BAN #333: Solar flux

[The planetary nebula M 2-9, winds from a dying star. Credit: NASA / ESA / Hubble Legacy Archive / Judy Schmidt]

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Blog Jam

What I’ve recently written on the blog, ICYMI

[Four images of the red supergiant Betelgeuse (from left to right: Jan. 2019, Dec. 2019, Jan. 2020, March 2020) showing not only that it dimmed, but also that only parts of it got fainter. From Wednesday’s article. Credit: ESO/M. Montargès et al.]

Monday 14 June, 2021: Star formation is beautiful and terrifying

Tuesday 15 June, 2021: How far away are supernovae? Astronomers find a way to tighten measurements

Wednesday 16 June, 2021: We may finally know why Betelgeuse dimmed so much. Bonus: No supernova. Yet.

Thursday 17 June, 2021: How long would it take for an alien civilization to populate an entire galaxy?

Friday 18 June, 2021: Perseverance is now ready to actively begin looking for life on Mars

Astro Tidbit

A brief synopsis of some interesting astronomy/science news

… also …

Number crunching

Because I think math is cool, and I think that because it is

The June solstice was on Sunday, June 20, 2021. For us in the northern hemisphere this heralds warmer temperatures and more time spent outdoors. That got me thinking…

Hold your hand up to the Sun. Feel the warmth.

Now ponder the photons of light hitting your hand that have traveled 150 million kilometers from the Sun to reach you. The light emitted by the Sun spreads out over that distance, diluting, but there are still enough of it to feel.

How big is your hand? Mine is about 10 x 20 centimeters. Big for a hand, maybe, but very small compared to, say, a square meter. How much sunlight is falling on that much area?

We have a unit called the solar constant, which is exactly that: How much energy from the Sun is falling on a square meter of Earth (assuming it’s directly facing the Sun) every second? The answer is about 1,400 Joules, or, in slightly more familiar units, 1.4 kiloWatts. Enough to power 14 100-Watt bulbs, assuming you could convert that energy into electricity with 100% efficiency. That’s also about the average electricity consumption of a US house.

And that’s just on one square meter. Imagine how many square meters the Earth is! In this case we can pretend the Earth is a flat circle facing the Sun (the math works out the same assuming it’s a sphere but also accounting for the fact that the ground curves; at the edges (where the Sun is low) the surface of the Earth is parallel to the sunlight, reducing its efficiency). That’s called the cross-sectional area of the Earth, and it’s equal to pi x radius squared, the area of a circle. Using the Earth’s radius of 6.4 x 10^6 meters, that area is about 130 trillion square meters.

So the energy of sunlight hitting the Earth every second is 130 trillion x 1,400 Joules = 1.8 x 10^17 Joules, or 180 trillion kW of power. That’s a LOT of power.

In fact, in less than an hour all the sunlight hitting Earth could power all of humanity’s energy use for a year. Go solar!

[The Sun in far ultraviolet light on the day of the June 20, 2021 solstice, taken by NASA’s Solar Dynamics Observatory. Credit: NASA / SDO / Helioviewer.org]

But. The Earth is small compared to the space around it. The Sun is emitting energy in all directions, and the Earth only receives a small fraction of it. How small?

Well, imagine the Sun is surrounded by an imaginary sphere with the same radius as Earth’s orbit. The area of a sphere is 4 x pi x radius squared, where the radius now is 150 billion meters. So the area of that sphere is 2.8 x 10^23 square meters.

That’s a whole lot of area. A mind-crushing amount, really. The Earth is only intercepting 130 trillion square meters of that. Dividing, the Earth receives only about one two-billionths of the energy the Sun emits!

That means the Sun emits 2 billion times more energy than the Earth receives.

2 billion x 180 trillion kW = 4 x 10^23 kiloWatts = 4 x 10^26 Watts

That’s enough energy to power 4 septillion 100-Watt light bulbs. Hmph. That’s cool but a bit hard to grasp. Let’s try something else…

4 x 10^26 Watts is also 4 x 10^26 Joules per second. But a Joule isn’t a very familiar unit, either, I know.

But, for example, a one-megaton nuclear bomb — extremely powerful, though by no means the most powerful ever detonated — releases a total of 4 x 10^15 (four quadrillion) Joules.

Dividing: 4 x 10^26 Joules/second  /  4 x 10^15 = 1 x 10^11 = one hundred billion

That means that the Sun emits energy at the same rate as detonating 100 billion 1-megaton nukes. Every second.

And it does this every second of every hour, day in and day out, 365.24 days a year. It’s done this for the past 4.6 billion years, and will continue to do so for the next, oh, 7 billion or so before turning into red giant… at which point it will emit far more energy.

The Sun produces staggeringly prodigious amounts of energy, so much that human adjectives are ridiculously ill-equipped to describe it.

I’ll note that it generates this energy by fusing hydrogen into helium in its core, the same process, more or less, that a hydrogen bomb uses. Except in the case of the Sun, it’s fusing about 700 million tons of hydrogen into 695 million tons of helium every second.

The leftover 5 million tons? That’s converted into energy via Einstein’s famous equation, energy = mass times the speed of light squared: E = mc^2. And we know how much energy that generates for the Sun. 100 billion megatons worth every second.

Nearly every star you see in the night sky is more luminous than the Sun, emits even more energy. An exploding star will emit energy at a rate billions of times the Sun’s.

The amount the Sun emits is vast, but it’s also a convenient unit for astronomers. So we talk about solar luminosity, the amount of energy emitted per second and compare things to that.

Sirius, the brightest star on the night sky, emits energy at a rate of 25 solar luminosities. A red dwarf is maybe 0.02 solar luminosities. A galaxy is a hundred billion. Some are more.

Imagine all that energy, sleeting through the Universe, all the time.

Now hold your hand up to the sunlight once more. Close your eyes and face the Sun. Feel it?

Some of that energy is going into you. A tiny, feeble trickle, an amount so small that compared to the Earth, the Sun, the Universe, it’s almost nothing.

But it’s something. Those photons are hitting you. That’s your connection to everything. Literally; they allow you to see. And some of those photons hit the ground around you, people around you, trees, clouds, oceans, buildings. Everything you can see on Earth. And even if you can’t see it for whatever reason, you can still feel it.

That connects all of us to everything. Even each other, in a very real way.

All that, from warming your hand in a beam of sunlight.

Some people say science is boring. I can’t imagine what they’re thinking.

[Credit: Phil Plait]

Et alia

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