1.4: Astronomy Toolkit

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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. This system eliminates the many zeros of very large or very small numbers. In scientific notation, if you want to write a number such as 500,000,000, you express it as 5 x 10⁸. This also works for very small numbers by using a negative number in the exponent. In this way, 0.00000003 can be represented as 3 x 10^-8.

A common unit astronomers use to describe distances in the universe is a light-year, which is the distance light travels during one year. Even though it has year in its name, it does not measure time. Because light always travels at the same speed, it makes a good standard for keeping track of distances. The speed of light is 3 x 10⁵ km/s and a light year is 9.5 x 10¹² km.

There is another reason the speed of light is such a natural unit of distance for astronomers. Information about the universe comes to us almost exclusively through various forms of light, and all such light travels at the speed of light. This sets a limit on how quickly we can learn about events in the universe. If a star is 100 light-years away, the light we see from it tonight left that star 100 years ago. If anything happened to the star between the time the light left the star and now, we won't know until the event is 100 years old.

What at first may seem a challenge is actually a tremendous benefit in disguise. If astronomers really want to piece together what has happened in the universe since its beginning, they need some kind of data from the past. Fortunately, the farther out in space we look, the longer the light has taken to get here. By looking billions of light-years out into space, astronomers are actually seeing billions of years into the past. In this way, we can reconstruct the history of the cosmos and get a sense of how it has evolved over time.

This is one reason why astronomers strive to build telescopes that can collect more and more of the faint light in the universe. The more light we collect, the fainter the objects we can observe. On average, fainter objects are farther away and can, therefore, tell us about periods of time even deeper in the past. As each new telescope comes online, astronomers are able to see farther into the past.

Examples and Exercises

Example: Scientific Notation

Scientific Notation

In 2015, the richest human being on our planet had a net worth of $79.2 billion. Some might say this is an astronomical sum of money. Express this amount in scientific notation.

Solution

$79.2 billion can be written $79,200,000,000. Expressed in scientific notation it becomes $\$7.92 \times 10^{10}$

Example: Light Years

Getting Familiar with a Light Year

How many kilometers are there in a light-year?

Solution

Light travels $3 \times 10^5$ km in 1 s. So, let's calculate how far it goes in a year:

There are 60 $(6 \times 10^1)$ s in 1 min, and $6 \times 10^1$ min in 1 h.
Multiply these together and you find that there are $3.6 \times 10^3$ s/h.
Thus, light covers $3 \times 10^5 \text{ km/s} \times 3.6 \times 10^3 \text{ s/h} = 1.08 \times 10^9 \text{ km/h}$.
There are 24 or $2.4 \times 10^1$ h in a day, and 365.25 $(3.65 \times 10^2)$ days in 1 y.
The product of these two numbers is $8.77 \times 10^3$ h/y.
Multiplying this by $1.08 \times 10^9$ km/h gives $9.46 \times 10^{12}$ 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.

Further Exploration

Watch this brief PBS animation that explains how scientific notation works and why it's useful.

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Example: Scientific Notation

Scientific Notation

Solution

Example: Light Years

Getting Familiar with a Light Year

Solution

Further Exploration