Ask an Astronomer at the IoA

Ever had a question about astronomy you've want answered? Have a look through the previous questions which we've been asked and if you can't find find your answer, ask 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.

Choice of degree to become an astronomer

Published on 26/01/2013
Question:

I'm currently a student who is majoring in chemistry. I love chemistry, but as of last year I developed a huge interests in astronomy. I read tons of books and that just fueled my interest even more. I go to a college that doesn't offer astronomy as a major, so I was wondering would it be best to major in physics and take some astronomy classes because my goal in life is hopefully to become a astronomer or a planetary scientist?

It is always good to hear from those interested in astronomy. In general, I believe that specialising in physics is a great background for studying astronomy. Many researchers here did their undergraduate degrees in physics, and this is a good background. If you are serious about astronomy you should consider picking up physics.

Chemistry would also be useful for many areas of astronomy, in particular looking at planetary atmospheres, so your background there may be an advantage. There are some planetary scientists who studied chemistry for their PhD and only migrated across later in their research career.

If you are considering a career in astronomy you shall really need a PhD. It would therefore be best to contact institutions you would be interested in attending to find out their requirements. A degree in applied mathematics is often a valid option too.

How can gravity act through empty space?

Published on 26/01/2013
Question:

How can empty space, which has no mass and is therefore not matter, curve? And how can it have an affect on the path of objects? In other words, how can empty space – which is nothing – actually do something (like curve) and how can nothing affect something?

That is an excellent question, and one that is difficult to explain. In general relativity, we talk about gravity being the effect of the curvature of spacetime. It can be difficult to imagine what this really means. There are a number of examples which are commonly used to illustrate a curved space, for example the surface of a sphere. However, when thinking about the surface of a sphere, you normally have the sphere underneath to give it substance. You don't actually need this: the surface can be thought of as a separate entity that can exist whether or not there is a sphere.

When we talk about the curvature of spacetime, what we are really describing are the properties of the metric. This is the quantity that tells us the distance between points. You can define the distance between points whether or not there is anything in between. Try to imagine two objects in a vacuum, even though there is nothing filling the gap between them, the gap could be 5 metres or 5 light-years, and that could be definitely measured. The metric exists whether or not the space is empty. In general relativity we treat the metric as a field, a physical quantity that varies with position. This isn't matter, but it is a something that does exist in a vacuum, and can be thought of as a representation of the gravitational field. You should think of spacetime (the structure of which is given by the metric), rather than a vacuum, as being curved.

Finally, how does the curvature effect matter? Matter always wants to travel in a straight line: what we mean by straight though, isn't what you might usually think of. In this case, we mean the shortest line that joins two points. For a flat space that is straight as you'd normally imagine, but try it on the surface of a sphere and you will get something that looks curved. We call these shortest paths geodesics. It takes a force to push an object off its geodesics, so when travelling unaffected through a vacuum, an object will continue happily along its geodesic. That this might look curved is just an effect of the metric, but the object would have no way of knowing without interacting with something.

I hope that goes some way towards helping you understand. Unfortunately this is a difficult subject. You can test that action at a distance works just by dropping something: it'll travel towards the Earth, even though there is nothing connecting them.

What to read on stellar theory?

Published on 26/01/2013
Question:

I am a current A2 Physics student and part of my course is a research project on a topic of our choice. Stars have always been interesting to me. To me, understanding how stars evolve and produce the elements that make up the world we see before us is fascinating. Could you recommend any scientific papers, journals or books?

Stars are indeed fascinating. There are many interesting areas of physics involved in understanding stellar evolution, from fluid mechanics to atomic physics. Understanding nucleosynthesis is not only important for understanding where the elements come from, but also how stars generate their energy.

You can find a lot of information online on this subject. Wikipedia is a good place to start (although you should know to be careful, as it's not a perfect source). I would also recommend this article by John Bahcall:

Bahcall worked a lot on stellar models, in particular looking at the solar neutrino problem (which may be an interesting aside for you).

In terms of journal papers, it is difficult to make recommendations as (i) they are likely mostly too advanced and (ii) you will usually require a subscription to read them. Many more recent articles are available for free via arXiv, however most of the key research on nucleosynthesis was done in the early 20th century before the arXiv existed. However, there are two Nobel lectures (that would later be published as scientific reviews) that you should be able to read:

This is by Hans Bethe, who was very smart. He invented quantum electrodynamics on a the train home from a conference. He was actually a theoretical particle physicist, and only did a little work on stars.

This is by Willy Fowler, who did spend much of his career on nuclear reactions.

Textbooks are similarly difficult to recommend, as they are expensive. Really you need a nice library to purchase things for you. It might be best to see if you can find any books on stellar evolution locally and work with what you have. If you are looking for concrete recommendations, then I would say Stellar Structure and Evolution by Kippenhahn & Weigert is a good choice. Principles of Stellar Evolution and Nucleosynthesis by Clayton would be more detailed, but is also a little more old fashioned, and perhaps not as readable.