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.