The Cosmic Perspective
We will begin studying the universe by examining our place in the cosmos. Here, we will take a look at how we fit in as far as size and distance. We will also take a look at how the relative motion of Earth affects our perspective of the universe around us. We will also consider some of the underlying physics that we will need to understand the dynamics of Earth and the universe as a whole.
The Hubble Deep field image shows us that there are very many galaxies, some similar to our own Milky Way galaxy. Since we reside within the Milky Way, we cannot yet see how it appears from a distance. Perhaps some day we will venture outside our galaxy, but for now, our earliest probes are barely leaving our solar system. Even so, astronomers have done a lot of work to understand our galaxy and how it is laid out in space. Estimates vary between 100 billion and 200 billion as to how many stars are present in the Milky Way.
The Milky Way is some 100,000 light years across. It is extremely hard for us to grasp distances that large. One way to gain an understanding of this vast distance is to compare it to sizes in our everyday lives, in decreasing scales by powers of ten. The link below takes you to one such journey, beginning with a representation of the Milky Way galaxy, decreasing to our everyday world, and continuing on down to subatomic sizes.
The above image shows the relative sizes of the planets in our solar system. The bottom row is Earth, Venus, Mars, Mercury and Pluto (minor planet).
This image shows how big the sun is compared to the planets in our solar system.
Our sun is actually a rather small star. Compared to these supergiant stars, our sun is only one pixel in this image.
Image credit http://apod.nasa.gov/apod/ap120119.html
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. These constellations became a backdrop for the stories and lore that was passed down through the generations.
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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 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, and really corresponds to how far 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.
The Celestial sphere
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 they 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.
Image source http://apod.nasa.gov/apod/ap150625.html
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.
Over the course of a year, earth takes a lap around the sun. At any given time of year, some stars will not be visible to us, because the lie behind the sun or are close enough to it that they are only “out” in the day. The constellations that lie along the path that the sun appears to take in the sky are known as the zodiac stars. Ancient people such as the builders of Stonehenge and other early “observatories” were very adept at keeping track of the apparent motions of constellations, and developed calendars built on the knowledge that they gained by watching the heavens.
The cosmic distance ladder
Measuring distances in astronomy is a very 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 requires a very different method than is necessary for calculating distances to galaxies.
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The method we use to calculate distances to the nearest stars is called "stellar parallax." It is basically just triangulation, based on knowing the area of a triangle if your know the length of the base and the base angles. Here, distance shown for the base is the diameter of Earth's orbit about the sun.
We define the distance called a "parsec" using the parallax method, as shown in the above equation. Here, the angle is measured in arc-seconds. If you divide up the sky into 360 degrees, 1/60 of one degree is called an arc-minute, and 1/60 of an arc-minute is called an arc-second. One parsec is defined as the distance to an object that subtends an angle of one arc-second.
As shown in the diagram, one astronomical unit (AU) is defined as the distance between Earth and the sun.
1 parsec = 206,265 AU = 3.3 light years = 19 trillion miles = 31 trillion kilometers
To get a better idea of how this works, please check out the "Stellar Parallax" simulation at highered.mheducation.com/sites/0072482621/student_view0/interactives.html#
This image shows the distances to a few nearby stars. The closest star is Alpha Centauri, 4.367 light years away.
We cannot use stellar parallax to measure distances to stars that are considerably farther away (over a hundred parsecs), since their apparent motion across the sky is so small that their parallax angles are not measurable. For more information, see the information at Las Cumbres Observatory.
To measure distances to more distant stars, we use a method called "spectroscopic parallax. Basically, the idea here is that stars spend most of their lives shining at a certain intrinsic brightness, or luminosity, that depends on their mass and surface temperature. We compare this intrinsic brightness to how bright they appear to us to estimate the distance. This method is good to about 10,000 parsecs away, and is covered in more detail in PH206. If you are interested, please see section 17.6 of your text. We will continue to study methods of measuring distances, increasing our range to a galactic scale.
One way to understand size scales is by considering a model. Here is one such model of our solar system. Please visit this link and investigate the various options.
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. What if we had more room? Let's look at how we could build a scale model of our solar system. We need to start by choosing one object's size. Let's assume that in our model, the sun is the size of a bowling ball. Comparing the size of a bowling ball will allow us to calculate the other relative distances in our scale model. We also need to know the real distances involved.
Here, dearth is the diameter of the earth, dball is the diameter of a bowling ball, dsun is the diameter of the sun, and 1 AU is the distance between the earth and sun.
The ratio of the ball to the sun is the same as the ratio of the size of earth in our scale model to the real size of the earth. In our model, Earth is the size of a small bead.
We can use the same ratio to calculate how far apart the bead would be from the bowling ball in our model. Here, we can see that the distance in our model would be 24 meters. Now, if the true distance to the nearest star, Alpha Centauri, is 4.0 x 1016 m, how far away would it be in our model?