If I want to learn about astrophysics, should I study up on mathematics?

If I want to learn about astrophysics, should I study up on mathematics?

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I am currently reading A Brief History of Time and while the book itself does not contain much mathematics in it, I want to learn more about the concepts Prof. Hawkings talks about more in-depth.

Now I am aware that I will never get the expansive knowledge that a university tuition in the field would give me, but I have already branched off into something else that does not allow me to pursue that field even if I really wanted to so I want to make do. (I also understand that any knowledge I do get will be basically useless to me, but I love space that much that, in spirit, the knowledge would feel useful to me.)

My question is, before I read books more technical, should I brush up on my math? I am aware that a more applicable subject like physics has more correlation with what I am interested in, but I don't want to read about physics if I have little to no knowledge what the hell each equation means. (Also, how I will learn is through online courses/websites/books. I know it is not the ideal way to go about it, but again, I will do what I can.)

Of course, if you believe I should somehow go back a few years and try my hardest at physics and follow the most tried path, I am all ears. It is just that I am now going to a technical college for IT and if I want to leave, I would have to spend a lot more time in education than most - meaning (as I live in the UK) will probably have to pay extra when I pass a certain age.

I know this question is not exactly linked to astrophysics, but I do not know where else to ask it. If I had read A Brief History of Time earlier in my life, I would not be in this sticky situation. Thanks in advance.

(ADDITION: I have always had a love for space and I was interested in physics, but my teacher was uninspiring and I was going through a tough period in my life. I am willing to work towards it now, even if my teacher is the worse thing to ever exist.)

Yes, absolutely. At bare minimum, you'll need to study some geometry to understand how distances are calculated and how the shapes of orbits are related. Next, you'll want to study some algebra, so you can understand the likes of the inverse square law for how the intensity of light drops off as you move away from an object emitting light equally in all directions. Algebra also helps in understanding the magnitude system astronomers use to describe how bright objects are in the night sky.

After geometry and algebra comes trigonometry, especially spherical trigonometry, because of its use in dealing with how we describe the location of objects in the sky, and how to relate positions in one coordinate system to positions in another.

Finally, if you want the really deep understanding, you'll want to go for integral and differential calculus. As my high school physics teacher used to say, the difference between an ordinary formula and one that uses calculus is like the difference between prose and poetry - the calculus encodes deeper meaning and is applicable in more situations than any single formula that can be derived from it.

It would help quite a bit but not absolutely necessary. Don't get me wrong, astrophysics, like most types of physics, is highly mathematical. If you wanted to study it in depth you would need much math. But astrophysics is a broad field and much can be learned, at least at a beginners level, with only a little calculus. This is my opinion of course. As StephenG said, knowing basic physics would be more helpful. I agree with that statement.

Yes, mathematics is essential for all branches of physics and critical for astrophysics. It is required that you improve your mathematical skills throughout school and university.

I agree with the answers here suggesting that geometry, algebra, trigonometry, and calculus are all highly helpful.

However, if I were you, I would reframe your approach a bit. Instead of asking yourself "I want to read more advanced sources on astrophysics, what math should I read first", I'd instead try to move towards this kind of process:

  • What particular subject do you want to start with (e.g. how stars form, or what is a black hole, etc.)
  • Read a general resource about this (e.g. Wikipedia articles, popular science pages online - long form books like Hawking's are useful, but can be hard to probe for just one topic)
  • Ask yourself how much deeper you want to go; what didn't you understand, what holes are left unfilled, etc.
  • Now, go find something more technical (a textbook, that mathy section of the Wikipedia article, whatever you can find)
  • If you start seeing math/physics you don't understand, you may have to dig around to find out what you are missing. You can ask questions on SE about this kind of "mathematics/physics orientation".
  • Learn what you need to progress, and then keep going. Repeat the above steps as necessary.

The main difference in this approach is that you spend less time moving through your "prerequisites" list, and more time reading about what you want to learn.

Now, there won't be any skipping algebra, trig, or calculus if you want to dig much deeper than A Brief History of Time. You will have to learn a lot of that stuff to understand basically any textbooks on astrophysics. It could be worth your time to go through some of the math and physics exercises on Khan Academy or another online learning resource.

The route I am recommending is filled with plenty of frustration, and might be annoying at times. But speaking as someone who's been learning a lot on-the-side of undergrad and graduate school for the last five years, I think it works better than trying to systematically learn everything in order. And it has the advantage of whetting your apetite with the "good stuff" you're trying to learn more frequently. YMMV, however.

