In articles and books about astronomy it is fairly common to see gravitational fields or wells represented as a three-dimensonal dent or hole in a two-dimensional coordinate system. Like it is done on this page.
I am trying to track down the earliest source that uses this type of illustration of a gravitational well. I would be very thankful if anyone here could help me track down the beginning of this type of visual representation of gravity.
If it helps, the word you’re looking for is “embedding diagram”.
First time I ever saw it was Hawking’s A Brief History of Time, but I’m sure it’s far older than that.
I first saw it in some documentary program in the late 1990s. The first pop culture (non-visual) reference I heard it in was in a “Babylon 5” ep. I’d have to look for a title, but they spoke of getting a Shadow vessel caught in Jupiter’s gravity well.
The earliest illustration I’ve found is the cover of this book from 1986. There are references to figures of embedding diagrams (thanks Chronos) in The Astrophysical Journal from 1972, but the illustration doesn’t quite seem to match the type I’m looking for.
How far back does the rubber sheet analogy go? Soon after a graphic artist may have suggested the familiar illustration.
I certainly read the rubber sheet analogy before graduating college (in 1971) and I recall seeing the exhibit in science museums in which balls “orbited” a central hole on a surface that was a hyperboloid (or paraboloid) of revolution in the 60’s as well. I was fascinated by those. That is a physical construction of the illustration in question I believe.
Einstein’s Zurich Notebook of ~1915, doesn’t contain such an illustration, but it could -
fourth photo down:
"Einstein recapitulates a result from Newtonian mechanics in Gauss’ theory of curved surfaces. A mass constrained to move in a curved surface (but otherwise unconstrained) moves along a geodesic of the spatial surface. "
Well, of course, that’s what I always thought. 
I’m fairly sure that I saw such an illustration used in Carl Sagan’s book and television show Cosmos, which dates from 1980.
Searching for the terms “Gravity well” or “embedding diagram” does seem to produce quite a few references to Sagan and Cosmos. I haven’t found any illustrations yet, though.
Using the Amazon.com “Search Inside This Book” feature, I found this quote on page 198 of Carl Sagan’s book Cosmos, “Consider a flat, flexible, lined two-dimensional surface , like a piece of graph paper made of rubber. If we drop a small mass, the surface is deformed or puckered. A marble rolls around the pucker in a . . .” I think the television show illustrated this with a short animation.
Edited to add that you can watch the show via Hulu.
No Hulu in Denmark, unfortunately. A friend of mine has the series on dvd, so it might just be the right time to watch it again. Unless, of course, someone can find an older reference.
I suspect that there must be older references, as I doubt that Sagan invented the metaphor for the series. Perhaps older physics or astronomy textbooks?
One, Two, Three…Infinity (copyright 1947) by George Gamow looks to have a relevent figutre in it on page 109:
1980? Heck, there’s an illustration of the same sort for Disney’s film The B;ack Hole in 1979 (and also for the poster for URCON I), and it old hat even then.
IBM had produced working models of such gravity wells (with large ball bearing rolling around the surface, since they react very much as they would under inverse-square law) for their Mathematica exhibit (one of which is still at the Museyum of Science in Boston, with the balls riolling around), the Chicago Museum of Science and Industry in Chicago, and another at the LA Science Museum. I’m not sure exactly when these went in, but their timeline stops circa 1960, and the artwork is about of that period. Certainly they were in place by 1970. Another IBM-sponsored exhibit with a gravity well was around at the Hayden Planetarium in NYC circa 1970 called Astronomica.
But the three-dimensional gravity well existed long before that. I had a science book from the early 1960s that showed how to make such a well by placing a sheet of rubber from a balloon in a circular stitching frame and pulling down on the center with a nut pick. You could then roll tint ball bearings around the inside to give you circular, elliptical, and parabolic orbits, or hyperbolic fly-bys.
I strongly suspect this was a big thing in the 1950s, but I’ll have to check the literature. Certainly gravitational potentials were graphed well before that.
Incidentally, Wikipedia’s entry says that Gravitational Potential odels are very distinct from Embedding Diagrams, despite the similarity:
A model of a gravitational potential well, used for roling-ball demonstrations of orbits, was fabricated at Harvard about the time of Sputnik:
http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/PotentialWell/PotentialWell.html
I am not so much looking for the origin of the metaphor itself as I am interested in the specific form of visualization of the metaphor (viz. the 3d hole in a 2d coordinate system). Squink’s link is interesting, and it is certainly the earliest example (or approximation) I have seen yet.
Great work, everyone! Keep it coming.
ETA: What about the origin of the term “Gravity well”? I suspect that is arose from the visual metaphor, but I cannot find out who coined the phrase.
Curved spacetime at Google’s Ngram viewer
There’s a peak at 1937, when Andrew Paul Ushenko’s “The philosophy of relativity” was published. That’s a likely place to look for an earlier diagram of a gravity well.
Incidentally, the term “gravity well” itself seemed to have something to do with automobiles in the early 1900’s.
I don’t know who coined the phrase, but the earliest reference I found with a cursory skim thru Google News Archives was in 1987, and it referred to one of these doohickeys. Within a year or two, the term started picking up steam (in Google News Archives) referring to celestial bodies.