<p>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.</p>

CC BY-SA 4.0
2022-10-08T13:23:43.183Z
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.
StephenG - Help Ukraine
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2022-10-07T18:47:15.563Z
2022-10-08T11:43:20.413Z
2022-10-08T11:43:20.413Z
bandybabboon
<p>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.</p>
<p>By the Stefan-Boltzmann Law, the luminosity of a star is given by</p>
<p><span class="math-container">$$L = 4\pi R^2 \sigma T^4$$</span></p>
<p>Assuming a radius of <span class="math-container">$200 R_\odot$</span> and a temperature of <span class="math-container">$3600 \text{ K}$</span>, we get a luminosity of about <span class="math-container">$6021 L_\odot$</span>, compared to a present-day luminosity of <span class="math-container">$1.5 L_\odot$</span>.</p>
<p>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.</p>

CC BY-SA 4.0
2022-10-07T03:21:27.543Z
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?
Nathan Merrill
CC BY-SA 4.0
2022-10-07T03:30:46.140Z
`the galaxy is expanding`.  huh?  the universe is, but the galaxy isn't.
Michael
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2022-10-07T03:32:20.947Z
Ah, my bad.  I meant the universe :)
Nathan Merrill
CC BY-SA 4.0
2022-10-07T06:30:59.477Z
For anyone wondering: Slightly dimmer in this case is about 1/25th the brightness
SirHawrk
CC BY-SA 4.0
2022-10-07T06:48:33.287Z
@NathanMerrill That's not the point. The point is that the expansion of the universe is irrelevant to how far stars _within our galaxy_ are from us. The galaxy is gravitationally bound, and does _not_ expand in the same way as the spacing _between_ galaxies (except for a few that are also gravitationally bound). None of the naked-eye visible points on the night sky correspond to stars that are affected by this expansion - Andromeda is a galaxy, but it's moving _closer_ ; others are inside our galaxy.
Luaan
CC BY-SA 4.0
2022-10-07T06:51:26.490Z
@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.
Luaan
CC BY-SA 4.0
2022-10-07T15:11:48.407Z
@Michael Fixed the slight ambiguity with the "expansion"
WarpPrime
CC BY-SA 4.0
2022-10-06T18:57:18.073Z
2022-10-07T15:11:21.270Z
2022-10-07T15:11:21.270Z
WarpPrime
<p>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?</p>

CC BY-SA 4.0
2022-10-07T05:23:40.330Z
Related: https://astronomy.stackexchange.com/q/45318/16685
PM 2Ring
<star><luminosity><apparent-magnitude><red-giant><future>
How bright will Alpha Centauri A be from Earth when it becomes a red giant?
Prince Pugs
# How bright will Alpha Centauri A be from Earth when it becomes a red giant?

(Asked by: username_0 on 2022-10-06)

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?

**Tags:** star, luminosity, apparent-magnitude, red-giant, future

> **Comments:**
> **username_1**: Related: https://astronomy.stackexchange.com/q/45318/16685  

---

## 2 answers

### Answer by username_4 on 2022-10-06. Score: 23 | Accepted answer

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.

> **Comments:**
> **username_5**: 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?  
> **username_6**: `the galaxy is expanding`.  huh?  the universe is, but the galaxy isn't.  
> **username_5**: Ah, my bad.  I meant the universe :)  
> **username_7**: For anyone wondering: Slightly dimmer in this case is about 1/25th the brightness  
> **username_8**: @username_5 That's not the point. The point is that the expansion of the universe is irrelevant to how far stars _within our galaxy_ are from us. The galaxy is gravitationally bound, and does _not_ expand in the same way as the spacing _between_ galaxies (except for a few that are also gravitationally bound). None of the naked-eye visible points on the night sky correspond to stars that are affected by this expansion - Andromeda is a galaxy, but it's moving _closer_ ; others are inside our galaxy.  
> **username_8**: @username_5 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.  
> **username_4**: @username_6 Fixed the slight ambiguity with the "expansion"  

---

### Answer by username_2 on 2022-10-07. Score: 5

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.

> **Comments:**
> **username_3**: 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.  

---

