Define the Hubble constant H_0 as the ratio of the speed at which the galaxy is moving away from the Earth to its distance from the Earth; recall and use the equation H_0 = v / d

6.2.3 The Universe 🚀

What is the Hubble Constant?

The Hubble constant, written as \$H_0\$, tells us how fast galaxies are moving away from us for each unit of distance. It’s a simple ratio:

\$H_0 = \frac{v}{d}\$

Where \$v\$ is the galaxy’s recessional speed (km s⁻¹) and \$d\$ is its distance from Earth (Mpc).

Analogy: Imagine a balloon with stickers on it. As you blow up the balloon, the stickers move apart. The farther a sticker is from the center, the faster it moves away. That’s exactly what happens with galaxies in our expanding universe.

Using the Formula – A Quick Example

  1. Galaxy A is 10 Mpc away.

  2. Its observed recessional velocity is 1000 km s⁻¹.

  3. Plug into the formula: \$H_0 = \frac{1000}{10} = 100\$ km s⁻¹ Mpc⁻¹.

Table of Sample Galaxies

GalaxyDistance (Mpc)Velocity (km s⁻¹)\$H_0\$ (km s⁻¹ Mpc⁻¹)
Galaxy A101000100
Galaxy B202500125
Galaxy C5600120

Exam Tip: Always check that \$v\$ and \$d\$ are in the same units before dividing. If you mix km s⁻¹ with light‑years, you’ll get a wrong answer. Convert distances to Mpc (1 Mpc ≈ 3.26 million light‑years) if needed.

Key Takeaway

The Hubble constant is a cornerstone of modern cosmology. It links the speed of a galaxy’s recession to how far away it is, giving us a measure of how fast the universe is expanding. Remember: \$H_0 = v/d\$ – simple, powerful, and always a good starting point for exploring the cosmos. 🌌