Constants and data
In the theory and data-analysis rounds each contestant is given a table of constants, and a problem may also give values of its own. When a problem gives a value, we use that one. The first two tables below reproduce the official IOAA 2025 data sheet, with its quantities in the same order. When we checked in September 2026, no separate sheet for 2026 had been published. The sheet in a future exam may differ in the last figure or have a few more rows.
We checked each value against the CODATA 2018 constants and the values the International Astronomical Union adopted for the Sun and the planets. Almost all the values on the sheet also agree with each other. The Sun's luminosity spread over a sphere of radius 1 au gives the solar constant of 1361 W m−2, and its luminosity and radius give an effective temperature of 5772 K.
There are two small differences. The gas constant is 8.314 J mol−1 K−1 to four figures, and the sheet's 8.315 is probably an older value, 8.3145, rounded up. The Sun's absolute V magnitude worked out from the sheet's apparent magnitude of −26.74 and a distance of 1 au is 4.83, while the sheet prints 4.82. The course uses 4.83. A difference of 0.01 magnitudes is far smaller than the uncertainty of any answer in the exam.
| Quantity | Symbol | Value | Used in |
|---|---|---|---|
| Avogadro constantNA, Section 3.10 | NA | 6.022 × 1023 mol−1 | Section 3.10 |
| Boltzmann constantkB, Section S4 | kB | 1.381 × 10−23 J K−1 | Section S4 |
| Elementary chargee, Section S4 | e | 1.602 × 10−19 C | Section S4 |
| Planck constanth, Section S4 | h | 6.626 × 10−34 J s | Section S4 |
| Speed of lightc, Section S4 | c | 2.998 × 108 m s−1 | Section S4 |
| Gravitational constantG, Section S4 | G | 6.674 × 10−11 N m2 kg−2 | Section S4 |
| Universal gas constantR | R | 8.315 J mol−1 K−1 | |
| Stefan–Boltzmann constantσ, Section 4.6 | σ | 5.670 × 10−8 W m−2 K−4 | Section 4.6 |
| Wien displacement constantb, Section 4.6 | b | 2.898 × 10−3 m K | Section 4.6 |
| Permittivity of free spaceε0 | ε0 | 8.854 × 10−12 m−3 kg−1 s4 A2 | |
| Permeability of free spaceμ0 | μ0 | 1.257 × 10−6 N A−2 | |
| Electron massme, Section 4.9 | me | 9.109 × 10−31 kg | Section 4.9 |
| Proton massmp, Section S4 | mp | 1.673 × 10−27 kg | Section S4 |
| Neutron massmn, Section 13.8 | mn | 1.675 × 10−27 kg | Section 13.8 |
| Deuteron massmD, Section 13.8 | mD | 3.344 × 10−27 kg | Section 13.8 |
| Helium nucleus massmHe, Section 13.8 | mHe | 6.645 × 10−27 kg | Section 13.8 |
| Quantity | Symbol | Value | Used in |
|---|---|---|---|
| Mass of the SunM⊙, Section S4 | M⊙ | 1.988 × 1030 kg | Section S4 |
| Radius of the SunR⊙, Section 4.6 | R⊙ | 6.957 × 108 m | Section 4.6 |
| Luminosity of the SunL⊙, Section 4.1 | L⊙ | 3.828 × 1026 W | Section 4.1 |
| Effective temperature of the SunTeff,⊙, Section 4.6 | Teff,⊙ | 5772 K | Section 4.6 |
| Apparent V magnitude of the SunmV,⊙, Section 4.2 | mV,⊙ | −26.74 | Section 4.2 |
| Absolute V magnitude of the SunMV,⊙, Section 4.3 | MV,⊙ | +4.82 | Section 4.3 |
| Apparent bolometric magnitude of the Sunmbol,⊙, Section 4.7 | mbol,⊙ | −26.83 | Section 4.7 |
