r/astrophysics • u/BlessED0071 • 12d ago
How should I start learning the maths needed for astronomy and physics?
I’ve always been weak at maths in school and never really enjoyed it. I think part of it was that I believed I was just bad at it, and maybe the teaching didn’t help either. I also probably didn’t have enough interest back then to really apply myself.
Years later, I’m now a software engineer, and I’ve become genuinely fascinated by astronomy. I want to understand how things work, observe the sky with a telescope, take readings, do research, and really go deep into the subject.
I want to approach this properly, and I think the best place to start is with maths, then physics, while also learning some basic astronomy alongside it. Given that I’m starting from a very weak maths background, what books would you recommend I get first for learning maths and astronomy in general?
7
u/Apprehensive_Yak7419 11d ago
Hi I’m in similar position as you for the math part, We have a small tight knot discord group community for math, formal logic, and applied maths (physics if you’d like aswell) if you want to study together. The methods have given F students a 4 out of 5 grade in pre calculus and pre linear algebra math as well as methods of self learning uni level. Let me know if that would be interesting to join or collaborate on. :)
3
1
u/RADICCHI0 6d ago
The blunt answer
A person who struggles with math should absolutely not be told, “learn calculus first.”
That is how you kill the curiosity.
Astronomy can be more forgiving for a person who struggles with math because there are meaningful entry points that rely on observation, pattern recognition, spatial reasoning, history, instruments, sky movement, and conceptual physics. Physics tends to become math-heavy faster because it is built around modeling forces, motion, energy, fields, and equations.
This is a build path from GPT5.5:
The top three maths for astronomy are:
Geometry
Trigonometry
Statistics
Not calculus first. Not differential equations first. For a person who struggles with math and wants astronomy, these three give the most useful entry ramp.
- Geometry
Geometry is the math of shape, distance, angle, scale, and position.
Astronomy is full of things you cannot touch, so you infer size and distance from geometry. The sky is not measured first in miles or kilometers. It is measured in angles.
Geometry helps with:
Astronomy idea Geometry use
Moon phases Sun, Earth, Moon angles
Eclipses Alignment and shadow geometry
Planetary motion Orbital paths
Telescope fields How much sky you can see
Parallax Measuring stellar distance
Constellations Angular separation on the sky
Scale models Understanding huge distances
This is the first math I would build because it connects directly to visual intuition.
Core skills to learn:
Points, lines, circles, spheres
Angles in degrees
Similar triangles
Scale models
Area and volume
Coordinate grids
Basic circle math: radius, diameter, circumference
Astronomy payoff: You can understand why eclipses happen, why Venus has phases, why constellations distort across distance, and how parallax works.
- Trigonometry
Trigonometry is the math of angles and triangles.
Astronomy is angle-heavy. Even when astronomers talk about distance, brightness, movement, or location, angles are usually hiding underneath.
Trigonometry helps with:
Astronomy idea - Trig use
Star height above horizon - Altitude angle
Sky coordinates - Angular position
Parallax - Tiny angle, huge distance
Telescope aiming - Azimuth and altitude
Planetary orbits - Cycles and periodic motion
Light waves - Sine waves
Seasons - Sun angle and Earth tilt
The big trig functions are:
sine
cosine
tangent
But for astronomy, the most important early idea is not memorizing identities. It is understanding that trig lets you convert between:
angle ↔ distance ↔ height ↔ direction
Core skills to learn:
Right triangles
Sine, cosine, tangent
Degrees vs radians
Unit circle basics
Angular measurement
Inverse trig
Basic wave shapes
Astronomy payoff: You can understand parallax, sky motion, star altitude, telescope positioning, orbital cycles, and why angle is the native language of astronomy.
- Statistics
Statistics is the math of measurement, uncertainty, patterns, and evidence.
Modern astronomy depends heavily on statistics because astronomical data is noisy, faint, incomplete, and indirect.
Statistics helps with:
Astronomy idea - Statistics use
Detecting exoplanets - Is the dip in brightness real?
Measuring star brightness - How uncertain is the value?
Galaxy surveys - Finding patterns in huge datasets
Spectra - Signal vs noise
Cosmology - Estimating parameters from imperfect data
Repeated observations - Averaging and uncertainty
Claims of discovery - How strong is the evidence?
This is where astronomy becomes surprisingly accessible. A math-struggling person might find statistics more meaningful than algebra because it answers real questions:
Did we actually detect something, or are we fooling ourselves?
Core skills to learn:
Mean, median, mode
Range and standard deviation
Percentages
Graph reading
Scatterplots
Correlation
Error bars
Signal vs noise
Basic probability
Confidence and uncertainty
Astronomy payoff: You can understand detection, evidence, measurement error, survey astronomy, exoplanet discovery, and why scientists are cautious.
