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.

... not only is it going to be a lot less work to take our atmosphere from 400ppm to 250, we're already here.

Yepperz. Realistically, it will "cost" governments tens of trillions of dollars to solve the climate problem. Over the next ten to twenty years, it will become glaringly obvious that we have no choice.

When people are like, "HEY, send me to start terraforming Mars RIGHT NOW!", I wanna tell them, "OK, have fun! I'll be here. Maybe you'll get the bandwidth to email me before you die, but maybe not". I think NASA is probably realizing that any serious attempt to colonize Mars needs to be an international endeavor if it will ever have a chance of succeeding (/affording it). With a staunchly anti-globalist president, there's no good reason for NASA to broadcast that, because they also probably realize that they're gonna have to pull a Vatican and think on timescales of human generations from the get-go, so what's four or eight years? I've been trash talking a Mars shot since I got here. The public simply doesn't understand how many challenges there are to colonizing Mars, and unlike asteroid mining, there are essentially zero business incentives for sending people to Mars. That I can think of, at least.

SETI & Drake Equation paragraph

It's not hydrogen emission, it's emission generated when hydrogen bonds to hydroxide and makes water. Had to look it up, I was so confused, I thought "Why would SETI be looking at... Lyman-Alpha..?". I don't think targeting water is a terribly bad idea. Water has so many unique properties (yuge heat index, less dense in the solid phase than the liquid, relatively small temperature difference required for phase changes, should occur everywhere in the universe near a previous supernova that produced the Oxygen, etc.), and although it certainly might drastically narrow the types of "life", it seems like a decent start.

I think I've said this before, but I wonder if there isn't something encoded into quasar outbursts, like if advanced civilizations ever systematically arrange matter to fall into the supermassive black holes at the center of galaxies. I doubt it's really possible to encode much on very short timescales, because the processes in the accretion disk and jets that create emissions are super turbulent and non-linear. Actually, we think the most common non-linear process energizing things there is probably magnetic reconnection (muh jerb), but anyway. The dots and dits could be days, weeks, months, or years-long, though, I guess. That'd be the best way to have an omni-directional signal, because you'd be modulating gamma-ray and relativistic particle fluxes, which are rare enough that your signal-to-noise ratio is muuuuuuch better than other wavelengths or lower energy particles, especially if it were coming from the center of your own galaxy. There are many many other considerations, though.

Didn't know that about Drake and the Navy. I still maintain that the galaxy might be teeming with life, and there's not really a reason for them to bother us. Apparently there are plenty of solar systems with rocky, watery planets. There might be only a relatively small span in a civilization's development when they broadcast radio waves up into space before switching to neutrino beams or whatever. Think of it like a spherical shell of radio waves, and however many years they broadcast for, that's how many light years thick it is, and the radius of the shell is obviously growing one light year per year. The strength of the signal inside the shell decays as a function of 1/r^2; quite quickly, as the radius expands outwards.

Give me the energy requirements for a tightbeam visual signal from, say, Alpha Centauri B. I wanna be able to read morse code at night.

Ho boy, here we go. Pinging Devac for peer review.

Like, with the naked eye? OK, you'll need an apparent magnitude of at least +6. Let's make it +4, because I don't want to voyage into the central Pacific Ocean to see this, I don't even wanna squint. We'll assume that the Alpha Centaurians (probably centaurs) have tuned their laser's beam divergence such that when it reaches us, the beam diameter is the size of Earth's diameter. And btw, they'll have to aim 4.3 years in advance, so (being nowhere near precise enough) 0.3 orbits ahead of wherever Earth is when they flip the switch. From the apparent magnitude wiki article, we'll just convert the m=0 flux for the "V"(= visible) band to m=+4 using Pogson's ratio, 2.512, raised to the (+4 - 0 =) 4th power: 2.512^4 = ~40. OK, so to have enough visible photon flux per unit area (we start with cm^2) for it to appear as an m+4 for everyone on Earth, we need 40 x 3.64E-20 (= ~1.5E-18) ergs/(s*cm^2*Hz). We need to get rid of the Hz. If we assume they're using a monochromatic beam smack dab in the middle of the visible light spectrum, say 550 nanometers (yellow) = lambda, and c = lambda*f (where c is the speed of light), so f = 3E8 (m/s)/5.5E-7 (m) = ~5E14 Hz. So 1.5E-18*5E14 = ~1E-3 ergs/(s*cm^2). 1 erg = 1E-7 Joule, so now we're at 1E-10 J/(s*cm^2) = 1E-10 W/cm^2. Sanity check before the final step: I guess this sounds kinda right. If cat toy laser pointers are around 1 mW (1E-3 W) and we're instructed to never shine them in peoples eyes (which are roughly a square centimeter), it makes sense that barely-discernible blinking lights in the sky should be around 10 million times less powerful. OK, best for last. Finally, we multiply by the cross-sectional area of the Earth... in square centimeters. Earth's radius is ~6000 km, = 6E8 cm, and pi*r^2 = ~1E18 cm^2. So those guys are rollin' with a 1E8 Watt laser. 100 million watts. Let's make it a "jiggawatt" (1E9 Watts) for funsies. According to gubbmint, you'd need about 400 windmills to power your laser. Only(?) 40 windmills for the 1E8 Watt laser. Problem is, you might want a lotta lasers. And the results for red and blue will be more or less similar, certainly well within an order of magnitude.

If they built a truly dispersionless laser (not quite possible, but play along), and knew exactly where your eyeball would be at all times 4.3 years in the future, they could just use something as powerful as the toy laser, and it'd still damage your eye. Hey, what're you up to just after January 28th of 2024? Asking for a friend.