Measuring distances in astronomy is an important aspect of understanding the interactions between bodies in the universe and the dynamics of the universe as a whole. Since there is such a wide range of distances to consider, we need several methods to determine distances between objects. We will find that calculating the distance to "nearby" objects like the nearest stars requires a very different method than is necessary for calculating distances to stars that are farther away.

Radar is a method for finding distance that uses light waves. Since we know how fast light travels, we can shine a light toward something and measure how much time it takes for the light to go there, reflect and return to us. Once we know that time, we can calculate how far away the object is.

We can use this method to find the distance from Earth to the Moon. This is called "Lunar Laser Ranging."

We placed reflectors on the surface of the Moon to use to get an accurate measure of the distance from Earth to the Moon. This is not an easy task, since the laser beam widens as it travels, becoming a few miles wide by the time it reaches the Moon. This means the light striking the reflector is dim. Similarly, the light reflecting back widens out and gets dimmer. Even so, we have successfully used this method to find the distance to the Moon. We used a similar method to measure the distance to Venus by bouncing light off its cloud layer.

As you can imagine, it gets increasingly difficult to use radar ranging for longer distances. It would be impossible to measure the distance to a star using this method. Stars are very much farther away and bouncing light off the surface of a star would not be possible anyway.

This image shows the distances to a few nearby stars. The closest star is Alpha Centauri, 4.367 light years away. We can measure distances to stars within this region using the stellar parallax method.

Image source

One way to understand size scales is by considering a model. Notice that it is not possible to view the relative size of the sun and Earth and also their distance apart in this small diagram. There is just too big of a difference in the relative length scales. One thing we can do to better understand the real sizes and distances of objects is to build a scale model.

Let's build a generic scale model as an illustration.

In this diagram, we have a real system and a scale model system. Let's think about what needs to be true for our scale model to be accurate.

In the real system, the blue ball is three times as big as the diameter of the red ball. So, in our scale model, the diameter of the blue model ball needs to be three times as big as the diameter of the red model ball.

In the real system, the Distance between the blue and red ball is four times the diameter of the blue ball. So, in our scale model, the Distance between the model balls needs to be four times the diameter of the model blue ball.

We could build a smaller scale model as well, as long as we kept the relative sizes the same between the diameters and distances.

How do we figure out how big to make the balls and distances in our model, to keep it accurate? We need to start by choosing one model object's size and compare it to the real object. This will determine the other sizes for our model.

We can go on to calculate other distances in our model, and use the same method to build a scale model of the Solar system. Please see this document for the details of the calculation if you are interested.

Since ancient times, people have noticed patterns in the stars of the night sky. Stories were built up around the groupings, or constellations, that ancient folks identified. The constellations became a backdrop for the stories and lore that was passed down through the generations.

Different cultures interpreted the groupings in their own ways, and named the constellations to fit their interpretations. For example, Orion the hunter is a constellation from Greek mythology, but the Sumerians named the constellation Uru An-na, and considered it to represent Gilgamesh, their equivalent of Hercules. The Chinese also regarded the constellation as a hunter, but called it Shen. Ancient Egyptians associated this constellation with Osiris, the god of rebirth and the afterlife.

Constellations look to us to be groupings of stars, but often the stars only appear to us to be close to each other because of our viewpoint. A side view of Orion (which we can only imagine seeing) would show that some of the stars are actually very far apart from each other, and not really grouped at all. This depiction shows that some stars are a hundred light years apart.

A light year is not a time a time at all; it is defined as the distance that light travels in a year. Since light travels at 300 million meters per second, a light year is about six trillion miles, or 63,000 times as far away as the sun is from earth. In astronomy, the typical distances that we talk about are so vast that we need really big units to discuss them.

Following the paths of stars through the night, we see that they trace out concentric circles about the North Star. Perhaps it is no wonder that ancient people thought the Earth was the center of everything.

The above image is a time-lapse photograph that shows the paths stars take over the course of a few hours. The constellations appear to move across the sky at night. Of course, it is really the result of earth’s rotation that we are noticing. Stars do move, but they are so far away that we cannot discern their motion over the course of one night. The star that happens to lie directly over the north pole seems to stand still. We call this the North Star, or Polaris. You can locate Polaris by finding the Big Dipper, and tracing a line from the front two stars to the tail of the Little Dipper. If you watch the Big Dipper over the course of a night, you will see that it rotates around Polaris. We call stars that do this “circumpolar stars.” If you look away from the north, you will see that the stars still seem to have a curved progression across the sky. There is currently no star that sits just above the south pole, but there are circumpolar stars in the southern hemisphere.

Ancient people mapped the heavens and thought of the stars as residing on the surface of a great sphere surrounding the world, called the celestial sphere. We now know that stars do not all lie at the same distance from us, but the idea of the celestial sphere is still used, since it is a convenient way to describe the locations of the stars in the night sky, as viewed from earth.