiny amount to make sure it misses us. There are two possible ways to do that.

Kinetic Impactor: a fancy way of saying ‘hit it with something to nudge it away’.

Gravity Tractor: this has nothing to do with farms, but instead means sending something heavy close to the asteroid so that its gravitational pull tugs the asteroid in a slightly different direction.

We use maths to calculate the risk of an asteroid coming near us so that we can do something to stop it hitting the Earth. Maths really is saving the planet - see if you can do our planet-saving puzzles below!

### Puzzle 1

Bruce the Astronaut has been sent into space to destroy a large asteroid.

When he blasts a large asteroid, it splits into two medium sized-asteroids.  When he blasts a medium-sized asteroid, it splits into three small asteroids. When he blasts a small asteroid, it vanishes. How many blasts does he need to make the asteroid completely vanish?

One blast gets rid of the large asteroid, but leaves Bruce with two medium-sized ones. Two more blasts get rid of the medium-sized asteroids, but leave Bruce with 2 × 3 = 6 small asteroids. Six more blasts make all the small asteroids vanish. Bruce needs 1 + 2 + 6 = 9 blasts altogether.

### Puzzle 2

A telescope has spotted an asteroid! We measured it as best we could and ran 10,000 simulations. Out of those, 140 hit the Earth. What is the probability of a collision? What are the odds?

0.014 or 1.4%; about 1 in 70 (or 1 in 71).

### Puzzle 3

You are a NASA astronomer. Your job is to decide which asteroids are the most important ones to study. A new telescope finds the following five asteroids- see if you can classify them using this scale:

*(Astronomers use a system called the Torino Risk Scale to decide how important it is to study a specific asteroid - this is a simplified version!):*

• If an object has a width below 20m, it is classified white (no risk).

• Otherwise, if it has a probability of greater than 0.99 of hitting the earth, it is classified red (certain collision).

For objects in between, we work out the risk factor: (the probability of a collision) × (the width of the object in metres) × (the width of the object in metres).

• If the risk factor is greater than 10,000, the object is classified orange (threatening).

• Otherwise, if the risk factor is greater than 100, or if the collision probability is greater than 0.01, the object is classified yellow (meriting attention by astronomers)

• Otherwise, if the risk factor is greater than 1, the object is classified green (normal).

If the risk factor is smaller than 1, the object is classified white.

Colin Beveridge worked as a researcher on NASA’s Living With A Star program, using data from satellites and telescopes to study the structure of the Sun’s magnetic field.

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