I've been considering this problem for about a year now (whenever I remember about it, that is), and I've come to the conclusion that I can't figure out a way to do what I want to see is possible, and so I've decided to ask it here to see if anyone else can.(adsbygoogle = window.adsbygoogle || []).push({});

The original question I considered was: could a classical astronomer determine the size of the moon to an arbitrary level of accuracy? Since then I've sort of refined the question, and here are my qualifications:

1) The process has to be able to be theoretically done from a single spot on the Earth (so triangulation is allowed, but only one point of the triangle can be on Earth).

2) You are only allowed one-way measurements, so you can throw something at the moon and measure that, or measure something coming from the moon (or somewhere else), but you can't involve the measurements of one object going to and from the moon (including light).

3) An arbitrary amount of accuracy is allowed with imaginary telescopes and the like.

4) You don't know any distance or velocity values for other solar system objects.

With that in mind, the question is: What is the radius of the moon?

My solution is to, using an extremely accurate telescope, measure the gravitational lensing of the moon, thereby getting its mass. Using a tide-measuring system, and knowing the moons mass, you could figure out the acceleration/force you are experiencing from the moon, and thereby figure out the distance to the moon, and then the radius.

However to me this fails on two counts. 1) I'm not positive the gravitational lensing test will produce a value for M instead of an M/D ratio, and 2) It feels like the use of GR goes against the original purpose of the question.

Does anyone have a more elegant solution? Or knowledge that there isn't one?

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# Half Question/Half-Challenge: Dimensions of of the Earth-Moon System

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