Question

Calculate the approximate age of the universe from the average value of the Hubble constant, H₀=20km/s⋅Mly. To do this, calculate the time it would take to travel 1 Mly at a constant expansion rate of 20 km/s.

(a)1×10¹⁰years
(b)1.5×10¹⁰years
(c)2×10¹⁰years
(d)2.5×10¹⁰years

Answer 1

The approximate age of the universe using the given value of the Hubble constant H₀ = 20 km/s·Mly is 1.5 × 10¹⁰ years, considering a constant rate of expansion. If deceleration is considered, the actual age would be older.

Step-by-step explanation:

To calculate the approximate age of the universe from the average value of the Hubble constant, H₀ = 20 km/s·Mly, we can determine the time it would take to travel 1 million light-years (Mly) at a constant expansion rate of 20 km/s. The Hubble time is the reciprocal of the Hubble constant, or 1/H. Hence, the age of the universe can be estimated as follows:

Age of the universe (in seconds) = = 1 Mly / (20 km/s)

Converting 1 Mly into kilometers, we have:

1 Mly = 9.461 × 1015 km

Therefore, the age of the universe in seconds is:

9.461 × 1015 km / (20 km/s) = 4.7305 × 1014 s

Now, converting seconds to years (using 1 year = 3.154 × 107 seconds), we find the age to be:

4.7305 × 1014 s / 3.154 × 107 s/year = 1.5 × 1010 years

This calculation provides an approximation because it assumes the rate of expansion has been constant over time. The correct answer to the question is (b) 1.5× 1010 years.

However, if deceleration is taken into account, the actual age of the universe would be greater because the universe would have expanded more slowly in the past than what is suggested by a constant rate of expansion.