Best Astronomy and Astrophysics Books

The universe through the eyes of an astronomer or astrophysicist is a fascinating place — and a good book can give you a glimpse of that world without requiring years of study. Here are the writers' and editors' recommendations of astronomy and astrophysics books that will thrill, puzzle, intrigue and blow your mind.

(We are constantly reading new and classic space books to find our favorite takes on the universe. Our recently-read books in all categories can be found at Best Space Books. You can see our ongoing Space Books coverage here.)

1 Answer 1

Speaking from my experience of doing an astrophysics degree in the UK, I would say that you don't need to do a transition year beforehand.

University lecturers are aware that students will be coming from a variety of backgrounds and structure the course to accommodate that. In particular, there will be at least one or two mathematics courses in the first year designed to get everyone on the same page mathematically. For example, in the first semester of my degree I had a module called "Algebra and Calculus" which covered things like set theory, matrices, differentiation, integration etc. Then we had "Further Algebra and Calculus" in the second semester and "Mathematical Physics" (this was about modelling heat transfer, waves on a string etc) in the second year.

Furthermore, if you've already been accepted by a university, then they clearly think you are mathematically prepared enough. If you're still not sure, get in touch with a lecturer or two there and ask about suitable preparation materials for example, a textbook or old problem sheets you could work on over the summer. If you're in the UK, take a look at the A Level Maths syllabus. This will give you an idea of the typical maths knowledge a first year physics undergrad will be starting with.

Also note that unless you go into very theoretical parts of astrophysics, you won't need that much complex mathematics, and certainly hardly any pure maths, so I wouldn't recommend studying too much of that beforehand, it's not necessary. If you can differentiate, integrate and know what a Fourier transform is, you're basically set.

One caveat: don't go into an astrophysics degree expecting every lecture to have an astro angle. The first half of my degree was almost purely maths and "classical*" physics-- you need that solid foundation before moving on to the specialised topics. Having said that, it makes it all the more worth it when you get there.

What is astronomy?

Astronomy is one of the oldest sciences, and focuses on celestial objects, such as planets, stars, comets and galaxies, and phenomena that occur outside the Earth’s atmosphere, such as cosmic background radiation. Although astronomy is a sub-discipline of physics, it can also be considered ‘applied physics’, as it applies the scientific hypotheses and basic rules of physics to further our understanding of space.

You should study astronomy if…

  • You know your main level of interest is non-Earthly physics, and you want to learn how to apply the main concepts of physics to the study of planets, celestial bodies, stars etc.
  • You want to study the answers to big questions relating to astronomy, such as ‘how was the universe created?’ and ‘how likely is it that life exists outside the Earth?’
  • You’re passionate about following developments in the news in answering these questions.
  • You want to pursue a career in astronomy research, education or outreach.

What Degree Do I Need to Work as a NASA Scientist?

If you have a desire to work in space exploration and plenty of scientific curiosity, a number of degrees could prepare you for work as a NASA scientist. The National Aeronautics and Space Administration seeks scientists with various educational backgrounds to help further the scientific community’s understanding of space and the universe.

Degree Options for Aspiring Astronauts

A bachelor’s degree in the physical and biological sciences can help you qualify for the astronaut candidate program. However, most NASA scientists complete their work from locations on Earth, according to the United States Bureau of Labor Statistics (BLS). Of the 17,000 workers employed by NASA, just 45 are active astronauts, the BLS reported.


Astronomy is the scientific study of the objects that compose the universe. Astronomers address questions about the stars, planets, comets, galaxies and other celestial bodies. To gather and evaluate data, astronomers use telescopes on Earth and probes that have been launched into space.

A degree program in astronomy includes coursework in introductory through advanced astronomy, computer science and mathematics classes such as statistics, linear algebra and calculus, according to the BLS. If you want to work with NASA studying the mysteries of the universe, a bachelor’s degree won’t be enough. You will need a Ph.D. in astronomy to work for the government space exploration entity. In your graduate-level work, you may choose an academic concentration in a subfield like planetary astronomy, stellar astronomy, galactic astronomy or cosmology, the origins of the universe.

Atmospheric Science

If you have never thought about weather phenomena in space, perhaps you should. Atmospheric scientists who work for NASA think about weather and climate events in outer space all the time. These scientists use equipment such as satellite images, radar systems and weather balloons to forecast weather and climate events in both the near future and the distant future. Just as broadcast meteorologists develop the local weather forecasts that appear on television and radio news, atmospheric scientists who work in the field of space exploration use data to predict what weather and climate changes will occur beyond the Earth.

Unlike astronomers and physicists, atmospheric scientists can qualify for employment with NASA with just a bachelor’s degree. Aspiring atmospheric scientists will take courses in subjects such as meteorology, computer programming, advanced mathematics and advanced physics, the BLS reported.


