How long would it take for the supernova to expand to a diameter of 6 light years? It doesn't expand at light speed, right?
Let’s again use a known supernova as an example to extrapolate from.
The Crab Nebula was formed from a supernova that exploded in the year 1054, or 957 years ago. It currently has a diameter of 11 light-years and is expanding at a velocity of about 1,500 km/s. To reach it’s current size, the average expansion velocity has been 1,723 km/s. If we assume the velocity has been slowing at a constant rate, then the initial velocity was 1,946 km/s and it has been decelerating 0.466 km/s-year.
Using these numbers, the amount of time needed to reach a diameter of 6 light-years is 491 years.
So is it safe to say that at it's brightest (before it expands and fades) the supernova will still only look like a bright star from that distance?
Naked eye, yes.
The light curve of a type II supernova decays at about 0.008 magnitudes per day (source:
http://en.wikipedia.org/wiki/Type_II_supernova). This means that Betelgeuse will decay to naked eye invisibility (magnitude 6) in about 6.25 years. Using the numbers above, the nebula will expand to a diameter of 0.08 light-years in that amount of time. This will give the nebula an apparent diameter of 26 arc-seconds, which is below naked eye resolution. (Naked eye resolution is about 1 arc-minute.)
In a telescope, however, a disc should be resolvable fairly quickly. For instance, the nebula should expand to an apparent diameter equal to that of Uranus in less than a year. Even my 8-inch telescope can easily resolve the disc of Uranus.
(Please note that the Sun has a diameter of 32 arc-minutes – you previously said “arc secondsâ€.)