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Or, say a cat's roughly a sphere of radius 10cm, capacitance of an isolated sphere is C=4(pi)(epsilon_0)(radius) = radius/k_e = .1/(9x10^9) = 11 pF

Ballpark. YCCMV.

That's the 2nd comment in the highest-voted answer...
huh. I ctrl-f'd for "sphere" and missed it.

There goes the high point of my saturday night. Maybe later they'll ask how many cats running in circles you need to levitate a dog wearing a ferrous vest.

I am not a cat fan, or a squirrel fan. I do know from observing squirrels crossing power lines that their dielectric constant is significantly lower than that of air, but I've never figured out how to determine it strictly from observation without actually doing an empirical measurement.
Squirrels act as inductors in DC circuits. Only once though. There's a high current surge that drops to zero as they turn rapidly into a carbon resistor!
a bit like the NED Noise Emitting Diode - makes a lound noise once
Having sat there, as a teenager, with a whole bag of 1N4148s and a mains test block, can confirm :)
We had a number of network outages at Apple due to squirrels inserting themselves in the NOC's power lines.

Note to self: Don't design any circuits that incorporate these animals. Squirrels make terrible fuses.

So true.

We had a different problem. They chewed through the fibre cables between our offices to get the fiberglass sheath for their nests. Eventually they ran Ethernet underground because they'd have broken it again in a couple of weeks.

Whereupon: Moles :-)
I imagine getting the kitty to hold still while you attach the clips from your ESR meter might be the tricky part
I laughed at one of the answers mentioning this:

"Connect one end of cap to ground - one end of cap to cat. .... ( How 'to cat' is achieved is left as an exercise for the reader.)"

I imagine this experiment may not have a high level of repeatability.
Next question: how much energy can it store, until the capacitance breaks down?
I don;t think there's a well-defined answer. The "capacitance of a cat" is actually the capacitance of the cat and some other condictor. For purposes of calculating the cat's capacitance you can treat the other plate as a grounded sphere at infinity. It doesn't really matter., you'd get pretty much the same answer with a grounded sphere a few feet away. But for figuring out how much energy you can store before you get an arc, it's all about how far away the second conductor is.
I'm feeling the desire to build a cat scratcher with multimeter right now... maybe with some nice bulb leds aligned forming the meow! word.

muahahah... is alive!!!

This reminds me of a throw-away comment a lecturer made once while discussing the maintenance of telecommunications equipment. He dryly observed that, “Burning technicians don’t smell very nice.”
Do we have to assume a spherical cat?