This page provides information to supplement one or more questions within the Kelvin Essay prize, Peterhouse.

### Information supplementary to question "How far is it to the moon?" set in October 2016 for submission by 17th March 2017

It could be said that, more than 200 years ago, it was much harder to be an experimental scientist than it is today. Computers, pocket calculators, computer generated tables of logarithms and trig functions didn't exist, and so all arithmetic was long hand. (How would you calculate the cosine of an angle without a calculator? How did people in the past do it?) Galileo couldn't go out and buy a telescope from Argos. At least Galileo may have been able to find a spectacle maker who could make him lenses, but poor old Leeuwenhoek would have had to make his own lenses in order to make the first microscope (and discover bacteria, spermatozoa, etc). Newton couldn't buy a red LED, or even a battery to run it for that matter. He would have had to put up with candles, sunlight, or go without. By comparison we have it easy. Arguably any sixteen year old with access to things about his/her house and in their school's science labs, is (materially speaking) better equipped to "do science" than those famous long-dead people of yesteryear.

So here's the challenge. Take a physical constant of nature, or an established law of physics, something that is nowadays such an established "fact" that we forget how tricky it may have been to measure or discover in the first place, and then see if you yourself can actually independently re-measure or re-discover it using a method that bears some resemblance to the original method.

There is a small catch, though: you are not allowed to use any of the (brilliant) topics chosen by last year's entrants, or those of the year before. So you may not measure the radius (or size) of the earth, may not measure Netwon's Graviational Constant, may not demonstrate that F=m*a, may not measure the length of the day or year, may not measure the speed of sound with a gun, and may not demonstrate Poiseuille's Law.

Allow yourself to use modern tech where to do so wouldn't appear to be "cheating". You'll have to decide what that means. What modern tech you can use will depend on what you are measuring. For example, suppose you try to measure the speed of light by looking at the moons of Jupiter in a telescope in a set of nightly observations. Then you might decide to use an off-the-shelf telescope (modern tech) but try to do all the maths without a calculator or a computer. Alternatively you might decide to keep the calculator or computer, but try to build your own telescope from things about the house. Measuring the speed of light in a microwave by measuring the wavelength in melted cheese and dividing by the frequency written on the bottom of the microwave would not be in the spirit of a measurement from the past. But perhaps doing the same thing with a device you've built that actually measures the microwave frequency might be in the spirit. Things need not be so "fancy" though. Something as simple as measuring the length of time it takes the earth to rotate once on its axis relative to the fixed stars provides a wealth of possibilities. [Though see note above about this particular idea being off limits for having been used last year.] Are you going to look nightly for the times at which a given star disappears behind a neighbour's chimney? How do you cope with the fact that its disappearance time is not only related to the period of the earth's rotation, but is also related to the earth's movement about the sun? Could you measure the distance to the moon? Could you measure the radius of the earth by a means similar to the method used by the Greeks? Maybe you need a friend who lives north or south of you by some distance. But you'll need to know how much further south they live from you. Are you going to look that up on a map? (No, that's cheating. If you look that up on a map, you may as well look up the radius of earth on the same map by measuring the equator!) You'll have to find the distance to your friend by some other means. [ Note that thes distance measuring ideas were very creatively and brilliantly used by entrants last year, and so are off limits this year. You need to find something else to measure ... ]

So there is the challenge: see if you can be a match for a scientist of the past. You've got it easy compared to him/her!

Write a report that describes what you chose to measure, why you chose it, and what you managed to accomplish. Submit that report as your "essay". Note that the report need not itself be "essay like", as such. It's more of a practical write up -- but the exact format is up to you. Do not feel the need to stick to an "abstract, method, results, conclusions" format if something else would capture what you did better. But do not exceed the essay word-count limit.

I am interested to see responses that "engage" with the spirit of the question. As you can probably see/guess, this question is an excuse to let you roll your sleeves up and plan something quite tricky but still hopefully achievable. A measurement need not be a success to have a good write up -- negative results and failures, if well understood and written up, are as much a part of science as apparent successes. I am looking for the right combinations of interesting choice of measurement, evidence that you had to think / plan what to do, and that you have had to take-apart some of the things we consider "obvious" or "well established" and imagine what it was like to have to do science without knowing those facts, or without being able to make use of certain pieces of technology.

In all honesty, although the write-up need only take an afternoon, the actual experimenting could take a long time -- far more time than answering any other essay in this competition. So I would not advise you to tackle this question unless you actually would *enjoy* the fun of setting yourself the experimental challenge even *without* the existence of the competition aspect. If you would enjoy the challenge and would do it for fun anyway, then look upon the submission of the write up for the essay prize as a fortuitous side-benefit. Do not tackle this challenge purely in order to submit something for the science prize. There are better uses of your time!

Note that the name "How far is it to the moon?" is just an example of a question you could set yourself and get you interested. Answers need have nothing to do with the moon or distances (unless you want them to!). When you submit your entry, please title it:

#### "I don't know how far away the moon lies, but XXX."

... where you should replace XXX with a short statement of what you are actually going to measure. For example "I don't know how far away the moon lies, but here is how I re-discovered bacteria."

Good luck!