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Devac · 166 days ago · link · · parent · post: Why the world is waiting for Betelgeuse to go supernova ·

I need to correct myself and point out that the *values* I got were wrong.

Formulae:

`t = sqrt(x²/c² + 2x/g) - time measured on Earth`

`t' = (c / g) * asinh(gt/c) - time measured by ship's crew`

Numerical values:

`c = 3.00E8 m/s`

g = 9.81 m/s²

`x = 4.3 ly = 4.07E16 m`

Time from the perspective of people on Earth (t): 1.63E8 seconds = 5.18 years.

Time from the perspective of people on the ship (t'): 7.27E7 seconds = 2.31 years.

Derivation was OK, had four other people check it for me and can show the work. It's not a new result anyway. Regardless, sorry for the mistake.

am_Unition, ButterflyEffect, nil - you also shared that post, so I'm shouting out just in case it has any relevance for you guys.

So, the final formula is:

` Power = (p ^ m) * F * (c / λ) * π * r²`

where:

p - Pogson's ratio [] (dimensionless)

m - magnitude [] (dimensionless)

F - flux [J / (s * cm² * Hz)]

c - speed of light [cm / s]

λ - wavelength [cm]

r - Earth's radius [cm]

π - pi [] (dimensionless)

Checking units:

`Power = ([] ^ []) * [J / (s * cm² * Hz)] * [cm / s] * [1 / cm] * [] * [cm²]`

Power = [J / (s * cm² * Hz)] * [1 / s] * [cm²]

Power = [J / (s * cm² * Hz)] * [Hz] * [cm²]

Power = [J / s] * [(Hz * cm²) / (Hz * cm²)]

`Power = [J / s] = [W]`

No problems here.

Using our values:

p = 2.512

m = 4

F = 3.64E-27 [J / (cm² * Hz * s)]

c = 3E10 [cm / s]

λ = 5.5E-5 [cm]

r = 6E8 [cm]

pi = 3.14

we obtain:

`Power = (2.512 ^ 4) * 3.64E-27 * (3E10 / 5.5E-5) * 3.14 * (6E8)²`

`Power = 8.94E7 [W]`

So… pretty close and the difference comes down mainly to rounding. Other than that, under your assumptions, I see no problems with reasoning or method. Sorry for taking so long to respond, though.

- Hey, what're you up to just after January 28th of 2024? Asking for a friend.

You need to double it, that's when Centaurs would get your message.

As of about an hour ago, I'm no longer a student. BSc² -> MSc², yo.

PhD application process in progress.