# How bright will Alpha Centauri A be from Earth when it becomes a red giant?

As of right now, both stars from Alpha Centauri are in their main sequence stages, but eventually Alpha Centauri A is going to quickly expand in a matter of time, and I’m pretty sure its luminosity is going to increase substantially. So, how bright would it be from Earth?

• Commented Oct 7, 2022 at 5:23

First of all, by the time Alpha Centauri A becomes a red giant, it will no longer be this close to the Sun due to the orbit of the stars around the galaxy so it probably wouldn't be visible. But let's assume it does stay 4.2 ly away.

By the Stefan-Boltzmann Law, the luminosity of a star is given by

$$L = 4\pi R^2 \sigma T^4$$

Assuming a radius of $$200 R_\odot$$ and a temperature of $$3600 \text{ K}$$, we get a luminosity of about $$6021 L_\odot$$, compared to a present-day luminosity of $$1.5 L_\odot$$.

This means that the red giant would be 4014 times brighter, corresponding to an apparent magnitude increase of 9 magnitudes to about -9 apparent magnitude. This is slightly dimmer than the brightness of the moon.

• Perhaps this deserves a separate question, but since the galaxy is expanding, the night sky is necessarily getting dimmer over time right? And therefore, when Alpha Centauri A becomes a red giant, will there be any stars visible? Commented Oct 7, 2022 at 3:21
• the galaxy is expanding. huh? the universe is, but the galaxy isn't. Commented Oct 7, 2022 at 3:30
• Ah, my bad. I meant the universe :) Commented Oct 7, 2022 at 3:32
• For anyone wondering: Slightly dimmer in this case is about 1/25th the brightness Commented Oct 7, 2022 at 6:30
• @NathanMerrill The only thing that matters for our naked-eye visible night sky is the position of our solar system within our galaxy (as well as the other stars, of course). When our solar system passes through volumes with higher density of luminous stars, the night sky is "brighter"; when there's relatively few bright stars nearby, the night sky gets "dimmer". Most of the stars on the naked-eye night sky are very close to ours, with a few exceptional red and blue giants (and galaxies :D) that can be visible over a very large distance. Commented Oct 7, 2022 at 6:51

In 1 billion years Sol and Alpha Centauri will have travelled about 4 times around the galaxy on different paths, so it could be 100k light years away. It's moving at 22km/s relative to Sol.

• I voted up (as this movement is rather important) but I'd prefer you added the calculation of it's apparent brightness from Earth as the question asked for that specifically. Commented Oct 8, 2022 at 13:23