Eddie’s pizza is especially tasty after a long walk down a stairwell. Vinnie and I are polishing off the last of our crumbs when he says, “OK, so we got these incredibly accurate clocks. Two questions. What do we use them for besides sending out those BBC pips, and what do they have to do with the new kilogram standard?”
“Pips? Oh, the top-of-the-hour radio station beeps we used to depend upon to set our watches. Kept us all up-to-the-minute, us and the trains and planes — but we don’t need 10-digit accuracy for that. What we do get from high-quality time signals is the ability to create distributed instruments.”
“Ones with pieces in different places. You know about the Jansky Very Large Array, that huge multi-dish radio telescope in New Mexico?”
“Been there. Nice folks in Pie Town up the road.”
“Did you look around?”
“Of course. What I didn’t understand is why they got 27 dishes and they’re all pointed the same direction. You’d think one would be enough for looking at something.”
“Ah, that’s the thing. All of them together make one telescope.”
<sets smartphone to calculator mode> “Lessee … dish is 25 meters across, πD2/4, 27 dishes, convert square meters to… Geez, 3¼ acres! A single dish that size would be a bear to keep steady in the wind down there. No wonder they split it up.”
“That was one concern, but the total area’s not as important as the distance between the pairs.”
“Why’s that even relevant?”
“Because radio telescopes don’t work the way that optical ones do. No lens or mirror, just a big dish that accepts whatever comes in along a narrow beam of radio waves.”
“About the size of the full Moon.”
“That can cover a lot of stars and galaxies.”
“It sure can, which is why early radio astronomy was pretty low-resolution. Astronomers needed a way to pick out the signals from individual objects within that field of view. Turns out two eyes are better than one.”
“Kinda related, but not really. Our two eyes give us 3D vision because each eye provides a slightly different picture of close-by objects, say, less than about 5 yards away. For everything further, one eye’s view is no different from the other’s. You’d get the same effect if distant things were painted on a flat background, which is how come a movie set backdrop still looks real.”
“You’re saying that the stars are so far away that each dish gets the same picture.”
“So why have more than one?”
“They don’t get the picture at the same time. With an atomic clock you can take account of when each signal arrives at each dish. Here’s a diagram I did up on Old Reliable. It’s way out of scale but it makes the point, I think. We’ve got two dishes at the bottom here, and those purple dots are two galaxies. Each dish sees them on top of each other and can’t distinguish which one sent that peaky signal. What’s important is, the dish on the right receives the signal later. See that red bar? That’s the additional path length the signal has to travel to reach the second dish.”
“Can’t be much later, light travels pretty fast.”
“About 30 centimeters per nanosecond, which adds up. When the VLA dishes are fully spread out, the longest dish-to-dish distance is about 36 kilometers which is about 120 microseconds as the photon flies. That’s over a million ticks on the cesium clock – no problem tracking the differences.”
“Same picture a little bit later. Doesn’t seem worth the trouble.”
“What makes it worth the trouble is what you can learn from the total space-time pattern after you combine the signals mathematically. Under good conditions the VLA can resolve signals from separate objects only 40 milliarcseconds apart, about 1/45000 the diameter of the Moon. That’s less than the width of a dime seen from 50 miles away.”
“The time pattern is how the dishes act like a single spread-around telescope, huh? Without the high-precision time data, they’re just duplicates?”
“Atomic clocks let us see the Universe.”
~~ Rich Olcott
2 thoughts on “For the VLA, Timing Is Everything”
Excellent post, as usual. But, an arithmetic slip. 😦 Moon diameter = 1000 * 40 milliarcseconds = 40 arcseconds ?? Off by a factor of 45, alas 🙂 Try again. (Maybe re-check dime width, too?) Sent from Yahoo Mail on Android
Yet another good catch, Richard. Here’s the arithmetic I should have done… Moon’s angular diameter is about half a degree = 30 arc-minutes (am). Comparing that to the VLA’s 40 milli-arcsecond (mas) good-conditions resolution
(30 am/40 mas)*(1000 mas/as)*(60 as/am)=45000, not 1000.
I have no idea where that factor of 45 went. I’ll fix up my text.
On the other matter… The sine of a small angle is approximately equal to the angle in radians. Converting the VLA resolution number to radians
40 mas*(1as/1000 mas)*(1 deg/3600 as)(*2pi rad/360 deg)=1.94×10^-7 rad.
A dime’s diameter is 0.7″. The hypotenuse of a right triangle with short side 0.7″ and that acute angle is
(0.7 inch/1.94×10^-7)*(1 foot/12 inch)*(1 mile/5280 feet) = 57.0 miles
so I’ll stick with my “dime 50 miles away” gee-whiz-timate.
Thanks for the help.