Physicists study matter. In the field of space exploration, plasma physicists are the most sought-after types of physicists. Plasma physicists focus their scientific inquiries on a state of matter called plasmas. The same state of matter that is manufactured for use on neon signs and television screens occurs naturally in stars and other bodies in space, the BLS reported. In particular, plasma physicists working in space exploration research the properties of naturally occurring plasma in space to learn more about matter in space as well as how it affects life on Earth.

Like astronomers, physicists who aspire to a role working at NASA need an advanced degree. A bachelor’s degree in physics often includes coursework in math and the natural sciences. Some of the subjects physics students will study at the undergraduate level include optics, thermodynamics, electromagnetism and classical and quantum mechanics, according to the BLS. At the graduate and doctoral levels, physics programs might offer students the opportunity to focus on a subfield like plasma physics, astrophysics or matter physics.

Scientists in all specialties play an important role in space exploration. If you want to work for NASA, you will need to stand out in whatever field of science you choose to study.

Students interested in pursuing and Astronomy or Astrophysics degree should have a strong background in mathematics. Professionals are often required to complete and explain complex calculations. Critical thinking and analytical skills will allow students to understand these calculations and apply them to the project they are working on. Since professionals often work with others, strong communication and teamwork skills are necessary.

Professionals in the Astronomy and Astrophysics field work full time in offices or observatories. Students should be prepared to work long hours, especially at night, in order to observe stars and other celestial bodies.

Although a master's degree will allow graduates to work in this field, most employers require a Ph.D. These programs typically take 5-7 years to complete and allow students to work in a variety of locations completing fieldwork or research. Internships or summer programs will allow students to gain experience in this field as they work towards an advanced degree.

Astronomy Degree Program Entry Requirements

astronomy and astrophysics degree applicants generally need have finished high school or their GED. Many schools may also have GPA and SAT/ACT score minimums that must be met. In addition to these basic astronomy and astrophysics program qualifications, to serve in some astronomy careers, special certification may be required outside of your degree.

Types of Astronomy & Astrophysics Degrees

59.1% of astronomy workers have at least a doctorate. See the chart below for the most common degree level workers in astronomy and astrophysics have received.

The education level required is different depending on the astronomy career you are seeking.

What Is Astrophysics?

Astrophysics is the science that uses the laws of physics and chemistry along with the tool of mathematics to explain how the universe works.

There is a quote that “god created this universe in the most beautiful language of mathematics.

While we can interpret that universe through our five senses, sometimes we run into questions that cannot be answered that way.

We need additional help prob more deeply, and it is that language of mathematics that allows us to do it.

For example, there is something called a point singularity. Something is there. It actually exists.

Yet, it has no dimension because it is so incredibly dense with matter. It is at this “singularity” where every law we know breaks down because there is so much energy there that everything gets pulled to it. Without math, we could not even begin to understand it.

Energy Explained by Matter and Antimatter

Energy is always conservative in this universe. That was made clear by the equation E=mc^2, which explains that all energy can be converted into matter. And, by that same token, all matter can also be converted into energy, i.e., photons.

Let’s look at an example of how matter works:

At the beginning of the universe, there was an immense amount of energy in the form of light.

The temperature of the universe was also much hotter then than it is now.

That energy, in the form of light, was used to create particles. However, whenever a photon was converted into matter, it produced two particles:

One was matter, and the other was antimatter, which is the mirror image of matter.

Let’s say if an electron particle is produced, then its antiparticle, i.e., positron, will also be created at the same time. It will behave exactly like the electron, but it will have an opposite charge.

Whenever these particles come close, they can annihilate each other. All that will be left are small packets of energy, and the process will keep going until the universe starts to cool down.

But, the next question becomes: If at the beginning of the universe, every matter and antimatter annihilated each other, how can we exist today?

Yes, it’s a mystery that somehow with billions and trillions of particles, one matter particle remained, which had no antiparticle. It is that one particle that led to the universe we see—all the galaxies, stars, planets, and everything else.

Because there might also be one loose antiparticle, we have theories that say there may be anti-planets, anti-galaxies, anti-stars, and even anti-universe or multiverses out there somewhere beyond our universe.

What Is the Chemistry of the Sun?

Astrophysics also explains the chemistry of the Sun, including the unique aspects of how the Sun behaves. Here are some examples:

  • Annihilation of particles in the core of this huge star.
  • The Sun’s bond with other planets.
  • How sunspots, which are actually cold spots on the Sun, can exist on something so incredibly hot.
  • It explains nebulae and neutron stars.
  • The rotations of galaxies and planets according to their mass and a way to calculate the orbital motion.
  • The fundamental building blocks of the universe.

