"The Earth is a very small stage in a vast cosmic arena. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves."
— Carl Sagan
Wow — it's October!
With last night's cold front, NEXRAD showed a tremendous amount of bird migration. This prompts me to consider a possible sparrow excursion at Pheasant Branch tomorrow morning—perhaps there will be a HASP or LCSP? Given that I've been blogging here for so long (+20 years), when looking at my early October posts from the past, it does seem a bit repetitive and predictable—I tend to do many of the same things over and over by the tick of phenological clock. Another 584 million miles later, should I do the same thing yet again?
Oh, that's the distance the Earth travels around the sun in a year.
Distance from the Earth to the Sun: ~ 93 million miles
The Earth's orbit diameter: ~ 186 million miles
Easy math!
So far nothing too controversial, other than the Earth is a oblate spheroid (or more precisely, a geoid).
No ... it is not flat. But they're out there.
Did you know that using the Earth's orbit diameter we can determine the distance of other stars within the Milky Way Galaxy using something called Stellar Parallax?
One uses a big telescope to photograph a star in June, then the same star 6 months later when the Earth is on the other side of its 186 million mile orbit diameter:
The nearby star appears to shift position against much more distant background stars.
The rest is basic geometry and trigonometry.
Ground-based optical telescopes can measure stellar parallax for relatively nearby stars, historically reaching distances of a few hundred light-years. Space-based astrometry, particularly Gaia, extends direct parallax measurements to tens of thousands of light-years, although the uncertainties become much larger at those distances. Radio VLBI can push direct trigonometric parallax even farther, reaching roughly 65,000–70,000 light-years for some radio-bright sources within the Milky Way.
Recall the basic way in which I said we could determine the distance to the Andromeda Galaxy (M31) , our galactic neighbor, by using its arc size against the celestial sphere knowing an approximate diameter of a similarly sized galaxy.
But there's more: Cepheid Variable Stars.
Cepheid variables are giant stars that regularly expand and contract, getting brighter and dimmer as they do. The rate at which they pulsate is tied to how much light they actually produce. The process involves layers of helium inside the star. When those layers are compressed and heated, the helium becomes more opaque and traps more of the star's energy, pushing the layers outward. As they expand and cool, the helium becomes less opaque, allowing more energy to escape, and gravity pulls the layers back inward. The cycle repeats, producing the star's regular pattern of brightening and dimming. By measuring how long it takes a Cepheid to complete one cycle, astronomers can determine its true brightness using the period-luminosity relationship, known as Leavitt's Law. Comparing that true brightness with how bright the star appears from Earth allows astronomers to calculate its distance.
Much like candle light.
Think of a lit candle sending out a sphere of light in every direction. As that sphere expands away from the flame, it gets bigger and bigger. The candle keeps producing the exact same amount of light, but as you step back, that same light is forced to spread thinner and thinner across a larger surface. Because the light stretches out across space in a perfectly predictable pattern, measuring how dim the flame looks to your eye tells you exactly how far away the candle is.
The beauty is that Cepheids not only exist in our galaxy, but others. Thus, we can determine the distance of other nearby galaxies using their Cepheids. With space-based telescopes, this puts the yardstick out to ~100 million light-years.
100 million times 5.88 trillion miles.
That's this many: 588,000,000,000,000,000,000
And there's still more: Redshift.
Redshift occurs when light from a distant galaxy is stretched to longer, redder wavelengths as the universe expands—much like the pitch of a siren drops as an ambulance drives away:
By measuring the shift in a galaxy's spectral lines, we can determine its redshift. For relatively nearby galaxies, Hubble's Law relates redshift and distance. At much greater distances, astronomers use the measured redshift together with models of the universe's expansion to estimate how far away the galaxy is. This allows astronomers to measure distances far beyond the reach of Cepheid variables, ultimately out to the most distant objects we can observe—46 billion light-years.
And that's how we get an observable Universe that's 92 billion light-years across.
That's 540,960,000,000,000,000,000,000 miles.
We don't know the actual number of galaxies in the universe, but it's estimated between 100 billion and 2 trillion.
Let's say there are 500 billion galaxies, each averaging 100 billion stars within. Since we now know nearly all stars have orbiting planets—our own solar system has 8 or 9 (poor Pluto)—let's assume 80% of stars host an average of just 3 planets.
This is how many planets there would be in that universe:
120,000,000,000,000,000,000,000
120 sextillion planets.
Even if only .000001% of them harbor life, that would be 1.2 quadrillion planets.
Have a lovely day!