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Astronomy calculator: light time, magnitudes and redshift

Light travel time for any distance, apparent and absolute magnitude from the distance modulus, and redshift to recession velocity (relativistic Doppler).

更新于 已验证的示例：9

试一试
Light travel time
8 min 19 s
Light travel time: 8 min 19 s
Light travel time
8.31675min
Distance
149,598,000km

Light from the Sun takes 8 min 19 s to reach us — we see it as it was that long ago.

Light travel time (log₁₀ seconds)

secondsminutes–hoursdaysyearsthousands to billions of years-11.84.97.510.517MoonSunProxima CenAndromeda8 min 19 s
计算方法 S

  1. Distance in metres

    d=149,598,000,000 md = 149{,}598{,}000{,}000\ \mathrm{m}

  2. Divide by the speed of light

    t=dc=149,598,000,000299 792 458=499.005 s=0.0000158125 yrt = \frac{d}{c} = \frac{149{,}598{,}000{,}000}{299\,792\,458} = 499.005\ \mathrm{s} = 0.0000158125\ \mathrm{yr}

    Years here are Julian years (365.25 d), the unit that defines the light-year.

关于Astronomy calculator: light time, magnitudes and redshift

Light travel time is the distance divided by the exact speed of light, 299,792,458 m/s. The distance modulus, m − M = 5 log₁₀(d/10 pc) + A, links a star's apparent magnitude m, its absolute magnitude M (how bright it would look from 10 parsecs), its distance d and the dimming A by dust; give any two of m, M and d to get the third. Redshift z converts to velocity with the relativistic Doppler formula 1 + z = √((1 + β)/(1 − β)), where β = v/c.

The default shows sunlight taking 8 min 19 s to cross 1 au (149,597,870.7 km), so we see the Sun as it was that long ago. Sirius, at apparent magnitude −1.46 and 2.64 parsecs, has absolute magnitude 1.43; from the same distance the Sun would shine at magnitude 1.94.

The Doppler formula treats redshift as motion through space. Beyond z ≈ 0.1 a galaxy's redshift comes mainly from cosmic expansion, so the velocity shown is not its recession speed and its distance needs a cosmological model.

计算示例

Sunlight takes about 8 min 19 s

Calculate
Light travel time
Distance to
Sun
Light travel time
8.31675 min
Distance
149,598,000 km

核验来源：Python 3.8 decimal: 149597870700 m / 299792458 m/s = 499.00478 s (IAU au, exact c)

Moon: 1.28 light-seconds

Calculate
Light travel time
Distance to
Moon
Light travel time
1.28 s

核验来源：Python 3.8 decimal: 384400 km / c = 1.2822204 s

One light-year takes one Julian year

Calculate
Light travel time
Distance to
Enter a distance
Distance
1 ly
Light travel time
1 year

核验来源：IAU definition: 1 ly = c × 365.25 d

Apparent magnitude of the Sun

Calculate
Magnitudes
Solve for
Apparent m
Absolute magnitude M
4.83
Distance
1 au
Apparent magnitude m
-26.742
Distance modulus m − M
-31.572

核验来源：Python 3.8 decimal: 4.83 + 5 log₁₀(4.848137e-6/10) = −26.742 (observed −26.74)

常见问题

How long does light take to reach Earth from the Sun?

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.

What is the difference between apparent and absolute magnitude?

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.

How do you calculate distance from magnitudes?

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.

How do you convert redshift to velocity?

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.

How far is a light-year?

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.

“Astronomy calculator: light time, magnitudes and redshift”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：9。 例如，“Sunlight takes about 8 min 19 s”根据Python 3.8 decimal: 149597870700 m / 299792458 m/s = 499.00478 s (IAU au, exact c)进行核验。

这种方法出自哪里？

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.

关于此计算器

t=dc;m−M=5log⁡10d10 pc+A;1+z=1+β1−β, β=vct = \frac{d}{c};\qquad m - M = 5\log_{10}\frac{d}{10\ \mathrm{pc}} + A;\qquad 1 + z = \sqrt{\frac{1 + \beta}{1 - \beta}},\ \beta = \frac{v}{c}

来源

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

已对照来源验证

此计算器包含 9 个已解示例，答案来自独立来源。这些示例会在测试套件中运行，你也可以在此运行验证。

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