# Back-of-the-Envelope Calculations: Spacecraft Acceleration

#### Summary

*Question*

Suppose someone offered you a ride to the nearest star in a new spacecraft that could travel at half the speed of light, or about 150,000 km/second. In order to reach such a cruising speed, you and the spacecraft must accelerate from a standstill to half the speed of light. Acceleration means uncomfortable (and maybe even fatal!) "g" forces, that pressed-into-the-seat feeling you get when a car or airplane accelerates. More than 3 g's of acceleration are tough to take for very long, so your spacecraft's engines are designed to accelerate you at not more than 29 meters/second/second (3 times the acceleration due to gravity at the Earth's surface). How long will it take you and your spacecraft to accelerate to half light speed?

## 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.

## Controlled Vocabulary Terms

**Subject**: Geoscience:Lunar and Planetary Science, Mathematics

**Resource Type**: Activities:Classroom Activity:Short Activity

**Special Interest**: Quantitative

**Grade Level**: High School (9-12), College Lower (13-14)

**Quantitative Skills**: Estimation

**Ready for Use**: Ready to Use

**Topics**: Chemistry/Physics/Mathematics, Solar system

**Theme**: Teach the Earth:Course Topics:Planetary Science