Skip to ContentGo to accessibility pageKeyboard shortcuts menu
Astronomy 2e

# 1.4Numbers in Astronomy

Astronomy 2e1.4 Numbers in Astronomy

In astronomy we deal with distances on a scale you may never have thought about before, with numbers larger than any you may have encountered. We adopt two approaches that make dealing with astronomical numbers a little bit easier. First, we use a system for writing large and small numbers called scientific notation (or sometimes powers-of-ten notation). This system is very appealing because it eliminates the many zeros that can seem overwhelming to the reader. In scientific notation, if you want to write a number such as 500,000,000, you express it as $5×1085×108$. The small raised number after the 10, called an exponent, keeps track of the number of places we had to move the decimal point to the left to convert 500,000,000 to 5. If you are encountering this system for the first time or would like a refresher, we suggest you look at Appendix C and Example 1.1 for more information. The second way we try to keep numbers simple is to use a consistent set of units—the metric International System of Units, or SI (from the French Système International d’Unités). The metric system is summarized in Appendix D (see Example 1.2).

A common unit astronomers use to describe distances in the universe is a light-year, which is the distance light travels during one year. Because light always travels at the same speed, and because its speed turns out to be the fastest possible speed in the universe, it makes a good standard for keeping track of distances. You might be confused because a “light-year” seems to imply that we are measuring time, but this mix-up of time and distance is common in everyday life as well. For example, when your friend asks where the movie theater is located, you might say “about 20 minutes from downtown.”

So, how many kilometers are there in a light-year? Light travels at the amazing pace of $3×1053×105$ kilometers per second (km/s), which makes a light-year $9.46×10129.46×1012$ kilometers. You might think that such a large unit would reach the nearest star easily, but the stars are far more remote than our imaginations might lead us to believe. Even the nearest star (other than the Sun) is 4.25 light-years away—more than 40 trillion kilometers. Other stars visible to the unaided eye are hundreds to thousands of light-years away (Figure 1.4).

Figure 1.4 Orion Nebula. This beautiful cloud of cosmic raw material (gas and dust from which new stars and planets are being made) called the Orion Nebula is about 1400 light-years away. That’s a distance of roughly $1.34×10161.34×1016$ kilometers—a pretty big number. The gas and dust in this region are illuminated by the intense light from a few extremely energetic adolescent stars. (credit: NASA, ESA, M. Robberto (Space Telescope Science Institute/ESA) and the Hubble Space Telescope Orion Treasury Project Team)

## Example 1.2

### Getting Familiar with a Light-Year

How many kilometers are there in a light-year?

### Solution

Light travels $3×1053×105$ km in 1 s. So, let’s calculate how far it goes in a year:
• There are 60 $(6×101)(6×101)$ s in 1 min, and $6×1016×101$ min in 1 h.
• Multiply these together and you find that there are $3.6×1033.6×103$ s/h.
• Thus, light covers $3×105km/s×3.6×103s/h=1.08× 109km/h.3×105km/s×3.6×103s/h=1.08× 109km/h.$
• There are 24 or $2.4×1012.4×101$ h in a day, and 365.25 $(3.65×102)(3.65×102)$ days in 1 y.
• The product of these two numbers is $8.77×1038.77×103$ h/y.
• Multiplying this by $1.08×1091.08×109$ km/h gives $9.46×10129.46×1012$ km/light-year.

That’s almost 10,000,000,000,000 km that light covers in a year. To help you imagine how long this distance is, we’ll mention that a string 1 light-year long could fit around the circumference of Earth 236 million times.

Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
• If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/astronomy-2e/pages/1-introduction
• If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/astronomy-2e/pages/1-introduction
Citation information

© Jan 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.