In summary, the supernova explosion of Betelgeuse is not expected to have a significant influence on Earth's climate or temperature, or the sun itself. Although it may appear as bright as the full moon, it is unlikely to cause any problems for our retina. The distance of Betelgeuse is still a matter of controversy, but it is estimated to be around 550 light years or 3.47 x 10^7 astronomical units. If it were to explode at the sun, it would be 1.2 x 10^15 times brighter. Compared to other supernovas, it is expected to peak at a magnitude of -11.3. However, based on a recent paper, it is predicted to
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Will the supernova explosion of Betelgeuse influence the Earth's climate and temperature or even the sun in any significant way?
According to a previous post, Betelgeuse may appear as bright as the full moon. I calculated that this may produce a problem for your retina given direct staring but it seems unlikely that the added power of the full moon is going to do much. Perhaps there would be a short burst of high energy particles but it seems unlikely that this would be a problem. Its the gamma ray bursters that we need to be terrified of...
The distance is controversial. Around 550 light years. 3.47 x 10^7 astronomical units. It would be 1.2 x 10^15 brighter if it were blowing up at the sun.
Wikipedia has this nice chart comparing supernova intensities over time. At 168 parsec add 6.8 for visual magnitude. A -15.17 absolute magnitude source is 100 million times as bright as the sun (absolute mag 4.83). A few types peak at with a few points higher. Based on the chart we might see up to -11.3.
Based on this paper it will be a magnitude -12.4. That should last for a few weeks and dim down for a few months. They say the shock wave will get here in about 6 million years. That pushes back on the solar wind and reverses it until about 2.5 astronomical units. Not much effect on Earth but it would be quite noticeable on the Pluto colony. The bow shock lasts for about 1000 years so the ice giant colonies will pass through it multiple times. Comet tails would look funky.