# no stairway?October 22, 2012 12:42 AM   Subscribe

Q: How many miles is it to the crab nebula? How does one even figure this out? A: The cosmic distance ladder! Here's a talk by Fields medalist Terrence Tao on methods for indirect calculation of distances to astronomical objects. Here's Tao's blog post on the subject, including the slides for the talk. And here's a Wikipedia page.

For my part, I remember in high school asking exactly how one could use star brightness to measure distance, given that we can't really measure absolute brightness of a star directly. Somehow I got pretty unsatisfactory answers from my high school science teachers; it's nice to fill in some blanks!
posted by kaibutsu (17 comments total) 21 users marked this as a favorite

You might think it's a long way down the road to the shops, but that's just peanuts compared to space.
posted by w0mbat at 1:02 AM on October 22, 2012 [4 favorites]

I'll tell you one thing, no one thinks in imperial units when talking science.
posted by wilful at 2:52 AM on October 22, 2012

If they find a way to integrate all this into, say, a Katamari Damacy level, I'm there!
posted by markkraft at 4:21 AM on October 22, 2012

You don't even use metric units in astronomy (well, wavelength, which is just a fancy way of describing color). You pretty much get parsecs (based on the diameter of the orbit of the earth) and light years (based on the speed of light).

Back in the day I used to TA a non-calculus astronomy class where the students worked through a rung of the ladder more or less every week. My job was mostly to help people realize that the twenty stars nearest Earth were probably more representative of stars in the universe than the twenty brightest stars in the sky and showing people with non-technical majors how one got a square root using a calculator.
posted by Kid Charlemagne at 8:22 AM on October 22, 2012

Velocities in km/s, column densities in cm-2 or g/cm2 just off the top of my head - metric units are hardly rare in astronomy.
posted by edd at 8:48 AM on October 22, 2012

I haven't listened to the talk yet, but based on the slides I'm gonna go ahead and say it's great. He walks through step by step from how the Greeks figure out the sizes and distances of the Earth, Moon, and the Sun all the way to measuring the distance to the galaxies at the edge of the observable universe. Thanks, kaibutsu. My kids are gonna eat this up!
posted by straight at 9:20 AM on October 22, 2012

(My kids have been wanting to know how we know how big the universe is since we did a rough calculation that the digits of pi they'd memorized were enough significant digits to figure the circumference of the known universe from the diameter, measured in plank lengths. In other words, more than enough. I said some vague things about redshift, but wasn't really able to answer them.)
posted by straight at 9:24 AM on October 22, 2012

Nice slides. But I do disagree with his suggestion that annual trigonometric parallax can get you out to only 30 parsecs (100 light years). I've published parallaxes to neutron stars that are 5 and 7 kiloparsecs away, about 15,000-21,000 light years. Okay, we used a network of radio telescopes (the VLBA), but it's exactly the same idea, and other groups are using a similar technique to measure the distance to the center of our Galaxy (8.5 kiloparsecs).

Someone once pointed out that I was personally disproving a formation date for all of the Universe 6,000 years ago, because the maximum distance we could measure should be 6,000 light years. (The speed of light is 1 light year per year, of course...) But God works in mysterious ways, and I'm sure faking up a parallax signature would be the least of Their tasks - the elaborate fossil record would be a much more interesting problem.
posted by RedOrGreen at 9:34 AM on October 22, 2012 [2 favorites]

But God works in mysterious ways, and I'm sure faking up a parallax signature would be the least of Their tasks - the elaborate fossil record would be a much more interesting problem.

Another sticky problem is stellar events. On the young-earth creationist view, when we see a supernova that is more than 6,000 light years away, (ie, all recorded supernovae) we are witnessing the evidence of an event that never actually happened seeming to occur to a star that never actually existed.
posted by jcreigh at 9:58 AM on October 22, 2012 [2 favorites]

If you have a pathetically anthropocentric view of the universe, you just say God created the light from stars and supernovae en route so we wouldn't have to wait a billion years to see pretty lights in the sky (just like he put fossils in the ground to give us oil for our cars and cut coastlines to give us bays for our boats).
posted by straight at 10:10 AM on October 22, 2012 [1 favorite]

Oooh, I get to show off:

My great-great-great-great-great-grandpa was astronomer/mathematician Friedrich Wilhelm Bessel. He was the first person to calculate the distance to a star by measuring its parallax (to be specific it was 61 Cygni in 1838 and, according to the linked Wikipedia article, he measured it to be 10.4 light years away which is off by 8.8% or ~1 light year based on current measurements for this star).
posted by Hairy Lobster at 10:51 AM on October 22, 2012 [4 favorites]

Here's a fingerspitzengefühl yardstick for the local neighborhood. Got a feeling for how far it is out to Pluto? (32.7 AU or 0.0005171 light-years). Then the nearest star is about 8444 times farther away.

To get to that star in only a year, then, your spaceship would have to be going fast enough to reach Pluto in roughly an hour.
posted by Twang at 10:52 AM on October 22, 2012

Or in other words, the fastest anyone can ever get to Pluto is 4 hours. (And that's at it's closest; at it's furthest Pluto is more like 7 light hours away.)
posted by straight at 11:06 AM on October 22, 2012

How fast does the sun move?

One of the things I couldn't quite wrap my head around about annual parallax when I first heard about it is how you could assume that the distance between your previous measurement and the current one was 2 AU --- wouldn't you have to add some to compensate for the whole solar system moving?

Some thought says you can probably work around it by repeating the experiment in subsequent years and comparing the absolute results -- but no one seems to mention that :-)
posted by smidgen at 11:52 AM on October 22, 2012

How fast does the sun move? [...] wouldn't you have to add some to compensate for the whole solar system moving?

Smidgen, yes, we do account for the solar motion (about 13 km/sec relative to the local standard of rest, LSR) and for differential Galactic rotation, which is often a larger effect. (The Galaxy does not rotate as a solid body; local rotation velocity is about 220 km/sec).) The distortion of the Earth's orbit from a closed ellipse is pretty small when measured from the LSR.

The way solar motion is measured (defined?) is by measuring the average motion of an ensemble of stars, and then defining that to be the standard of rest. Here are a couple of papers from a cursory search - Vera Rubin, 1951; and the RAVE collaboration, 2012. You can see from a glance at the abstract that the basic method hasn't changed much. As per Einstein, there's no absolute frame of reference anyway - these days, we define our International Celestial Reference Frame (ICRF) according to the "average" position of distant quasars measured by radio VLBI. In a few years, once the Gaia mission starts returning data and it is digested, we expect that the ICRF definition will switch to the Gaia frame.

Honestly, astrometry is a rather boring branch of astronomy (and I do this professionally!) but it is shockingly fundamental to a whole slew of stuff. Distance ladder, yes, but also continental drift, leap seconds, GPS time, and a variety of basic physics results...
posted by RedOrGreen at 1:12 PM on October 22, 2012 [3 favorites]

Aha... I assumed you did, but wasn't sure what was involved. cool.. thanks.
posted by smidgen at 1:56 PM on October 22, 2012 [1 favorite]

Here I am wishing there were a 'Best Answer' button in the Blue, with which to reward RedOrGreen...
posted by kaibutsu at 3:52 PM on October 22, 2012 [1 favorite]

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