Astronomy calculator: light time, magnitudes and redshift

8 minutes 19 seconds on average (499.0 s): 1 astronomical unit is exactly 149,597,870,700 m (IAU 2012) and light travels exactly 299,792,458 m/s. Earth's distance from the Sun varies from about 147.1 to 152.1 million km, so the delay ranges from roughly 8 min 11 s in January to 8 min 27 s in July. Moonlight takes 1.28 s.

Apparent magnitude m is how bright a star looks from Earth; absolute magnitude M is how bright it would look from a standard 10 parsecs (32.6 light-years). The scale runs backwards and is logarithmic: 5 magnitudes is exactly a factor of 100 in brightness, so 1 magnitude is 100^(1/5) ≈ 2.512 times. The Sun is m = −26.74 from Earth but only M = 4.83.

d = 10^((m − M − A + 5)/5) parsecs, the distance modulus solved for d. A star with m − M = 10 and no dust lies at 10³ = 1,000 pc, about 3,262 light-years. Every 5 magnitudes of difference multiplies the distance by 10; Cepheid variables and Type Ia supernovae, whose absolute magnitudes are known, are measured this way.

Use the relativistic Doppler formula, β = ((1 + z)² − 1)/((1 + z)² + 1), then v = βc. At z = 0.1 that gives 28,487 km/s, 5% below the simple estimate cz = 29,979 km/s, and at z = 1 it gives 0.6c, not c. For distant galaxies the redshift is cosmological, so a Hubble-law or ΛCDM calculation replaces this formula.

9,460,730,472,580.8 km, the distance light travels in one Julian year of 365.25 days, as defined by the IAU. A parsec is 3.2616 light-years, or 648,000/π astronomical units (IAU 2015 Resolution B2). Proxima Centauri, the nearest star after the Sun, is 4.2465 light-years away, so its light is 4.25 years old when it arrives.

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 9 worked examples whose answers come from independent sources; for example, “Sunlight takes about 8 min 19 s” is checked against Python 3.8 decimal: 149597870700 m / 299792458 m/s = 499.00478 s (IAU au, exact c).

IAU 2012 B2 (astronomical unit), IAU 2015 B2 (parsec = 648000/π au); c exact (SI); OpenStax Astronomy 2e, §17.1 The brightness of stars (magnitudes) and §19.1 Fundamental measures of distance; OpenStax University Physics Volume 3, §5.7 Doppler effect for light.