Hubble's law — the expansion of the Universe

What just happened?

You doubled the galaxy's distance, and its recession velocity doubled as well. The farther a galaxy is, the faster it recedes from us — and the relationship is linear.

Hubble's law:

— a galaxy’s recession velocity is directly proportional to its distance. v — recession velocity (km/s), d — distance (Mpc), H₀ — the Hubble constant (≈ 70 km/s/Mpc).

The invariant — one constant for the whole cosmos:

For every galaxy the ratio of velocity to distance is the same. That is why all points on the v–d graph fall on a single straight line with slope H₀. This is direct evidence that the Universe is expanding.

How do we know how fast? Redshift.

Light from a receding galaxy is stretched toward longer wavelengths (the red end): $z \approx v/c$. The larger the redshift, the greater the velocity — this is how we measure v and determine distances across the cosmos. It connects to the “redshift” experiment.

Are we at the center of the Universe?

No. It is space itself that expands — like raisins in rising dough. Every observer, in any galaxy, sees the same thing: everything recedes from them, and the farther away it is, the faster. The recession of galaxies singles out no special point.

Why this matters for your exam:

v = H₀·d solves problems about the velocity and distance of galaxies and about the age of the Universe (≈ 1/H₀). The trick: compute v from the formula or from the redshift z = v/c, and the ratio v/d always gives H₀.

Remember: the farther a galaxy, the faster it recedes — v = H₀·d. This is evidence that the Universe is expanding, not that we are at its center.