Monday, October 26, 2015

Pritt Sticks to Mars

Some time ago I was at Chichester Skeptics in the Pub to see James Ward talk about his book Adventures in Stationary. The talk was fantastic, and whilst I haven't gotten around to reading the book yet, it's on my list of books to read (that list grows faster than the time available to read them). During the talk, James referenced a press release from Pritt Stick's makers celebrating their 40th anniversary, saying that the 2.5 billion Pritt sticks sold in their 40 year was history was "Enough to leave a line of adhesive extending from the Earth, past our satellite the Moon, on to Mars and then all the way back again"

James Ward was unsure how they came about with such a statistic. I don't know how they did it either, but here's how I would do it:

Firstly, what are we using for the distance? At it's maximum the Earth could be on one side of the Solar System, and Mars on the other, we would be as far from each other as possible. Or, the Sun, Earth and Mars could be in a perfectly straight line in that order, as close as we can be to each other currently. The ranges for these distances are:

Smallest: 56 million km or 34 million miles.
Furthest: 401 million km or 249 million miles.

To see where on this range the current distance is, see here. Consequently, we'll calculate two values, one for Mars at its closest, the other Mars at it's furthest.

The next thing to consider is what is meant by a Pritt Stick, for they are not a standard unit. Pritt Sticks come in a range of sizes. Let's just go for the medium size, which has a stick of glue in it with a diameter of 2.0cm and a height of 5.1cm. This gives a volume of 16.02cm3

The diameter of the Pritt Stick gives us the width of our glue trail to Mars - we'll assume it's smeared across our hypothetical surface that extends to Mars evenly. Volume = length x width x height, so some simple rearranging is need to get our height of Pritt stick smear, also remembering this smear is there and back.

One medium Pritt stick would be able to leave a trail of glue to Mars and back, so long as it was only 7.2fm to 1fm thick. This is not possible, given that our largest estimate is smaller than the radius of a gold atom's nucleus, and our smallest is not much bigger than a proton. Pritt stick cannot get this small without splitting the atom.

However, we're dealing with 2.5 billion Pritt sticks. This leaves us with a smear of Pritt stick some 17.9μm to 2.5μm thick. This seems more realistic, though my experience of Pritt stick is a smear thicker than this. For comparison a single skin cell is about 35μm across.

Let's be more charitable and go for 2.5 billion large Pritt sticks. These have a diameter of 2.5cm and a height of 6.6cm, giving a volume of 32.4cm3

Using the same mathematics as above, this gives us a smear that ranges from 28.9μm to 4.03μm which still seems pretty thin.

So, after all this, I'm with James here in not understanding how Pritt stick came up with their statistic either. If only they'd shown their working in a press release.

Either way, we've been dealing with some very different units: femtometres, micrometres, centimetres and kilometres. That's quite a range - one kilometre is 1,000,000,000,000,000,000 femtometres. Here's a lovely website to help you appreciate the scale of the universe, from the very big to the very small: The Scale of the Universe.

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