Paper clips

Rainbow of paper clips.
Mostly sorted.

There’s a funny thing about important scientific discoveries. The effort and time and careful data collection and building atop previous understandings and innovations and everything else is daunting, difficult, and a massive undertaking. Critical details and a fine understanding may take months, years, or entire careers. A general grasp, though?

Sometimes, you can explain the gist of things with stuff that’s just lying around.

Hubble’s Law, also known as the Hubble-Lemaître Law, describes the expansion of the universe. Galaxies are moving away from ours, and the further away they are, the faster they’re moving. Getting there relied on the Friedmann equations – themselves built upon Einstein’s general relativity – plus Slipher’s redshift measurements of distant galaxies, plus the debates between Shapley and Curtis, plus an understanding of the relationship between luminosity and period in the pulsations of Cepheid variable stars. (They’re like the drinking bird toys of stars.) Plus more, and more, but you get it. A lot goes into explaining the expansion of the universe when all you’ve got is a telescope and spectrometer.

Hubble ran into a real hiccup here. If everything in the universe is moving away from us, and we can correlate the distance and speed in any direction, doesn’t that imply that we’re at the center of the universe? Turns out, no. We’re not.

And you can illustrate the principle with a Slinky, a ruler, and some paper clips.

We get a lot of mileage out of the Slinky.

Pendulum bobs

Aluminum and brass pendulum bobs.
Shiny!

Does the mass of a simple pendulum affect its period of oscillation? The small-angle formula doesn’t include mass, just the length from the pivot to the center of mass and g, the gravitational constant. It’s an approximation that’s pretty good for angles up to 15-20°, and after that it’s into introductory differential equations. Which still don’t use the mass, as it cancels out when applying Newtonian mechanics.

That, however, is for an ideal pendulum, with a massless string and point mass bob in a system without friction and other losses. We’re all out of massless string at the moment, and those point masses are proving elusive. And as neat as it might be to swing a pendulum in a vacuum, the setup sounds like a real challenge.

On top of that, it’s an interesting question that’s really addressing a student’s understanding of measurement and uncertainty. Equations and models illustrate principles, and sometimes do an excellent job of making sense of the world. It’s just that the real world is messier, and wading into that mess – even a little bit – can be enlightening.

Two new pendulum masses, machined to the same dimensions, or close enough that you won’t notice without accurate calipers. Threaded to screw on and off. Aluminum (2.7 g/cm³), checking in slightly under 50 grams each. Brass (8.7 g/cm³), a little over three times the mass, a shade above 150 grams apiece. If we can work with the material, we could make more from anything available.

Lightweight plastics, like Delrin acetal (1.4 g/cm³)? Sure. Denser stuff, like lead (11.3 g/cm³)? Not impossible, but okay, well, no. Even denser? Tungsten, gold, and depleted uranium are all in the 19 g/cm³ range. McMaster-Carr has a range of tungsten alloy rods in stock! (For a small fortune.)

For now, though, it’s two masses, a string, and a stopwatch. Real physics in action.

Astronauts

Cardboard box.
Acquired just in time to go into long storage.

Some storage containers simply have more entertaining labels than others. Case in point: the cardboard box labeled “Astronauts & Space Toys,” which is neither large nor sturdy enough to contain a real astronaut, let alone several.

A find like this is just begging for exploration. We refer to a lot of things around here as “toys,” but these are the real deal.

Toy label.
Astronaut pieces.

There are buckets – buckets! – of astronauts inside! Or possibly pieces of astronauts. It’s unclear.

There is a choking hazard warning. One can reasonably assume that choking hazards in space are worse than here on Earth.

Box of toys.
Buckets upon buckets.

The jackpot: toys! Fewer astronauts than advertised, but a substantially higher proportion of Lunar Module Eagles and Hubble Space Telescopes than expected. (Always entertaining to write those as plurals.) Chalk it up in the win column.

If this is how you convince the next generation that astronomy is cool, sign us up.