Sibling Sciences of Astrophysics

Astrophysics also has two sibling sciences:

Let’s start with astronomy.

If I want to learn about astrophysics, should I study up on mathematics? - Astronomy

Qualification: BSc

Duration: 3 years

Study mode: Full-time

Astrophysicists interpret astronomical data gathered by astronomers to understand how our universe works. Astronomers view the entire electromagnetic spectrum – called “Multi-Frequency Astronomy” – through optical telescopes, radio telescopes, microwaves, gamma-rays, and X-rays.

An exciting career awaits you in Astronomy and Astrophysics in South Africa, which was awarded the Square Kilometre Array (SKA) project.

This comprises a core of radio telescopes in the Karoo, and is one of many projects supported by our own South African Large Telescope (SALT), an optical telescope sited at Sutherland.


Computational and Applied Mathematics I

  • Multivariable Calculus II
  • Introduction to Mathematical Statistics II
  • Linear Algebra II

Computational and Applied Mathematics II

Cosmology: The Origin and Evolution of the Universe

  • Quantum Mechanics III
  • Applications of Quantum Mechanics III
  • Statistical Physics III
  • Waves and Modern Optics III
  • Advanced Experimental Physics and Project III
  • Relativity: The Basis of Cosmology and Astrophysics III
  • Advanced Astrophysics III
  • Modern Radio and Gamma-ray Astronomy III

English Home Language OR First Additional Language Level 5

Mathematics Level 6

Physical Science Level 6


Applicants with 40-42 points may be wait-listed, subject to place availability.

National Benchmark Test

All Faculty of Science applicants must write the National Benchmark Tests (NBT) before being considered for admission.

There are two tests: The Academic and Quantitative Literacy Test and the Mathematics Test. Your test results are used in addition to your Grade 12 results to identify students who may need additional support during the course of their studies.

Rules for the NBT

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The test fee can be paid once you have registered to write the test. The tests must be written by 31 October 2021. You are encouraged to write the tests as early as possible. For a comprehensive list of test dates, registration dates and available venues, please refer to the NBT website. Both tests must be written in one session. ONLY the first attempt results will be considered so we advise against writing the tests more than once in a year.

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I want to study Astrophysics.

Hey. I am 16 right now, studying in a high school, focusing on mathematics and programming. I'm really interested in astronomy and astrophysics, though, and I want to build a career in this sphere. I am not a newcomer - I've been solving problems at junior olympiads for the last 3 years and have qualified for IAO 2016. I don't have serious problems with math either - my trigs and precalculus are fine, but I'm still struggling with calculus.

I have still 2 years to work on my background in order to impress uni commissions, but you know, the early bird catches the worm. Are there, say, any public online projects I can get a part in and present as a part of my CV some day? It does not really have to include programming, I'm fine with observations as well. In general, what can I do now presently that would make a good impression to the universities I am applying to?

I know several Bulgarian astronomers! :) But none that still live in Bulgaria I'm afraid- lots of folks go abroad for their MSc/PhD from Bulgaria.

So I'll be honest, I think it sounds like you're on a fantastic track if you're doing IAO. It will really stand out- it could be fun to do physics and math ones too, depending on your interests. As the other poster said though, I think you are a bit limited in terms of getting in the lab is the best thing you can do, and I know that's not really an option in your country.

So as a result, the only research I can think of one can do online is something from Zooniverse. The issue there is this isn't serious research usually, but rather "look at images and classify stuff" or similar, but maybe there's a way to get involved in one particular one and find an extra way to volunteer. I mean, if I saw a university application from a student who did list a Zooniverse project, I wouldn't be impressed on my own. but if it turns out that student explained in their CV they actually did several thousand classifications, helped organize reports, etc etc, it would definitely show someone being enthusiastic in addition to having skills you would show in grades/ Olympiad despite not living next door to MIT. Does that make sense?

The other one I can think of is Coursera does have some awesome classes online- I got my Python skills from courses there. Iɽ be impressed with a student who took motivation to finish one of those courses- you can get a certificate for completing it, but have to pay (varies by class though I think).

In the Dark

A chance encounter with the parent of a prospective student the other day led eventually to the question What’s the difference between Astronomy and Astrophysics? This is something I’m asked quite often so I thought I’d comment on here for those who might stumble across it. I teach a first-year course module entitled “Astrophysical Concepts”. One of the things I try to do in the first lecture is explain that difference. The Oxford English Dictionary gives the following primary definition for astronomy:

The science which treats of the constitution, relative positions, and motions of the heavenly bodies that is, of all the bodies in the material universe outside of the earth, as well as of the earth itself in its relations to them.