| Absolute bolometric magnitude of the SunMbol,⊙, Section 4.7 | Mbol,⊙ | +4.74 | Section 4.7 |
| Solar constant above the atmosphereS, Section 4.1 | S | 1361 W m−2 | Section 4.1 |
| Apparent angular diameter of the Sunθ⊙, Section 1.1 | θ⊙ | about 32 arcmin | Section 1.1 |
| Mass of EarthMEarth, Section S4 | MEarth | 5.972 × 1024 kg | Section S4 |
| Radius of EarthREarth, Section S4 | REarth | 6.378 × 106 m | Section S4 |
| Tilt of Earth’s axisε, Section 1.6 | ε | 23° 26′ | Section 1.6 |
| Inclination of the Moon’s orbit to the eclipticSection O1.7 | 5° 8′ 43″ | Section O1.7 | |
| Mass of JupiterMJ, Section S4 | MJ | 1.898 × 1027 kg | Section S4 |
| Radius of JupiterRJ, Section S4 | RJ | 6.991 × 107 m | Section S4 |
| Astronomical unitau, Section 1.1 | au | 1.496 × 1011 m | Section 1.1 |
| Parsecpc, Section 1.1 | pc | 3.086 × 1016 m | Section 1.1 |
| Light-yearly | ly | 9.461 × 1015 m | |
| JanskyJy, Section 4.4 | Jy | 10−26 W m−2 Hz−1 | Section 4.4 |
| Tropical yearSection 2.1 | 365.2422 solar days | Section 2.1 | |
| Sidereal yearSection 2.1 | 365.2564 solar days | Section 2.1 | |
| Precession of the March equinoxSection 2.7 | 1° in 71.6 years | Section 2.7 |
| Quantity | Symbol | Value | Used in |
|---|---|---|---|
| Sidereal daySection 2.1 | 23 h 56 min 4.09 s | Section 2.1 | |
| Sidereal monthSection 2.1 | 27.32 days | Section 2.1 | |
| Synodic monthSection 2.1 | 29.53 days | Section 2.1 | |
| Obliquity of the eclipticε, Section 1.6 | ε | 23.44° | Section 1.6 |
| Arcseconds in a radianSection S3 | 206 265 | Section S3 | |
| Mass of the MoonMMoon, Section S4 | MMoon | 7.342 × 1022 kg | Section S4 |
| Radius of the MoonRMoon, Section S4 | RMoon | 1.737 × 106 m | Section S4 |
| Mean distance of the MoonSection S4 | 3.844 × 108 m | Section S4 | |
| Atomic mass unitu, Section 3.10 | u | 1.661 × 10−27 kg | Section 3.10 |
| ElectronvolteV, Section S4 | eV | 1.602 × 10−19 J | Section S4 |
| Frequency of the 21 cm line of hydrogenν0, Section S4 | ν0 | 1420.406 MHz | Section S4 |
| Absolute V magnitude of the SunMV,⊙, Section 4.3 | MV,⊙ | +4.83 | Section 4.3 |
| Ratio of total to selective extinctionRV, Section 4.7 | RV | 3.1 | Section 4.7 |
| Hubble constant of the course modelH0, Section 13.1 | H0 | 70 km s−1 Mpc−1 | Section 13.1 |
| Density of matter in the course modelΩm, Section 13.4 | Ωm | 0.3 | Section 13.4 |
| Density of dark energy in the course modelΩΛ, Section 13.4 | ΩΛ | 0.7 | Section 13.4 |
| Temperature of the cosmic microwave backgroundT0, Section 13.7 | T0 | 2.725 K | Section 13.7 |
The last table lists the values that the sections use but the sheet does not give. The Hubble constant and the densities are those of the model of the Universe used throughout Chapter 13, and a problem in the exam usually gives its own. Where a problem does not, the official solution may have assumed a different value, so an answer should state the value it uses. The sheet gives the tilt of Earth's axis as 23° 26′, and the course uses 23.44°, which is the same angle to the nearest arcminute.