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Problem sets

44 problems across 8 topics. Each one opens with a hint you can ignore and a solution you can hide.

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Interactive star mapsSky-coordinate questions get easier once you can picture the sphere. Open the 25 key constellations, their asterisms and a clickable planisphere.Data analysis study guideThe IOAA data round has its own skills: error bars, linearising, least squares, periods and O−C diagrams. Learn them chapter by chapter, with fitting tools to check your work.

Spherical Astronomy & Coordinates

2

Equatorial, horizontal and ecliptic coordinates, sidereal time, precession, and the geometry of the celestial sphere. The foundation every other topic leans on.

Which stars never set?IntroductoryWhy the sidereal day is shorterIntermediate

Celestial Mechanics & Orbits

2

Newtonian gravity, Kepler's three laws, the vis-viva equation, binary star systems, escape velocity and Hohmann transfers.

Total mass of a visual binaryIntroductoryHohmann transfer to MarsAdvanced

Stellar Astrophysics

2

Luminosity and flux, the magnitude system, Stefan-Boltzmann and Wien's laws, the HR diagram, hydrostatic equilibrium, nuclear timescales and stellar endpoints.

Distance modulus of a CepheidIntroductoryRadius of a red supergiantIntermediate

Planetary Science

2

Equilibrium temperatures, Roche limits, tidal forces, atmospheric escape, transit and radial-velocity detection of exoplanets.

Equilibrium temperature of an exoplanetIntermediateReading a transit light curveAdvanced

Observational Astronomy & Photometry

2

Aperture and focal ratio, angular resolution, limiting magnitude, signal-to-noise, atmospheric extinction, CCD photometry and spectral analysis.

Resolving a double starIntroductoryAtmospheric extinction and airmassIntermediate

Galactic & Extragalactic Astronomy

2

Galactic rotation and Oort constants, the interstellar medium, galaxy classification, distance ladders, active galactic nuclei and dark matter evidence.

Dark matter from a flat rotation curveAdvancedDo stars collide when galaxies merge?Intermediate

Cosmology

20

Hubble's law, redshift and lookback time, the Friedmann equations, critical density, the cosmic microwave background and Big Bang nucleosynthesis.

Hubble time and the age of the UniverseIntroductoryRecombination and the CMBAdvancedCritical density of the UniverseAdvancedThree distances to a quasarAdvancedLookback time in a matter universeAdvancedMatter radiation equalityAdvancedTolman surface brightness dimmingAdvancedStretched supernova light curvesAdvancedThe angular size minimumAdvancedWhen does the Hubble flow win?AdvancedWhen did acceleration begin?AdvancedOur motion through the CMBAdvanced13.1 | The CMB horizon and the end of inflationAdvanced13.2 | A supernova distance and the Hubble timeAdvanced13.3 | Dark matter versus vacuum energy at recombinationAdvanced13.4 | Neutrinos and the critical densityAdvanced13.5 | Estimating a quasar's distanceAdvanced13.6 | When did a distant galaxy form its stars?Advanced13.7 | CMB temperature as a function of redshiftAdvanced13.8 | How long until the Universe cools by 0.1 K?Advanced

Data Analysis

12

Real data from past IOAA data analysis rounds: plotting by hand, linearising, least squares fitting, error propagation, periods and phases, photometry and radial velocities. The full study guide lives on the Data Analysis page.

2007 Q2 | The Moon's age on Einstein's birthdayIntermediate2015 P1 | Distance to the Cepheid HV 2257Olympiad2015 P2 | The extinction law and the distance to IC 342Advanced2016 D1 | Timing a binary millisecond pulsarOlympiad2016 D2 | The Moon's size, orbit and the distance to the SunAdvanced2016 D3 | Stretching Type Ia supernova light curvesAdvanced2017 D1 | Calibrating the distance ladder to the LMCAdvanced2017 D2 | Dark matter in a low surface brightness galaxyOlympiad2018 D1 | Dust and young stars: the IRX–β relationAdvanced2018 D2 | An unseen companion in AurigaOlympiad2023 DA1 | Distance to the LMC from eclipsing binariesAdvanced2023 DA2 | Weighing an isolated black hole with astrometric microlensingOlympiad
Difficulty scale:IntroductoryIntermediateAdvancedOlympiad