Astrophysics, on the other hand, is described as

That branch of astronomy which treats of the physical or chemical properties of the celestial bodies.

So astrophysics is regarded as a subset of astronomy which is primarily concerned with understanding the properties of stars and galaxies, rather than just measuring their positions and motions. It is possible to assign a fairly precise date when astrophysics first came into use in English because, at least in the early years of the subject, it was almost exclusively associated with astronomical spectroscopy. Indeed the OED gives the following text as the first occurence of astrophysics, in 1869:

As a subject for the investigations of the astro-physicist, the examination of the luminous spectras of the heavenly bodies has proved a remarkably fruitful one

The scientific analysis of astronomical spectra began with a paper William Hyde Wollaston in the Philosophical Transactions of the Royal Society Vol. 102, p. 378, 1802. He was the first person to notice the presence of dark bands in the optical spectrum of the Sun. These bands were subsequently analysed in great detail by Joseph von Fraunhofer in a paper published in 1814 and are now usually known as Fraunhofer lines. Technical difficulties made it impossible to obtain spectra of stars other than the Sun for a considerable time, but William Huggins finally succeeded in 1864. A drawing of his pioneering spectroscope is shown below.

Meanwhile, fundamental work by Gustav Kirchoff and Robert Bunsen had been helping to establish an understanding the spectra produced by hot gases. The identification of features in the Sun’s spectrum with similar lines produced in laboratory experiments led to a breakthrough in our understanding of the Universe whose importance shouldn’t be underestimated. The Sun and stars were inaccessible to direct experimental test during the 19th Century (as they are now). But spectroscopy now made it possible to gather evidence about their chemical composition as well as physical properties. Most importantly, spectroscopy provided definitive evidence that the Sun wasn’t made of some kind of exotic unknowable celestial material, but of the same kind of stuff (mainly Hydrogen) that could be studied on Earth. This realization opened the possibility of applying the physical understanding gained from small-scale experiments to the largest scale phenomena that could be seen. The science of astrophysics was born. One of the leading journals in which professional astronomers and astrophysicists publish their research is called the Astrophysical Journal, which was founded in 1895 and is still going strong. The central importance of the (still) young field of spectroscopy can be appreciated from the subtitle given to the journal: Initially the branch of physics most important to astrophysics was atomic physics since the lines in optical spectra are produced by electrons jumping between different atomic energy levels. Spectroscopy of course remains a key weapon in the astrophysicist’s arsenal but nowadays the term is taken to mean any application of physical laws to astronomical objects. Over the years, astrophysics has gradually incorporated nuclear and particle physics as well as thermodynamics, relativity and just about every other branch of physics you can think of. I realise, however, that this isn’t really the answer to the question that potential students want to ask. What they (probably) want to know is what is the difference between undergraduate courses called Astronomy and those called Astrophysics? The answer to this one depends very much on where you want to study. Generally speaking the differences are in fact quite minimal. You probably do a bit more theory in an Astrophysics course than an Astronomy course, for example. Your final-year project might have to be observational or instrumental if you do Astronomy, but might be theoretical in Astrophysics. If you compare the complete list of modules to be taken, however, the difference will be very small.

Over the last twenty years or so, most Physics departments in the United Kingdom have acquired some form of research group in astronomy or astrophysics and have started to offer undergraduate degrees with some astronomical or astrophysical content. My only advice to prospective students wanting to find which course is for them is to look at the list of modules and projects likely to be offered. You’re unlikely to find the name of the course itself to be very helpful in making a choice. One of the things that drew me into astrophysics as a discipline (my current position is Professor of Theoretical Astrophysics) is that it involves such a wide range of techniques and applications, putting apparently esoteric things together in interesting ways to develop a theoretical understanding of a complicated phenomenon. I only had a very limited opportunity to study astrophysics during my first degree as I specialised in Theoretical Physics. This wasn’t just a feature of Cambridge. The attitude in most Universities in those days was that you had to learn all the physics before applying it to astronomy. Over the years this has changed, and most departments offer some astronomy right from Year 1. I think this change has been for the better because I think the astronomical setting provides a very exciting context to learn physics. If you want to understand, say, the structure of the Sun you have to include atomic physics, nuclear physics, gravity, thermodynamics, radiative transfer and hydrostatics all at the same time. This sort of thing makes astrophysics a good subject for developing synthetic skills while more traditional physics teaching focusses almost exclusively on analytical skills. Indeed, my first-year Astrophysical Concepts course is really a course about modelling and problem-solving in physics.


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