Astronomy calculator: light time, magnitudes and redshift

How long does light take to travel a distance?

Divide the distance by the speed of light, exactly 299,792,458 m/s: t = d/c. Sunlight crosses 1 astronomical unit (149,597,870.7 km) in 499.005 s, about 8 min 19 s, and moonlight takes 1.28 s from 384,400 km. A light-year is one Julian year of light travel.

Light travel times from the Moon to Andromeda

• Moon, 384,400 km: 1.28 seconds
• Sun, 1 au: 8 minutes 19 seconds
• Proxima Centauri, 4.2465 light-years: 4.2465 years
• Galactic center, 8,178 parsecs: 26,673 years
• Andromeda galaxy, 765,000 parsecs: about 2.5 million years

The travel time is also the age of the light, so you see the Sun as it was 8 min 19 s ago. That figure is for the mean distance of 1 au; Earth sits slightly closer to the Sun in January and farther in July.

The distances come from NASA's Moon fact sheet, the IAU astronomical unit, Gaia DR3 for Proxima Centauri, the GRAVITY collaboration's 2019 Galactic-center measurement and NASA/ESA's figure of about 765 kpc for Andromeda.

Light-years, parsecs and astronomical units

• 1 astronomical unit = 149,597,870.7 km exactly (IAU 2012).
• 1 light-year = 9,460,730,472,580.8 km, the distance light travels in 365.25 days.
• 1 parsec = 648,000/π au = 206,264.8 au = 3.26156 light-years (IAU 2015).

A parsec is the distance at which 1 au spans one arcsecond, which is why parallax distances come out in parsecs.

How to find distance from apparent and absolute magnitude

Apparent magnitude m is how bright an object looks from Earth. Absolute magnitude M is how bright it would look from 10 parsecs. The distance modulus links them: m − M = 5 log₁₀(d / 10 pc) + A, where A is dimming by dust.

Solved for distance, d = 10^((m − M − A + 5)/5) parsecs. A star with m − M = 10 and no dust lies 10³ = 1,000 pc away, about 3,261.56 light-years.

The scale runs backward and is logarithmic: five magnitudes is a factor of exactly 100 in brightness, so one magnitude is 100^(1/5) ≈ 2.512 (OpenStax).

The same equation works in reverse. The Sun, M = 4.83, seen from 1 au (4.848 × 10⁻⁶ pc) has m = 4.83 + 5 log₁₀(4.848 × 10⁻⁶ ÷ 10) = −26.74, its observed brightness.

How dust extinction changes the distance

Interstellar dust dims starlight, adding A magnitudes to m. Leave it out and every magnitude of dimming is read as extra distance.

With m − M = 10, one magnitude of extinction brings the distance down from 1,000 pc to 631 pc. Setting A to zero would overstate that distance by 58%.

Extinction depends on the line of sight and on the photometric band, so use a value measured for your object in the same band as m and M.

How to convert redshift to velocity

Redshift is the fractional stretch of a wavelength: z = (λ_observed − λ_emitted)/λ_emitted. A line emitted at 500 nm and observed at 550 nm has z = 0.1.

For motion along the line of sight, the relativistic Doppler formula gives β = ((1 + z)² − 1)/((1 + z)² + 1) and v = βc. At z = 0.1, β = 0.0950 and v = 28,487 km/s.

The shortcut v = cz gives 29,979 km/s, 5% too high. At z = 0.01 the two differ by only 0.5% (2,983 against 2,998 km/s), but at z = 1 the shortcut says c while the Doppler formula gives 0.6c.

Negative z is a blueshift from an approaching source: z = −0.1 means 31,470 km/s toward you. In reverse, a source receding at 0.5c shows z = √3 − 1 = 0.732 (OpenStax).

Beyond z ≈ 0.1, a galaxy's redshift comes mainly from the expansion of space. Its Doppler velocity is then not its recession speed, and its distance needs a cosmological model such as ΛCDM with a value of H₀.

Light time, distance and redshift results

Default is sunlight over 1 au, and Moon is 384,400 km. One light-year is a typed distance of 1 ly. Distance modulus ten uses m = 10 and M = 0 with no dust, and Doppler z1 is a redshift of 1.

Common mistakes

• Reading a light-year as a time. It is a distance of about 9.46 trillion km.
• Assuming a bigger magnitude is brighter. Magnitude 1 is 2.512 times brighter than magnitude 2.
• Mixing photometric bands. Compare m and M in the same band; the Sun's 4.83 is a visual (V) magnitude.
• Using v = cz at large redshift. It overshoots, reaching c at z = 1.

Units and conventions

• Light-time distances accept km, au, light-years, parsecs and miles; magnitude distances accept pc, ly and au.
• Light travel in years uses Julian years of 365.25 days, the unit that defines the light-year.
• Extinction A is in magnitudes and is added to the apparent magnitude.
• Velocities can be in km/s, m/s or fractions of c, and must stay below c.

For orbital speeds and periods around a planet or star, use the gravity and orbit calculator. To turn an observed wavelength into frequency or photon energy, use the wavelength, frequency and energy calculator.