How to Measure Astronomically Distant Objects

Light years, parsecs and more: these units of measurement are used to describe the distances between planets and other astronomical objects

If you want to determine the size of a basketball, you can use a regular ruler to measure its diameter. You should get a value of about 0.24 meters. Please do not use inches – they are more difficult to work with. In any case, you are probably not using imperial units, since only three countries officially use this system: Myanmar, Liberia and… the United States. They should switch to the metric system, like everyone else.

But what if you want to know the distance from New York to Los Angeles? Sure, you could use meters, which is about 3.93 x 10^6 meters, or kilometers (3,930 km). But kilometers are just a fancy way of using meters. They're the same unit of distance, just with a prefix. Meters (or kilometers) work well enough for big things like the Earth, which has a radius of about 6.37 x 10^6 meters.

Beyond Earth, however, things get very big. For very big things, it is often useful to use very large units of distance. Let's look at three of the most common units of distance in astronomy.

Astronomical unit

The name of this unit makes it sound a little more important than it actually is — it is important, but not to the rest of the universe. In short, an astronomical unit (AU) is the distance from the Earth to the Sun. Technically, that's not quite right, since the Earth's orbit around the Sun is not perfectly circular. Let's just say that an AU is the average distance to the Sun — that'll do for now.

The AU makes it much easier to measure distances in the solar system. For example, the distance from the Sun to Mars is about 1.52 AU, and to Pluto it is about 40 AU. But there is an even more compelling reason to describe distances in AU than just convenience. People first used the astronomical unit because they didn’t know the distance from the Earth to the Sun. Yes, it sounds crazy, but it’s true.

So here's the deal. The ancient Greeks made some amazing measurements of the Earth and the Moon (and tried to figure out the distance to the Sun), but it's pretty complicated. But even without an exact distance between the Sun and the Earth, later astronomers were still able to make some good models of the Solar System. Johannes Kepler discovered that the time it takes a planet to orbit the Sun is proportional to its distance from the Sun (again, technically these orbits are ellipses). Using this, he could figure out the distances of the other planets from the Sun in terms of their distance to the Earth. And presto, you've got your distance in AU.

Of course, no one wants to stop and leave all the data about the solar system in terms of AU. What we really need is a conversion factor between AU and meters. To get that, we need to actually measure the distance between the Earth and the Sun. This is not an easy task, but one way to get a reasonable value is to use the transit of Venus. This happens when the planet Venus passes between the Earth and the Sun (this does not happen as often as you might think). By measuring the exact start and end times of the transit from different points on Earth, you can get the AU value in terms of the size of the Earth (which we mostly know). Here are all the details of this calculation, if you are interested.

So we ended up with a distance between the Earth and the Sun of about 1.496 x 10^11 meters. Yes, that's quite a lot.

Parsec

How far away is the nearest star? It's Alpha Centauri at 2.67 x 10^5 AU (you can convert that to meters for homework). So you see, we're back to the same problem. Maybe it makes sense to use a unit of distance that doesn't involve gigantic numbers. That's where the parsec comes in.

The parsec depends on one big idea: parallax. Let's start with a simple experiment you can do at home. Hold your arm straight out in front of you, thumb up. Don't worry about looking silly – let me do it too.

Now look at your thumb and close one eye (it might help if you also say “camera one”). With one eye closed, identify which object in the background your thumb is aligned with. It doesn't matter which one – just be aware that it's there somewhere. Then switch eyes (and say “camera two”), but don't move your thumb. You should notice that the position of your thumb relative to the background changes. This is parallax. It's the apparent change in the position of an object when you look at it from a different place. The closer the object is to your face, the greater the apparent change.

If you want to calculate the distance to an object, you can find it using the magnitude of the angular shift and the distance between the two observation points using the following equation (assuming that the distance to the object is much greater than the distance between the observation points):

Distance to object = Change in observed distance / Angular shift

In this case, you need an angle measured in radians (not degrees). It is clear that to get a measurable angular shift, it is necessary to shift the observation locations quite a lot, if we are talking about objects like stars (i.e. very distant ones). What if we observe an object from Earth when it is on one side of the Sun, and 6 months later – on the other? In this case, the star will give a small angular shift. Like this:

Knowing the distance from the Earth to the Sun (yes, we still need this distance) and measuring the angular displacement of a star, we can calculate the distance to the latter. Yes, this measurement also depends on other stars that are very far away and do not move very much. If all stars were the same distance from our Sun, we would have a hard time measuring the angular displacement.

Now about the parsec. It is defined as follows: 1 parsec is the distance at which a star must be located so that its apparent angular displacement is 1 arc second of a degree. Let's find the conversion of parsecs to AU – just for fun.

Step one is to get the angular displacement per 1 arc second in radians.

The rest is easy. Just take 1 AU and divide by that angular shift. If you plug that into a calculator, you get 2.06 x 10^5 AU. Repeat this to convert parsecs to meters. It'll be fun.

Light year

Parsecs are cool. They sound so cool that they could be used in a movie about space, but used to describe time instead of distance (since it sounds like distance). And then, 40 years later, they could make another movie that somehow justified the misuse of a parsec. That would be awesome (hint: I'm a huge Star Wars fan).

But wait. There's another unit of distance that sounds like time. It's the light year. Yes, a year is a unit of time, but a light year is a unit of distance. It's defined as the distance light travels in one year.

The speed of light is finite and constant, and is approximately 2.998 x 10^8 m/s. The distance that light travels in a given period of time can be found using the definition of speed (in one dimension):

Calculating the size of a light year means finding the time interval (Δt) in units of seconds rather than years, since speed is measured in meters per second. I skipped the part where I convert 1 year to seconds, but after that I can calculate the conversion between light years and meters.

What if you converted 1 AU to light years? I’ll leave the math for you to do, but the answer is 1.58 x 10^-5 light years. That’s 8.3 light minutes. Think about it. It takes 8 minutes for light to travel from the Sun to the Earth. And consider this: Jupiter is about 40 light minutes from Earth (distance varies). So when you look at Jupiter in the night sky, you’re actually looking at it in the past. Forty minutes in the past. Your eyes are a time machine.

The farther we look, the further back we look. Even when you look at very close things, like a computer screen, you are looking into the past (the very near past). Because light takes a finite time to travel, and because we see with light, you are looking into the past.

This is why the light-year unit is so useful for astronomy. When we look at a galaxy 10 billion light-years away, we are looking 10 billion years into the past. And that is amazing.