# Back-of-the-Envelope Calculations: Position and Dimensions of the Moon

## Summary

*Question*

Suppose you could scale the Earth down to the size of your head. At that scale, how big would the Moon be, and how far away would it be from your head?

## Assessment

*Answer*

The Moon would be slightly less than 5 cm (2") in diameter and would be about 5.5 m (18') away from your head! The ratio of Earth to Moon diameter is about 3.6 to 1. If your head is about 18 cm (7") in diameter, that makes the scale Moon about 5 cm (2") in diameter. The scale factor for the model is about 1:71 million. That scales the Earth/Moon distance down to about 5.5 m, or 18'. Have a friend hold a small lemon 18' away from your head in order to get a feel for scale and distance in the Earth/Moon system!

## References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.