Hey everyone, today i’ve got another exam video for you. This time it’s an astrophysics exam and it’s from mit. So this is a real exam paper from their website and even better than usual, this exam paper contains the full worked solutions to the content so i think that would be really helpful. I’ll go through it, i’ll show you what you can expect from an astrophysics exam, like what the kinds of questions are and what answers look like in this subject. So on some of my other exam videos a few people in the comments seem a bit salty that the content I cover is not that hard or it’s too easy. I’m showing you exams that are what you can definitely expect to see if you major in one of these courses so something that’s an undergrad, first, second or third year, something like that. I haven’t been showing you guys graduate content. So there’s definitely harder things than what i’m going to show but I think the things that are in these exams are representative of what you can expect so let’s have a look. In this exam we’ve got eight questions and it looks like we’re expected to attempt all of them. It’s a closed book exam but it says you may use two pages of notes, usually this means that before you come in you can write up two pages of handwritten notes that you’re allowed to have with you and that’s usually where you’re just going to write some formulas. So let’s have a look. First we’ve got a sheet of constants, that’s going to be helpful. It’s good because you don’t have to memorize numbers like this. You never have to, you can get through your whole degree without knowing with the speed of light but you use it so often that it’s probably ingrained in your brain anyway. First problem is… looks like it’s about stellar astrophysics. We’ve got a neutron star is in orbit around a normal star. Matter is flowing from the normal star into the collapsed star at a certain rate and then we’re just ask to find some information about this like calculating the luminosity of the neutron star and also computing the temperature. To work out both of these, you can see the solution, it’s actually reasonably simple. Once you find an equation that you know is relevant, so we’ve got a couple of equations here, it’s really just a matter of rearranging it, putting in the constants, putting in the relevant numbers from the question, it’s not too hard. And in fact I think most of the maths involved in astrophysics, at least what i’m going to show you in this paper, is not very advanced maths. It’s mostly algebra, mostly rearranging equations. All right so our second question is about a similar topic, we’re asked to find a mass of a star, and yeah similar sort of thing, rearranging the formula. You might see here that we have these symbols m with a little circle in it, that means solar mass so you’re calculating the mass of a star in terms of solar masses, that’s the mass of our sun. It’s a nice little constant that we can use to simplify problems and even get a intuitive understanding of how big some of these stars are. Okay this problem we have H-R diagrams, those are Hertzsprung-Russel diagrams and you will see these all the time if you study astrophysics. They essentially tell you about the life cycle of stars. You can plot the apparent visual magnitude, so how bright a star looks against things like its temperature and you can see essentially the evolution of a star over time. What happens to it as it burns through its mass, as it changes in brightness over its lifespan and these plots are essentially a bunch of stars plotted based on those factors. So the questions here are deducing things from the hertzsprung-russell diagram, again i don’t think this is too complicated, you’re looking at the diagrams and by the time you reach the exam you should know how to read them. Over here we’re coming into the short answer part of the exam so a few small shorter questions to answer. We’ve got a dimensional analysis problem, so looking at units and making sure that you understand those and that they make sense to you. And then we’ve got some explain type questions, these will be your favorite if you don’t like to rearrange equations and do the math. You can just explain a concept that you’re asked to. Here we’re talking about what is 21 centimeter radiation and what can we learn by studying it? Some more short problems, a couple more explanations and plugging something into a formula really. We’re asked about the cosmic microwave background radiation and asked to talk about three effects that dust has on starlight. Alright we’ve got another question about stars, this time it’s variable stars that are changing in brightness and then were asked about standard candles which are a way in astrophysics to estimate distances between objects because these so called standard candles are objects that you know they have a constant brightness and you know the distance to them so you can use that to map out the distances to other places. This problem here is about galaxies, now it kind of looks a bit intimidating, you’ve got a very big write-up and then a lot of math down here but actually these are just like four short questions that all relate to the same topic. So once you get one should be a bit of a flow-on effect and the others shouldn’t be too hard. Here we’ve got some spectra, this is also pretty typical of astrophysics, a lot of what you’re doing is taking light from stars, getting spectra of it so that you can find out something about the chemical composition of the star or the object and knowing how to read spectra is pretty important. So here we have some and a few of these questions here involved basically reading off peaks in wavelength from these graphs. So the first question is find a redshift, which involves looking at the shift in wavelengths between these plots. And then I think a few other sort of short questions there. Again these formula are probably stuff that you’ve written down on your little cheat sheet or your a sheet of paper you’re allowed to bring in. If it’s a closed book exam entirely then you’ll probably be given these relevant formula you need and then in the exam it will be more a matter of picking the right one off the formula sheet. Exams are not supposed to be too hard like things like looking at a formula sheet and finding the right formula are things that you should be able to do if you’ve paid attention In the course and i think that’s all this exam is trying to do. It’s trying to show that you paid attention and you understand the concepts that have been talked about. It doesn’t necessarily mean you have a deep understanding of the physics in terms of having a lot of your own independent thoughts behind it, which i’ve spoken about before is something i don’t really like about university courses but exams are i guess not the place to be testing that because it is quite a stressful environment. Our last question here is a plot about the recession velocity of galaxies as a function of distance. Now this question actually comes I think more into the classification of cosmology which is really cool so you’re talking essentially about the expansion rate of the universe because you’re being asked to estimate the Hubble constant from this information. Part b is using the Hubble constant to estimate the age of the universe and then we’re asked a question relating to newtonian cosmology, to derive a More exact relation between the Hubble constant and the current age of the universe. So I think there’s a few cool cosmology questions there. The link to this exam is in the description so I encourage you if you’re curious to download it and have a read through yourself and actually read through some of the solutions. You can go at your own pace then and it’s probably a lot easier to read. I enjoy making these and let me know if you have any ideas for future ones and thanks for watching.