# Ask an Astronomer at the IoA

## Light escaping from black holes

Published on 21/02/2013
Question:

Why can't light escape from black holes?

Nothing, not even light can escape a black hole if it gets too close. This is why they are called black holes. It is difficult to explain precisely without introducing some complicated ideas.

The simplest analogy is to consider throwing a ball up in the air: if you throw it fast enough it can escape off into space, but if not gravity will pull it back down to Earth. If we were to increase the gravity you would need to throw the ball faster and faster. Eventually there would come a point when you would have to throw the ball at the speed of light, which is the maximum speed anything can travel. At this point we have a black hole, and nothing will be able to escape. This is quite easy to understand, but has a number of flaws. For example, in this picture light would slow down, then stop, and then fall back towards a black hole: this isn't right, as light always travels at the speed of light.

A slightly more accurate but complicated picture is to think about gravity as the effect of the bending of space. In general relativity, which is our best theory of gravitation, mass bends space. This is often visualised as a rubber sheet being stretched by something heavy. Particles (whether light or matter) want to travel along straight lines, but when space is curved these become bent: they instead follow curving paths which we describe as the effect of gravity. Black holes have very high curvature, beyond a certain point (known as the event horizon), all straight lines are curved such that they point inwards towards the black hole. There is no direction you can go that will take you outside the event horizon! That might sound a little odd, but black holes are strange places. It's best to keep a safe distance.

## Stellar mass and supermassive black holes

Published on 21/02/2013
Question:

What is the difference between a stellar mass black hole and a super massive black hole?

In terms of physical properties, the difference between stellar mass black holes is their mass: stellar mass black holes are around 3-10 times the mass of the Sun, whilst supermassive black holes are 105-1010 times the mass of Sun. Supermassive black holes are just bigger versions of stellar mass black holes, but behave in the same way (just scaled up).

There are other differences, which are related to their formation. Stellar mass black holes form from the collapse of massive stars at the end of their lives. You can then find them scattered throughout galaxies, just like you find massive stars.

Supermassive black holes are found at the centres of galaxies. We are not exactly sure how they form, although we do have a number of ideas. They are too big to have formed from a collapsing star. We believe that quasars are powered by matter accreting onto supermassive black holes, and measurements of these show that these can grow to a billion solar masses in less than a billion years from the big bang. This means will need a highly efficient way for them to gain mass. We also observe that the properties of the surrounding galaxies are correlated to their central black hole's mass (this is most famously known as the M-σ relationship in astronomy, as we use M for the black hole mass and the Greek letter sigma for the velocity dispersion, a speed characterising how fast stars are moving). This correlation indicates that the growth of the black hole and galaxy are probably linked somehow.

## Earth-like moons

Published on 18/02/2013
Question:

I wonder what would happen if neptune somehow ended up in earth's orbit and turned the earth into one of its moons? what would happen to the earth assuming neptune kept its new orbit in the habital zone of the sun and what would happen to neptune and its moons. color changes and melting for ex. and would neptune stay blue? thanks

Assuming that we could arrange a bit of magic such that one day we woke up in orbit around Neptune with Neptune occupying Earth's current orbit there would initially not be much change, aside from the rather obvious one of a large deep blue orb taking up a substantial fraction of the sky.  We'll also assume that we arranged our magic transition such that Earth is not too close to Neptune's other moons, so that there are no immediate major impacts, let's put ourselves at the nice healthy distance of a million km from Neptune, giving us an orbital period of about 30 days.  Triton is the only moon we really need to worry about in that sense as it is far larger than all of the rest of Neptune's moons combined (99.5% of all the mass in Neptune's moons is in Triton).  Some of the others are large enough that we wouldn't want to hit them from the point of view of human civilisation, but it would do any long term damage to Earth itself if we did.

The first thing we would notice after the sudden appearance of Neptune in the sky would be the dramatic increase in the height of the tides.  Although our nominal orbit is around 3 times further from Neptune than the Moon presently is from us, Neptune is much more massive, and so the tidal field strength would be around 50 times higher.  This wouldn't directly translate into a tidal range that is 50 times larger, since the much stronger tidal forces would be more effective at deforming Earth's crust as well as the oceans, so the sea floor itself would rise and fall along with the oceans.  It is difficult to say exactly how much larger the tidal range of the water would be than at present, but the mid-ocean tidal range would almost certainly be in the range of a few metres rather than half a metre as it is now.  This would mean that large swathes of low-lying coast around the world, including many of the worlds major cities, would become tidal plains flooded twice a day.  The much greater tidal flexing of the crust would also lead to a significant, and permanent, increase in earthquakes and volcanic activity.  In the long term the extra energy pumped into the Earth through tidal heating would also become a contributor to global warming, though given the other problems I don't think we would notice.  Life on Earth would take a while to get used to these changes, but it certainly would in time, the new tidal plains would become major new habitats, and although modern civilisation would take some heavy knocks I expect that humans would get used to it too.  We could potentially decrease the effect by placing ourselves in a wider orbit, but the tidal effects are always going to be rather larger than at present.

Assuming we manage to pull ourselves away from our new problems long enough to take a look around the next thing that we would notice would be the lack of our old Moon, which, since Neptune's gravity is much stronger, would become another separate moon of Neptune.

Another thing we would notice would be the monthly total eclipses that would occur every time we passed behind Neptune.  We are used to the usual solar eclipses produced by our Moon, which are only fleeting and cover only a small fraction of Earth's surface, these new eclipses however would last for hours and cover the whole world.

