The Cosmic Distance Ladder

November 4, 2014 3:10 AM

How do we determine distances between the earth, sun, and moon, and from the sun to other planets, stars, and distant galaxies? We can't measure these directly, but indirect methods, combined with some basic high school math, can provide convincing and accurate results. A public lecture by Fields medalist Terry Tao (SLYT)
posted by Another Fine Product From The Nonsense Factory (24 comments total)

Actually, they've been able to directly measure the distance to the moon since 1968.
posted by Chocolate Pickle at 3:32 AM on November 4, 2014 [2 favorites]

Oh right, they put a laser reflector up there, didn't they.
posted by thelonius at 3:35 AM on November 4, 2014 [1 favorite]

Haha cool! I nicked the description from the youtube because I didn't think I could explain it better but maybe I was wrong!
posted by Another Fine Product From The Nonsense Factory at 5:17 AM on November 4, 2014 [1 favorite]

Yes, the apollo retroreflectors, the first space-based weapon justified with some flimsy claim of being a "scientific device".
posted by jepler at 5:18 AM on November 4, 2014 [1 favorite]

They use the parallax?
posted by grobstein at 5:19 AM on November 4, 2014

An interesting factoid/infographic from last week:

You Could Fit All the Planets Between the Earth and the Moon
posted by fairmettle at 5:20 AM on November 4, 2014 [11 favorites]

You Could Fit All the Planets Between the Earth and the Moon

Whaaaa? Now, that's a factoid I'd never run across before. That's actually very cool and amazing and kind of mind-blowing in that space-is-unbelievably-big way.
posted by Thorzdad at 5:25 AM on November 4, 2014 [1 favorite]

You Could Fit All the Planets Between the Earth and the Moon

And then Jupiter eats all of them. Because Gravity. (Seriously good demo, though.)

Seriously -- as the Guide said "Space is really really big." Interplanetary distances are huge compared to the diameters of the planets.
posted by eriko at 6:23 AM on November 4, 2014

Also -- distance to another object is very much not a static number. Orbits are ellipses. Other stars are in elliptical orbits around the core of the galaxy, or in other galaxies. But even the distance of the moon? It's 384,400±21,296km, rounded to the nearest kilometer. That's not an error bar, that's the actual change in the distance from the Earth to the moon over the course of the moon's orbit. It's enough of a change that a full moon at lunar perigee (aka supermoon) has a 12% larger apparent diameter than a full moon at apogee.
posted by eriko at 6:36 AM on November 4, 2014 [1 favorite]

You Could Fit All the Planets Between the Earth and the Moon

The figure of an average distance of 384400 km is an average center-to-center distance. They forgot to take into account the radius of the Earth (6380 km) and the radius of the Moon (1740 km), which unfortunately means that the total diameters of the planets are about 3700 km more than the distances between the surfaces of the Earth and the Moon.
posted by Johnny Assay at 7:18 AM on November 4, 2014 [3 favorites]

Yeah, but the gas giants are all really smushy. Don't worry, they'll fit.
posted by sexyrobot at 7:38 AM on November 4, 2014 [7 favorites]

Terry Tao doing trig? This is like getting a taxi ride from Dale Earnhardt Jr.. I.e. fantastic. With bonus points for one of my favorite arguments, showing that the moon is a sphere, and not a round disc.
posted by benito.strauss at 7:49 AM on November 4, 2014 [2 favorites]

You could not, however, fit the sun in there.
posted by wobh at 7:50 AM on November 4, 2014

This is Terry Tao. I think he knows about the Banach-Tarski Paradox, and could find a way to run it backwards to fit the sun in anywhere.


Bonus terrible nerd joke -
Q: What's an anagram for "Banach Tarski"?
A: "Banach Tarski Banach Tarski"
posted by benito.strauss at 8:22 AM on November 4, 2014 [2 favorites]

One of my fave astronomical stories is that of the measurement of the Transit of Venus and the attempt to compute the distance from the Earth to the Sun.
posted by RobotVoodooPower at 8:24 AM on November 4, 2014 [2 favorites]

Man, I'm afraid the Banach-Tarski paradox has jumped the shark. Everyone knows about it now.
posted by grobstein at 8:24 AM on November 4, 2014 [1 favorite]

For a while I had this image as my desktop wallpaper. I had to change it because I could no longer stand the terrifying sense of cosmic vertigo.
posted by narain at 9:17 AM on November 4, 2014 [4 favorites]

Even before Apollo, we were able to measure distances to solar system objects directly using radar. Some of the best estimates of the distance from the Earth to the Sun (a fundamental rung in the distance ladder) have been obtained that way.
posted by janewman at 11:47 AM on November 4, 2014

You Could Fit All the Planets Between the Earth and the Moon

Whoa. That strikes me as a coincidence just as freaky as the fact that the Sun and the Moon appear to be the same size when viewed from the Earth. IT MUST MEAN SOMETHING!
posted by straight at 1:22 PM on November 4, 2014 [1 favorite]

Orbits are ellipses.

True. But I work on binary neutron stars, and we measure elliptical orbits that are so close to perfect circles that ... well, consider the pulsar J1909-3744. Its measured eccentricity (remember, a circle has e=0, an open parabola has e=1) is 0.00000026, or 2.6x10^-7.

The orbit diameter is 1.897992(4) light-seconds, or 570,000 kilometers, or 356 thousand miles. And the major and minor axes of this binary pulsar elliptical orbit differ by (ugh I have to do this by hand) ... 38.5 microns.

So yep, elliptical, and measurably so, but imagine an ellipse 356 thousand miles across (the moon is 239 thousand miles away from the Earth) that differs from a perfect circle by about the thickness of a rather fine human hair. Pretty neat.

(I measure distances to neutron stars, and use a technique dating back to the Greeks - as the Earth goes back and forth in its orbit, the stars appear to wobble a tiny bit against the distant background quasars. Basic parallax. It's just that we're measuring wobbles tinier than the Greeks could have ever believed... my personal record is about 27,000 light years.)
posted by RedOrGreen at 1:53 PM on November 4, 2014 [7 favorites]

(Link for J1909-3744. Just missed the edit window...)
posted by RedOrGreen at 2:00 PM on November 4, 2014

Favoriting RedOrGreen so hard because those are amazing and they're STILL ELLIPSES.

Well, circles are still ellipses, actually.

STILL AWESOME. Fave the hell out or that. Deserves it.
posted by eriko at 6:47 PM on November 4, 2014 [1 favorite]

So....

A circle is an ellipse, but an ellipse is not a circle.

just as...

A square is a rectangle, but a rectangle is not a square.

I feel cheated by my geometry teacher since I'm only now realizing this.
posted by InsertNiftyNameHere at 11:13 PM on November 4, 2014 [2 favorites]

Always nice to see Terry Tao. I met him a few times between the ages of about 10 and 14, and he was always remarkably calm and well-adjusted for someone living in a very high-pressure world of gifted & talented programs, and out on the bleeding edge of those as well. (When he was 14, I believe he was already doing postgrad-level mathematics work.) I saw a fair number of people break down under that pressure, and it's encouraging to see that he both emerged largely unscathed and went on to do amazing things.
posted by McCoy Pauley at 9:30 AM on November 5, 2014