Now let's consider what it would be like to be a little piece of dust in the accretion disk around a black hole. Since our piece of dust is in orbit along with all the other little pieces of dust, we say that it has both angular momentum which prevents it from falling further inward and gravitational potential which is trying to pull it further inward. How can these particles migrate through the disk? Well, on their own they can't. So what do we know so far? For one, we know that due to Kepler's laws that the orbital speed of a piece of dust is related to the distance it is from a central object. When a dust particle is far away from a central object, its orbital speed is low but when it's close to the central object the orbital speed is high. To really understand what's happening, we need a second piece of dust. Let's say that our first piece of dust, dust A in the accretion disk around the black hole is sitting at distance little a. Now let's consider dust A's buddy, dust B. A little further away but not too far from the central black hole. Since dust A is closer, it'll be moving a little faster and since dust B is further, dust B will be traveling a little slower. Every once in a while, dust A will catch up and bump into dust B. What this does is it causes dust A to slow down and dust B to speed up. The result is that the slower dust A will fall further into the disk gaining kinetic energy, and dust B will use its little speed boost to find a stable orbit further away from the black hole gaining potential energy. In an ideal case, we aren't losing any energy but reality is far from ideal. Which means that both dust A and dust B will be slightly hotter than they were before the collision and that heat can be carried out of the disk by thermal radiation, which is how we see them. As energy is being carried away from the system, material in the disk will be pulled further inwards. In a real disk, there are countless dust particles participating in these collisions. So, instead of looking at individual collision, scientists often consider the physics of a large number of interactions. Material moves inward through the disk by losing energy through a viscous force. This process turns the gravitational potential energy of the disk into heat which is then carried away by radiation allowing more material to feed into the black hole. Until now, we haven't really considered what effects the black hole has on the accretion disk other than gravity obviously. But now we shall briefly discuss how gravitational time dilation, gravitational red shift, and the Doppler effect have on the properties of the disk. Our friendly little dust particles that were exchanging energies were also aging at different rates. If each of dust A and dust B were carrying tiny dust clocks with them, they would tick at different speeds. Clock A being close to the black hole would appear to a distant observer to tick more slowly compared to clock B, which is further out in the disk. Practically what this means is that if you wanted to time travel into the future, all you'd need to do is get very close to a black hole for a small amount of time. In that way, the clocks in the rest frame of the universe would appear to tick faster and you would reemerge from near the black hole into a time shifted future. Astrophysicists need to account for gravitational time dilation when they're accounting for the rates that particles emit radiation. A hot particle for example emitting radiation near a black hole would appear to be radiating at a much slower rate. On top of that, due to gravitational redshift, the light being emitted from the accretion disc close to the black hole will lose energy as it climbs out of the black hole's gravitational well, thereby becoming red shifted from its original wavelength but wait there's still more. Due to the rotation of the accretion disk, observers will also measure a difference in the intensity and wavelength of light depending on whether material in the accretion disk is approaching or moving away from the observer. For a spinning disk, the material moving away will be dimmer and redder. Whereas the material moving towards will be brighter and bluer. In order to truly understand black holes, each of these effects along with many more need to be taken into account. Talk about a fun puzzle for theoretical physicists. Now that we have a good grasp on what we would see in the environment around a black hole, we should now ask what an observer would feel in the environment around the black hole. Normally when we think of a spacecraft in orbit around Earth, we imagine an astronaut experiencing the sensation of weightlessness. With gravity only serving to keep them from being flung out into deep space. But there's another effect that becomes significant around black holes that will be noticeable to an astronaut nearby, tidal forces. Tidal forces are named after the tides here on Earth which we experience as the rise and fall of sea levels that occurs periodically. Humans have speculated about the cause of tides for millennia and today we know that they're caused by a combination of the gravitational forces of the moon and the Sun gently pulling on the water in the ocean or rather tidal forces act on everything on earth but it's really only the oceans that we notice. For a simple spherical object, gravity acts to pull the objects towards the center of mass. However, when a second gravitational body is introduced, the forces are now the sum of the gravitational forces due to both of the bodies. This presents an interesting dilemma. Since the gravity from the second body changes strength with distance and thus the tidal forces will have a different value and direction over the surface of the first. These tiny differences in gravitational forces are all that are needed for an object to experience tidal forces. On Earth, we observe this tiny change in force as a major change in the height of the seawater. In some cases, like the Bay of Fundy in Canada, the sea level can vary by as much as 16.3 metres, tall enough to swamp an entire five story building. If small forces like these can create big changes here on Earth, what do you imagine the tidal forces near a black hole might be like. In our daily lives, we experience one Earth gravity worth of acceleration. It's the force that keeps us stuck to the ground. However, there's a very slight difference in the forces that pull on our feet compared to the forces that pull on our head unless of course you're laying perfectly level. Let's calculate the difference in acceleration by rearranging a version of Newton's formula for universal gravitation. Here acceleration A is equal to two times G times M times H divided by R cubed. Here A is going to be the difference between the acceleration of two points separated by a height H above a body of mass M and radius R. Let's see what the differences for a person on the surface of the Earth by inputting Earth's mass 5.97 times 10 to the 24 kilograms and radius 6.3 times 10 to the six meters. For someone my height about 1.8 meters, they experience a difference in acceleration of a miniscule 5.5 times 10 to the minus six meters per second squared. Compared to one Earth gravity, that's less than two parts per million. Definitely not something that we can sense. But let's do the same thing again, this time taking the mass and radius of the nearby black hole Cygnus X-1. It has a mass of approximately 15 solar masses, or three times 10 to the 31 kilograms. For simplicity, let's just say it's a Schwarzschild black hole with a radius of 44 kilometers. Plugging in these numbers, give us a difference in acceleration between my head and my feet of 8,000,000 times the force of gravity. Of course, we wouldn't survive such incredible differences and forces and scientists have named this effect Spaghettification, which isn't so much delicious as it is horrifying. Essentially, as you approach a stellar mass black hole, you'll eventually be pulled into a thin strand that once called itself a human. Not a pretty way to go but that was for a small stellar mass black hole. Let's see how would it affect someone around a super-massive black hole. Sagittarius A star is the name of the black hole at the center of our Milky Way galaxy. Weighing in at 4,000,000 solar masses Sagittarius A has a corresponding Schwarzschild radius of 12,000,000 kilometers which is more than eight times the diameter of our own Sun. Putting these values into our equation, yields a difference in acceleration of a measly one 10,000s the gravity on earth. So, what's going on here? As it turns out the larger a black hole, the more gradual the changes in the gravity field as one approaches. In the movie Interstellar, the writers chose to use a fictional super-massive black hole called Gargantua, which is why the crew of Endurance were able to get so close to the event horizon without feeling tidal forces. However, massive tidal forces were apparent on Miller's planet when gigantic waves circulated the planet. For super-massive black holes, the tidal forces at the event horizon are much gentler than the forces around a smaller black hole. In fact, if you were a space traveler, you'd need to be extremely careful in the area around a super-massive black hole because it's possible you could cross the event horizon and not even realize it.