On Neptune it would be the dramatic increase in temperature that would be noticed, at present Neptune has a surface temperature of around -200C and emits two and a half times as much energy from internal sources as it receives from the Sun.  The huge change in the energy balance would certainly affect the Neptunian weather, which would probably become more violent.  It would also almost certainly affect the chemical balance in the atmosphere, though exactly how the colouration would change is uncertain, the methane that gives it its present blue colouration would still be present, but other compounds would likely change.

The changes for Neptune's moons would be dramatic, most of them have large amounts of water and other frozen volatile compounds and elements like ammonia and nitrogen, which would melt, but because they are rather small they would not be able to retain the liquids and gases, and probably would mostly disintegrate due to the outgasing.  Triton would be a different case, almost as large as our moon it may not have hugely strong gravity, but it is enough that it would not immediately loose it's new atmosphere to space.  The new atmosphere would probably be quite thick, composed of nitrogen, carbon dioxide and probably ammonia, and would overly a massive, deep global ocean, since water makes up about 30-40% of Triton's mass, much more than Earth.  In fact if the atmosphere is not too thick, and we could get rid of the carbon dioxide (the ammonia would be destroyed by the Sun fairly quickly) it could become quite a nice second home for us.

## About the properties of black holes

Published on 09/02/2013
Question:

I have two questions in regards to black holes:

1. What is the relationship between the size of the star, the size of the black hole, the size of the event horizon, and the size of the general field of influence(area where there is a possibility of being sucked in)? Is there a formula, say, for example, star with mass of 10 tons = black hole with radius of 10 cm = event horizon with radius of 10 kilometers = field of influence with radius of 100 kilometers?
2. What is the relationship between the size of the black hole and its life span? For example, radius of 10 cm = dissolves in 10 years?

Thank you for your questions about black holes. Some are easier to answer than others. Black holes are described by a mass that is equivalent to the mass of the object from which they formed, so a 10 ton star (which is too light to really exist) would form a 10 ton black hole. Actually, it's not quite that simple, as when a star collapses some of the outer layers could be blown off and escape, but the important point is that the mass of the black hole is determined by the mass of the material that fell into it.

It is difficult to give a size to a black hole, as the theory says that everything is crushed down to an infinitesimally small point. (Some people argue that this is a reason to improving our theory, but the general consensus is still that everything would be crushed down to something so small that it might as well be infinitesimal: about the size of the Planck length, which is about 10-35 m).

We usually define the size of black holes by their event horizon, which is the point of no return: nothing, not even light, can escape from that point. (This is why they are called black holes). The size of the event horizon for a non-spinning black hole is

r = 2GM/c2,

where G is the universal gravitational constant, M is the mass and c is the speed of light. For our 10 ton black hole, that would give r = 1.5 × 10-24 m (depending exactly on your definition of the ton, I've actually used the metric tonne). For a black hole the same mass as the Sun r = 3 km.

Rotating black holes are slightly more complicated, but the numbers are similar, perhaps a factor of two smaller.

Gravity behaves the same for all objects. It gets weaker the further you are away, but there is no clear cut-off point. Therefore, it is difficult to define a field of influence. You will be able to pass closer to black hole and still escape if you are travelling faster. I would suggest that the event horizon is a suitable distance to consider, as this is the point at which there is absolutely no chance of avoiding getting sucked in.

The lifetime of black holes is an interesting questions. We believe that they should lose energy via Hawking radiation. If left on their own, they would eventually radiate away all of their energy and dissipate. The time taken to evaporate is

t = 5120πG2M3/(ħc4),

where π is the mathematical constant, M is the initial mass and ħ is the reduced Planck's constant (often called h-bar). However, in reality astrophysical black holes are not left on their own; they are constantly absorbing background radiation (as well as any gas or other material that gets too close). This means that they gain mass quicker than they radiate it away, so they will live much longer! No black hole that formed from a collapsing star should have evaporated yet, and none will until the Universe is much older. Some may last effectively forever.

## The speed of rockets in space

Published on 09/02/2013
Question:

I have a question my son wants an answer to. When a rocket blasts out of the earths atmosphere does the speed of the rocket change after it reaches space. In what way?I

That depends upon whether or not its rocket engines are still firing. The rocket engines accelerate the craft. As it gets higher in the Earth's atmosphere there is less air and so less drag to slow it down. Therefore the same amount of push will change its speed more. Note that the Earth's atmosphere doesn't have a hard boundary, it just gets thinner until it is effectively no longer there.

Aside from air resistance, there is another force that acts on a spacecraft: gravity. This will pull it towards the Earth, but its effect gets weaker the further you are away. If you are heading straight up, then gravity will slow you down, unless your engines are pushing you enough to overcome this. Of course, if you start fast enough, you can keep going up even though you are slowing down. Eventually you would get far enough away that the Earth's gravity is no longer important, but you will still have to worry about the gravity of other bodies, most notably the Sun.

If you were to settle into an orbit about the Earth, then gravity just keeps you going in a circle. It doesn't slow you, just changes the direction you are moving. You can think of it as falling with style.

If we were now to consider being in deep space, far from anything, then a spacecraft would keep going in the same direction at the same speed without its engines firing. This is just Newton's First Law of Motion. There are no forces to slow it down, no friction like here on Earth. This is one of the things that science fiction authors often get wrong: if a ship's engines were to fail, it shouldn't shudder to a halt, but continue to coast along at the same speed.