Can I learn astrophysics and astronomy with my basic math?

I want to learn astrophysics and astronomy, I'm very interested in it because there are many questions that popped up in my head, and really curious about things, but I'm afraid of a little bit on math, but I'm a fast learner, I can understand things quickly and easily especially if it is translated on my native language, I have learned basic trigonometric functions, special angles, trigonometry, algebra, quadratic equations, and some basic math but not calculus, will proceed on that later, and I have learned basic physics, until vertical dimension, but still afraid a little on math and equations, how can I counteract that fear? I mean I really want to learn astrophysics but I'm afraid of numbers, can you give me tips? And can you suggest me some book? Or can I learn astrophysics without interacting too much with math? Btw, I'm just taking advancement because I'm really curious and interested in astrophysics, I'm still at high school, hope you can help me.

• Just as encouragement: Learning math peroperly can come from a good teacher or from your own motivation. In high school I had terrible math teachers, but then an astronomy course that taught me many important fundamentals and basics. Once you have the motivation to self-study and you know how, you can achieve a lot without anyone else. – AtmosphericPrisonEscape May 22 '19 at 10:58
• Basic Calculus is a minimum requirement for almost anything in physics and astrophysics. Consider trying a Schaum Outline series book (from a library ?) as a way of getting basic Calculus skills. – StephenG May 22 '19 at 14:38
• You cannot make any headway with astrophysics without engagement with mathematics that goes well beyond high school level. – ProfRob May 22 '19 at 19:12
• Statistics is also heavily required in many parts of Astronomy. – Wayfaring Stranger May 23 '19 at 15:52
• Have you found Phil Plait's "Bad Astronomy" ? You can learn a lot and get some idea of what sorts of math is involved. – Keith McClary May 23 '19 at 23:27

Generally, astrophysics (and astronomy) is math-heavy. That should not discourage you, but rather act as a way of learning math: it is often easier to learn topics that you have a use for and are part of some personal project than just getting lectured about them.

Astrophysics is based on math because it is based on many forms of physics - mechanics, thermodynamics, nuclear physics, relativity theory and so on - plus chemistry. Mathematics is a common language that binds these fields together and allows you to combine them to build models to understand what is going on. Some parts just use some basic math, but in general calculus really is needed.

Mathematics in the more common "calculations with numbers" form also matters because it all starts with measuring things - where things are, how much they change, brightness and so on - and then we build and test our models and understanding from this. That also means that statistics is important for handling measurement noise and finding patterns in data.

One cannot really do astronomy and astrophysics without math. It would be just looking at things and making up explanations without actually checking if and how they hold true.

• So does that mean that I can learn it even I'm afraid a little on math but I'm fast learner, what do you think? I'm just discourage after I find out that it is math-heavy – James May 22 '19 at 8:53
• Being a fast learner is useful: start by learning the non-math parts as framing, and then as you try to understand them you have a good reason to dig into the math which will now be easier because you know what you want to learn. But some maths is quite general - like calculus - and it is better to learn it once and for all. Just keep an eye on the prize of understanding astrophysics. – Anders Sandberg May 29 '19 at 14:02

For most parts of astronomy and astrophysics the level of mathematics required is not very high, compared to what a mathematician would call mathematics. (You are not going to spend much time on proving theorems, for example). So that is the first reason for telling you not to be discouraged by feeling nervous about maths. Much of the time, you only need to understand it well enough to be comfortable with using it as a tool. (It depends on the field, obviously: the shape of black hole event horizons is going to be a lot more advanced than the orbits of exoplanets).

The second reason not to be discouraged is that not only is most of the mathematics easier, it also comes with a built-in relevance to real life. What I mean is this. When you are studying maths as maths, your teacher (or your book) gives you a problem and you have to find the answer, and the answer could be anything at all. When you are using maths as a tool in astrophysics, the answer can't be "anything at all". It has to make physical sense.

For example, a recent paper I was reading was trying to answer the question "When did the violent neutron-star merger occur in which our heavy elements (such as gold and uranium) were created?". They measured the relative abundance, in cosmic dust grains, of certain pairs of elements which would have been the ultimate decay products of the original radioactive elements which were created in the merger. If you did such a calculation, and came up with the answer "the neutron stars merged 400 years ago", you would know the answer was nonsense. If you did it, and came up with the answer "the neutron stars merged 4 trillion years ago", you would also know the answer was nonsense. This built-in sanity check is actually reassuring, when you compare it with theoretical, "mathematical" mathematics. You know in advance what sort of answer you ought to be getting.

A book suggestion: The Big Bang by Joseph Silk

The main text is descriptive only, yet deep enough into the topic to be recommended for my third year cosmology course as an undergraduate. The math that supports the concepts is covered in the Appendices and may be the best indication on how much you need to learn and in which areas to support your interests.

Math is just the language that you use to do the science. The more math you know, the more types of analysis you can do. Some simple math has far reaching implications, as in Hubble's Law where you can get an estimate on the age of the universe by taking the inverse of Hubble's parameter. Likewise, Special Relativity only requires high school algebra, but the implications are mind-blowing.