Back-of-the-Envelope Calculations: Collision with Asteroid
We have located an asteroid heading directly for the Earth. It is now 1.6 million km away from the Earth, about 4 times the distance from the Earth to the Moon. The asteroid is travelling at 25 km/second. How long will it be from the time of discovery at a distance of 1.6 million kilometers to impact on the Earth?
Only about 18 hours. At the rate of 25 km/second, it will take 64,000 seconds for the asteroid to travel 1.6 million kilometers. At 3,600 seconds per hour, that's about 18 hours. 25 km/second is a typical asteroid velocity. This puts into perspective how far away from Earth we would have to detect an asteroid if we wanted to have any hope of doing something about a possible collision!
References and Resources
This SERC page describes the use 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.