Earth, Moon distance solution!

This is my solution to this problem. I have not finished yet…

NB: I know we could just Google the distance from the Earth to the Sun, but please do not – who would benefit from that? This is eduation kids!

So to solve this I used ideas I picked up from teaching ‘enlargements’, a subset of ‘geometric transformations’, in highschool Math classes. Some people would call it Thales theorem, to give credit to the chap who originally figured this out about 2500 years hence.

StepĀ 1
I loaded up the image and used the ‘circle through 3 points’ tool in Geogebra to construct a circle which modelled the outlines of both Earth & Moon. I zoomed in a lot to enable me to position the 3 points as close to the circumferences as possible, to minimise errors.

Worked out the ratio of their actual diameters, which is in proportion to their
actual radii.

Used the ratio of diameters to divide radius of Earth in photo to get what the moon’s radius would be if it were at the same distance from the camera as the Earth.

Then I looked at the difference and figured it….

the Moon appears 1.327 times larger than it should were it the same distance as the Earth. So it must be….errr. Trouble is, we don’t know where the observer is… think on Dan!

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