What would a red giant Sun look like from Proxima b? As of now, Proxima b is the only confirmed planet (or dwarf planet if it didn't clear its orbit - sorry, couldn't resist) around Proxima Centauri, the nearest-known star to the Sun about 4.2 ly away. From that distance, the Sun looks just like an average star in the night sky. Now if the Sun became a red giant, at 256 times its current diameter (if I recall correctly), what would it look like from Proxima b's night sky? On a good telescope, Betelgeuse is recognizable as more than a dot, its surface is visible, that would surely be the case for a red giant Sun too. What would it take to recognize the Sun's surface from the Proxima system? Would the Sun perhaps even cast a visible shadow?
The Sun will not become a red giant for approximately 7 billion years, so there is little chance that Proxima Cen will be anywhere near it.
[EDIT: To answer a comment, the current helocentric radial velocity of Proxima Cen is -22 km/s. The Sun's escape velocity at the distance of Proxima Cen is about 0.1 km/s. So the Sun and Proxima Cen are totally unbound. With a relative speed of 22 km/s (at least - I haven't calculated the additional tangential velocity difference) they will be at least 100 pc apart within 7 million years, let alone 7 billion years.]
The Sun goes through TWO red giant phases. In the first, hydrogen shell-burning phase, the Sun will achieve a peak absolute V magnitude of around -3 at the tip of the first ascent red giant branch. It wil have a temperature of around 2700 K, be 256 times its present size and 2800 times more luminous according to Schroeder &amp; Connon Smith (2008).
From a distance of 0.77 pc (the current distance of Proxima Cen) it would have an apparent magnitude of about -8.5 (about 40 times brighter than Venus).
Its apparent size in the sky would be 1.54 arcseconds, so would have a disc that was resolvable using a small telescope at a good site and would be orange/red in colour.
According to Schroeder &amp; Connon Smith's model, the asymptotic giant branch phase of the Sun, when it has an inert carbon/oxygen core and He + H-burning shells will be slightly smaller and less luminous.
The exact values for both these phases are somewhat dependent on the details of the mass loss model used for the strong stellar winds expected.