Guesstimating the distance to the moon

Here's a neat trick for estimating the distance to objects.  Stick out your thumb and look at it with just one eye open, then with just the other eye open.  The distance to the object is the distance it appears to jump multiplied by 10.  This works because the distance from your eyes to your thumb on your outstretched arm is about 10 times the distance between your eyes.  

I thought I'd have a go at using this to measure the distance to the moon


That was easy.  The moon jumps 6 moon diameters, which means it's 60 moon diameters away!

Problem: How do we find out the diameter of the moon?  Fortunately, there's another trick we can apply, and I learned this from Kitty Ferguson's book Measuring the Universe.  Here's how it goes: wait for a full lunar eclipse and time how long it takes for the shadow of the Earth to fully eclipse the moon.  Also time from the start of the eclipse to the end of the full eclipse.  The ratio of the two then tells you how much bigger the Earth is than the moon.  (Note that this assumes the moon is relatively nearby compared to the Sun.)

Credit: Kevin Burkett CC-BY-SA 2.0

 
I'm too impatient to wait for a lunar eclipse, so I'm happy to take Kitty's word for it that when you do this you find that the moon has about half the diameter of the Earth. So, we've now got the distance in much more convenient units: the moon is 30 Earth diameters away.  The Earth's diameter is about 13,000 km. You can trust Eratosthenes on this, or if you're like me and you don't trust anyone you can measure it for yourself. So this gives us (approximately) a distance of 390,000 km to the moon.  Wikipedia says it's 384,000 km. But what do they know.

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