Know that the current estimate for H_0 is 2.2 × 10^-18 per second

6.2.3 The Universe 🌌

Overview

The universe is expanding, meaning galaxies are moving away from each other. The rate of this expansion is described by the Hubble constant ($H_0$). Knowing its value helps us understand the age and size of the universe.

Hubble’s Law

Hubble’s Law states that the recessional velocity ($v$) of a galaxy is directly proportional to its distance ($d$) from us: $$v = H_0 \times d$$

The Hubble Constant ($H_0$)

$H_0$ is measured in units of inverse seconds. The current best estimate is: $$H_0 \approx 2.2 \times 10^{-18}\ \text{s}^{-1}$$ This means that for every second, the distance between two galaxies increases by $2.2 \times 10^{-18}$ times their current separation.

Analogy: The Expanding Rubber Sheet 🚀

Picture a rubber sheet with dots representing galaxies. If you slowly stretch the sheet, the dots move apart. The speed at which they separate depends on how far apart they already are—just like the universe’s expansion.

Example Calculation

Suppose a galaxy is 10 million light‑years away. First, convert light‑years to meters:

• 1 light‑year ≈ $9.46 \times 10^{15}$ m
• 10 million light‑years ≈ $9.46 \times 10^{22}$ m

1. Use $v = H_0 \times d$
2. $v = (2.2 \times 10^{-18}\ \text{s}^{-1}) \times (9.46 \times 10^{22}\ \text{m})$
3. $v \approx 2.08 \times 10^{5}\ \text{m/s}$
4. So the galaxy is moving away at about 208 km/s.

Table of Hubble Constant Estimates

Summary

- The universe is expanding, described by Hubble’s Law. - The Hubble constant $H_0$ is currently estimated at $2.2 \times 10^{-18}\ \text{s}^{-1}$. - This value tells us how fast galaxies recede from each other per unit distance. - Using $H_0$, we can estimate the age of the universe (~13.8 billion years) and predict future expansion.