If the universe has been expanding at a constant rate, then the age can be estimated as $t
Astrophysics & Cosmology - OCR A-Level Physics
- If the universe has been expanding at a constant rate, then the age can be estimated as $t \approx 1/$H_0.
- This is because $v = H_{0} d$ and $d = vt$, so $t = d/v = 1/H_{0}$.
- Using $H_0 \approx 70$ km $s^{-1}$ $Mpc^{-1}$: convert to SI units first.
- 1 Mpc = $3.086 \times 10^{22}$ m, so H_0 = $70 \times $\(10^{3}\)$ / ($3.086 \times \(10^{22}\)$) = $2.27 \times \(10^{-18}\)$ $\(s^{-1}\)$.
- t = 1/H_0 = 1/($2.27 \times 10^{-18}$) = $4.4 \times 10^{17}$ $s \approx 14$ billion years.
- This is an overestimate if the expansion has been decelerating (gravity slowing it down) or an underestimate if it has been accelerating (dark energyThe capacity to do work. Measured in joules (J).).
- CurrentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). best estimate: the universe is approximately 13.8 billion years old.
Common Mistake
MEDIUM
Wrong: Forgetting to convert H_0 from km \(s^{-1}\) Mpc^{-1} to \(s^{-1}\) before calculating 1/H_0.
Right: 1/H_0 only gives the age in seconds if H_0 is in \(s^{-1}\). You must convert: 1 Mpc = 3.086 \times \(10^{22}\) m and $km = 10^3 m$.
Right: 1/H_0 only gives the age in seconds if H_0 is in \(s^{-1}\). You must convert: 1 Mpc = 3.086 \times \(10^{22}\) m and $km = 10^3 m$.