# Simple Mathematics

### Inspired by a certain Doctor.

While watching a rerun of a favourite series, I noted that a character states that the Earth rotates at a thousand miles an hour. This piqued my curiosity; how fast am I moving while sitting still? All that is required for this little exercise is rudimentary mathematics, and a good encyclopedia. The circumference of the Earth at the equator is 40,075km, and there are 86,164 seconds in a day, which means we spin right round, baby, right round at about 465 metres per second, or 1,674km/h. Which is pretty damn fast, fast enough to keep water in the sea, dirt on the ground, air neatly fixed just above, and us in between. On the other hand, it’s not that fast when you consider that the land speed record is 1,223km/h; someone has built a car that rockets along almost as quickly as the planet it is driving on spins. Which make you wonder, if it drove in the opposite direction to the rotation, and if it could achieve the same speed, would it actually be stationary?

Image via Wikipedia

If you think that’s a laudable feat consider the Blackbird. This is possibly the most mind-bending machine ever made by man, a plane so wonderfully fast it’s gone before you realise it’s there. It set a record for the fastest flying manned vehicle at over 3500km/h; the pilots could fly so fast they could see the dawn twice. If they flew in the opposite direction they might have been able to reverse time and save Lois Lane. Oh no, wait, that requires a cape, never mind.

Image via Wikipedia

### But wait, there’s more!

So we are spinning around quite quickly on the face of the Earth, but we have managed to build machines which can go even faster. And then I begin to wonder how fast is the Earth itself? Sure it’s spinning on its axis, but it’s also flying through space, sitting softly in the Goldilocks Zone (that’s what it’s called, seriously) between fiery death and freezing death. My mathematical skills are not good enough to play with ellipses, so I’m going to assume a neat circular orbit based on an average distance from the Sun of 150 million km. 2πr x 8742 (hours in a year) giving us 107,807 km/h. Which is pretty damn fast. The Earth is moving faster than the speed of sound, 1,236km/h, a lot bloody faster. Faster even than a speeding bullet, roughly 3,182km/h (M4 Carbine muzzle velocity).

Image via Wikipedia

### I had to look the rest up…

So we know how fast the Earth spins, and how fast it is flinging itself through space, but the whole solar system is orbiting the galaxy, which is itself moving at great speed towards something aptly called the Great Attractor. The speed of the first is 792,000km/h, and the second is 3,600,000km/h.  I’m not going to even consider the cumulative speed of all these various factors, I think it would blow my mind. How can we possibly be moving that fast and not notice? It may be due to the fact that it’s all happening in a vacuum over tremendously incomprehensible distances, kind of like how far away aeroplanes appear to fly slowly. Also, someone once said that time and speed and all that jazz are relative. The speed of the Earth that we perceive is relative to the Sun, the Sun to the galaxy, the galaxy to the Attractor. But what about the Universe itself? Thanks to the discovery of Cosmic Microwave Background Radiation we have a fixed point in space, the very edge of the observable universe, and in relation to this the whole freaking galaxy is moving at 2,257,200±79,200km/h. Even the variable is hideously fast.

### Universe, challenge accepted.

These numbers are ridiculous, they are beyond human comprehension, it’s hard enough to imagine how fast the Blackbird flies, and that’s only a fraction of these numbers. There’s no way we could build a machine that could even come close to these speeds, it would be impossible. Right? Well, yes, if you think big. We could never move a big thing that fast. While gravity is a terribly weak force over short distances (it really is, and you can prove it yourself, jump; if gravity was really strong you’d stick to the Earth, but even flimsy human limbs can defeat it briefly) it is tremendously strong over vast ones, especially when given enough time to get its act together. As luck would have it, gravity just happens to live in the universe, the biggest and oldest thing there is. So of course it can fling galaxies about at mind-boggling speeds with ease, it has had all of time to practice.

But what about a small thing, the smallest things in fact? It turns out we have created a machine which can build up to the galactic speeds achieved by gravity, and surpass them, but on a very small scale; the Large Hadron Collider flings sub-atomic particles at each other at near the speed of light, which is, for comparison, 1,079,250,548km/h. Scientists have built a machine which fires something at a billion kilometres an hour at another thing which is also moving at a billion kilometres an hour. Just to see what happens. How cool is that? One result for this experiment was the setting of a record for high-energy collisions at the combined energy of 7TeV. No, I have no idea what that really means either. Luckily some has worked out the mathematics on this (http://www.physicsforums.com/archive/index.php/t-101327.html). It appears that 1TeV is like having a thousand Little Boys (the Hiroshima atomic bomb) in a bullet. So these scientists fired a bullet packing 3,500 Hiroshima bombs at another bullet which also had 3,500 in it just for kicks. I’m sure some science was done also, but purely as a secondary goal, the primary aim being ‘to be awesome’.

Here we are being flung through space by gravity at roughly 0.2% the speed of light, while we fling atoms at each other at 99.999% the speed of light. We frail creatures, having existed for less than an astronomical instant, have built a machine which can impel particles to speeds beaten only by light, and light can’t be beaten, there’s a law against it. We learned to fly just over a century ago, a few decades ago we were playing golf on the moon, and now we investigate the very fabric of reality. It’s amazing what can be done with mathematics…