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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).

Cập nhật Ví dụ đã kiểm tra: 9

Thử
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
Cách tính 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.

Giới thiệu 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.

Ví dụ có lời giải

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

Nguồn đối chiếu: 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

Nguồn đối chiếu: 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

Nguồn đối chiếu: 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

Nguồn đối chiếu: Python 3.8 decimal: 4.83 + 5 log₁₀(4.848137e-6/10) = −26.742 (observed −26.74)

Câu hỏi

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” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 9. Ví dụ, “Sunlight takes about 8 min 19 s” được kiểm tra bằng Python 3.8 decimal: 149597870700 m / 299792458 m/s = 499.00478 s (IAU au, exact c).

Phương pháp này lấy từ đâu?

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.

Về công cụ tính này

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}

Nguồn

  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

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