[BLANK_AUDIO] The advent of X-ray telescopes have allowed us to detect millions of X-ray sources in our Universe. Now one of the very first ones that was detected was Cygnus X-1. And this very quickly became candidate for being a black hole, because the X-rays that were being emitted from this object were changing every 100th of a second. So let's start off with a simple model of Cygnus X-1, as a black hole with a disc of spiraling infalling matter. Now, just like water going down a plug hole, the closer the matter gets to the black hole, the faster it moves. And the faster it moves the hotter it gets and the more X-rays it will emit. Now, if different regions of this disk were emitting X-rays in different ways, we'd measure just an average X-ray brightness. But the X-rays we observe from Cygnus X-1 are changing that tells us that the whole disk is changing together. And this sets a maximum upper limit on the size of this object. And we can work that out. The distance is going to be the speed of light times the time, with which this disc is changing. Now the speed of light is just, 3 x 10^8 metres per second. And we know that the X-rays are changing every 100th of a second. So you can put that together, and you can see a distance of 3,000 kilometers, which is roughly the distance between Edinburgh in Moscow or if you are in the US, the distance between New York and Seattle. If we point an optical telescope towards Cygnus X-1, then we find that there is a massive blue supergiant star, really close to the X-ray source. And careful monitoring of this star shows that it's orbiting an invisible friend every six days. How do we know that? Well, imagine you're standing on the side of a Grand Prix [SOUND] race course and you've got your eyes closed and a car goes past you. [SOUND] I bet you can tell me which way it went. Now, that effect has got a grand name called the Doppler effect, and we can use it to tell us whether things are moving towards us or away from us, and if we monitor this massive blue, supergiant star, we can see that it comes towards us for three days, and then away from us for three days. And so it's orbiting something every six days. Now in physics we like to start a problem by looking at the simplest model. So, let's take our black hole, Cygnus X-1, and our blue supergiant that's orbiting it. But, let's assume that the mass of our supergiant is much smaller than our black hole, and then we can assume that it orbits in a perfect circle. Now, our black hole mass, we'll say that's a mass, capital M, and our blue supergiant, we'll say that's got a mass, little m. Now we've measured the velocity of the blue supergiant. We know that it's moving with a speed v, and there's going to be some separation between these two objects radius, r. Now the velocity that we measure with the Doppler shift is just going to be 2pi r, the distance that the supergiant travels in one orbit, divided by the time that it takes to go around that orbit. And we know that it orbits every six days. Now, what's keeping these, two objects bound together? Well it's gravity. And there's equation for the force of gravity, and that is Newton's gravitational constant times the mass of the two objects divided by their separation squared. Now our blue supergiant is orbiting round and round so it has a centripetal force and the equation for that is given by it's mass times it's velocity squared over the radius. Now its the gravitational force that's sourcing this centripedal force so I can equate these two things. [SOUND]. And then, I can just do some algebra to tidy those equations up. Now it's the mass that I want to find out because I'm trying to find evidence that this is a black hole. I have measured the velocity using the Doppler effect, but I don't know this radius. I don't know the separation between these two objects. However, I do have some information here. [SOUND]. So I can rearrange this equation. The separation between these two objects, it's just the velocity times the time over two pi. And I can put that equation back into here and rearrange things, and I'll leave that as an exercise for you. You'll find the mass of the black hole. It's just the velocity cubed times the time over two pi G. So, just by using the physics of gravity and observations of the speed with which the blue supergiant is moving, and the time that it takes to orbit its invisible black hole friend, I can calculate the mass for our black hole. Now what I've shown you there, is how we can use gravity to measure mass. And unfortunately, in the case of Cygnus X-1, it's not quite as simple as the physics I outlined there, because the massive blue super giant star is actually more massive than the black hole that it's orbiting. But it at least gives you an idea of how we can measure masses in the Universe. If you do the calculation correctly, taking into account the mass of the supergiant star as well, we find out that the black hole, Cygnus X-1, is about 16 times the mass of our own sun. Now let's put that fact together with the size of the object that we discovered earlier, which was 3,000 kilometres. Put those two things together, 16 times the mass of the sun within 3,000 kilometres. You've got a very very dense object there. Now this isn't proof that it's a black hole, but it's very strong evidence supporting that theory. And to be honest, we're never going to know whether the Cygnus X-1 really is a black hole or not, but it's the best evidence that we've got. Today we focused on a single black hole, Cygnus X-1, but the X-ray technology can be used to map out black holes in our whole Universe including the supermassive black holes that exist at the centre of each and every galaxy. Recently astronomers have discovered that there's a secret relationship between the black hole and its galaxy, with the most massive galaxies hosting the most massive beasts at their core. If it wasn't for X-ray telescope technology, we wouldn't have discovered these amazing black holes. The stuff of science fiction shown to be reality.
