Based on estimates using Hubble's Law and the expanding universe, what is the approximate age of the universe?

Question

BlackTom AI · Accepted Answer

Hubble's Law relates recessional velocity v to distance d by v = H0 d, so the inverse of the Hubble constant H0 gives a characteristic timescale (the Hubble time) that estimates the universe's age.

1) Relevant knowledge points and concepts
- Hubble's Law and the Hubble constant H0 (units of velocity per distance).
- The Hubble time tH ≈ 1/H0 is a first-order estimate of the universe's age under steady expansion.
- Unit conversion is required to convert H0 into s^-1 and then into years.
- More detailed cosmological models (ΛCDM) slightly modify this number (giving ≈13.8 Gyr), but 1/H0 gives an excellent approximate value.

2) Step-by-step reasoning
- Choose a representative H0 value used in modern estimates: H0 ≈ 70 km s^-1 Mpc^-1.
- Convert H0 to inverse seconds, then invert to get time in seconds, and convert seconds to years.

3) Calculations (all intermediate steps)
- H0 = 70 km s^-1 Mpc^-1 = 70,000 m s^-1 per 3.0857 × 10^22 m
- H0 (s^-1) = 70,000 / (3.0857 × 10^22) = 2.2685 × 10^-18 s^-1
- Hubble time tH = 1 / H0 = 1 / (2.2685 × 10^-18) = 4.408 × 10^17 s
- Seconds per year ≈ 3.15576 × 10^7 s
- tH (years) = 4.408 × 10^17 / 3.15576 × 10^7 ≈ 1.397 × 10^10 years ≈ 14 billion years

4) Why the correct answer is correct
The inverse of the measured Hubble constant yields this timescale; using the contemporary measured H0 produces ≈14 billion years. More sophisticated cosmological fits (including matter, radiation and dark energy) refine this to ~13.8 billion years, consistent with the 14 billion-year choice.

5) Why the other options are incorrect
- 500 million years: far too small; would require an H0 an order of magnitude larger than observed.
- 100 years and 6,000 years: astronomically impossible given observed galactic recessional velocities and redshifts; these imply absurdly large H0 values inconsistent with measurements.

6) Conclusion
The approximate age derived from Hubble's Law and current H0 measurements is about 14 billion years, which matches the provided correct answer: 14 billion years old.

Based on estimates using Hubble's Law and the expanding universe, what is the approximate age of the universe?单项选择题

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