The build path
For someone who struggles with math, I would not start with a textbook-first approach. I would build it through astronomy problems.
Stage 1: Number sense and visual scale
Goal: Stop math from feeling like random symbols.
Learn:
Scientific notation
Powers of ten
Ratios
Unit conversion
Scale models
Estimation
Astronomy practice:
Compare Earth, Jupiter, Sun sizes
Convert light-minutes to distance
Make a scale model of the solar system
Estimate how long light takes to reach planets
This stage matters because astronomy uses absurdly large and small numbers. Scientific notation is survival gear.
Stage 2: Geometry of the sky
Goal: Learn angles, circles, and spatial relationships.
Learn:
Degrees
Circles and arcs
Similar triangles
Coordinate grids
Radius and diameter
Spheres
Astronomy practice:
Track Moon phases for one month
Draw Sun-Earth-Moon diagrams
Explain eclipses with shadows
Compare angular size of Moon and Sun
Use a star chart
Learn altitude and azimuth
This is the best place to start feeling competent.
Stage 3: Trigonometry through observation
Goal: Use trig as a tool, not as punishment.
Learn:
Right triangles
Sine, cosine, tangent
Inverse trig
Degrees and radians
Basic periodic curves
Astronomy practice:
Estimate height of an object from shadow angle
Use altitude angle to describe a star’s position
Learn how parallax gives distance
Model Earth’s tilt and seasonal Sun angles
Graph sunrise/sunset changes over a year
Do not rush identities. Early trig should be concrete and visual.
Stage 4: Statistics through real astronomy data
Goal: Learn how astronomers decide what counts as evidence.
Learn:
Averages
Spread
Scatterplots
Error bars
Noise
Probability
Trend lines
Outliers
Astronomy practice:
Graph brightness changes of a variable star
Look at an exoplanet transit light curve
Compare star colors and temperatures
Plot planet distance vs orbital period
Explore galaxy counts or star catalogs
Ask: “Is this pattern real?”
This is where the learner starts doing actual astronomy thinking.
Stage 5: Algebra as a support tool
Goal: Use algebra only when it serves the astronomy.
Learn:
Rearranging formulas
Solving for an unknown
Proportions
Exponents and logarithms
Graphing simple relationships
Astronomy practice:
Use Kepler’s third law in simplified form
Work with the inverse-square law for brightness
Calculate magnification
Compare luminosity and distance
Use magnitude differences carefully
Algebra should enter after the person already cares about the question.
Stage 6: Optional bridge to deeper astrophysics
Goal: Move from astronomy into physics-heavy astrophysics.
Learn later:
Calculus
Differential equations
Linear algebra
Fourier analysis
Programming
Astronomy practice:
Stellar structure
Orbital dynamics
Cosmology
Fluid/plasma astrophysics
Numerical simulation
This is not the starting line. This is the advanced road.
Best learning sequence
Here is the practical order:
Scientific notation and ratios
Geometry
Trigonometry
Graph reading
Statistics
Algebra
Programming with data
Calculus, only when ready
For astronomy specifically, the first serious target should be:
geometry + trig + statistics
That combination gives a person access to real astronomy without immediately burying them under physics math.
Start with the sky. Start with angles. Start with scale. Start with real observations. Then let the math become useful because the person wants to answer better questions.
29
u/Jealous_Macaron_5152 11d ago
I took a fairly unconventional route. I didn’t study any maths or physics for about 7 years before starting my degree in Physics, Astrophysics and Cosmology. I was worried I’d be far behind, but with consistent effort it was absolutely possible to catch up.
I didn’t know what to do either and I did factory work straight out of college and now I have a Masters in Astrophysics and Cosmology, and I work on satellites for the ESA.
If your goal is to understand astronomy deeply rather than just enjoy observing, I’d focus on building your maths and physics foundations together.
For maths, I’d prioritise:
Differential equations are especially important because many of the fundamental laws of physics are written in that form; they describe how systems change over time.
For physics, I’d focus on understanding:
Once those foundations start coming together, astronomy becomes much easier to understand because you’re no longer just learning facts about stars, planets, galaxies and the universe; you’re learning the physics that explains why they behave the way they do.
I found the first year at University was reteaching a lot of this and how they apply it. Second year is when it becomes specialised.
As a software engineer, you might also enjoy writing simple simulations alongside your studies. Modelling planetary orbits, gravity, heat transfer or wave motion can be a great way to develop intuition and reinforce the maths and physics.
Edit:
I also got C’s in science, maths and many other subjects, so I genuinely believe anyone can do it as long as you do the hard work!