University of Michigan - Department of Astronomy

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The Size of the Solar System

According to the map, we've only gone about four inches!

-- Harry ("Dumb and Dumber", New Line Cinema, 1994)

Overview

Introduction

It is easy to flip to the index of an astronomy textbook to discover that, say, the Sun lies 150 million kilometers away from Earth. It is far more difficult (if not impossible), however, to picture this distance in the human mind. In this exercise, we will learn to access the often unpalatable distances encountered in astronomy by simply scaling the huge distances to more recognizable, pedestrian numbers. We can’t see the actual objects or walk the real distances, so we will create a scale model. So long as every distance within the system of interest is scaled by the same factor, we retain the meaningful information about relative distances between objects.

In a scale mode, a smaller distance is substituted for a large distance. For example, you might build a 1:20 scale model of an airplane, so that 1" in you model represents 20" on the real plane. Similarly, 1" on a map might represent 100' of real distance.

We will also be looking at the overall structure of the solar system. 99% of the mass in the solar system is contained in the central star, which we call the Sun. Everything else, the planets, asteroids, comets, etc., orbit the Sun. Some of these objects (including some asteroids and comets) have their own satellites. The Earth for example has the Moon, and the Earth and Moon together go around the Sun. Denser objects, like the iron-cored terrestrial planets orbit close to the Sun, and the less dense but more massive Jovian planets are farther out.

In this version, you'll be using Google Earth to create the model. By doing this, you'll be able to create a more realistic model than the traditional model, where all the planets are in a line. If weather and time permit, you'll be able to go outside and set up part of the solar system as a real model.


Constructing the Model

Even when expressed in the one of the largest units (km) used to describe Earth-bound distances, the sizes of and distances to the planets require numbers raised to large powers of ten.  In order to fully appreciate the relative sizes and distances within the solar system, it is necessary to scale these numbers down to values small enough so that we can "see" them in terms of more familiar distances.  We can accomplish scale value.  

  1. The scale value should make the planet Mars 1 mm or 0.001 m in diameter. Given that Mars is 3.4 x 103 km in radius, determine what the scale value is in terms of how many km of real distance = how many mm and m of scale distance. Show your work, where necessary.
  2. Alpha Centauri is the closest star system to our solar system, although it is 4x1013 km away. What is the scaled distance to Alpha Centauri? Show your work.




Table 1 gives current measurements for the actual sizes and orbital distances of the planets, as well as the distances in our scaled model.

Table 1: Measured and Scaled Astronomical Distances in Solar System
Object
Radius (km)
semi-major axis (km)
Scale R (mm) Scale a (m)
Sun
6.96 x 105
--
205 --
Mercury
2.44 x 103
5.83 x 107
0.718 17.1
Venus
6.05 x 103
1.08 x 108
1.78 31.7
Earth
6.38 x 103
1.50 x 108
1.88 44.1
Mars
3.40 x 103
2.27 x 108
1.00 66.8
Jupiter
7.14 x 104
7.78 x 108
21.0 228
Saturn
6.03 x 104
1.43 x 109
17.7 420
Uranus
2.56 x 104
2.87 x 109
7.53 844
Neptune
2.43 x 104
4.50 x 109
7.15 1320
  1. Your GSI will put you in groups and assign an object to you. Place a star next to your object's name in table 1.
  2. Using the information from table 1, draw a scale picture of your object on plain white paper. Label the picture so that the label can be seen from a distance.

Google Earth

  1. In the Dock at the bottom of the screen on the Astronomy Computer Lab computers, you'll find a file called "The Diag, UM.kmz" inside the Astroclass folder (between the trash and Documents folder on most of the computers. Opening the kmz file should also open Google Earth. If you don't have it, you can open Google Earth and search for TheDiag, UM. Under the Layers section, turn off everything except "Boarders and Labels" and "Roads."
  2. Find the location of the flagpole, between the Chemistry and Kraus buildings. Put a placemark placemark iconon the flagpole so you have an easy reference point.
  3. Click the Ruler Ruler iconbutton set the ruler to meters. Click the location of the flagpole to start your measurement, then move to a position that is the "Scale a (m)" distance away for your planet . If your selected position fits on the map of the diag, mark the position on the map and label it. If not, on the back of the map write a COMPLETE sentence including the name of the planet to describe where it goes.
  4. Repeat the above step 3 - 5 times, until you know where the orbit of the planet would go. If it fits on the map of the diag, sketch the orbit on the map. Make the line dark enough that you'll be able to show it to the rest of the class. If it does not fit on the map, note several landmarks so you can describe where the orbit is.
  5. Use the Ruler to determine where Alpha Centauri would be. Give the heading from the Ruler, and the name of the place you end up.


Inside version:

  1. Your GSI will go around the class, starting with Mercury, and have each group hold up their map and their picture so the rest of the class can see the orbit. Roughly sketch the orbit on your own map, making sure it is lighter or different from the orbit of your planet. If your group has a planet whose orbit does not fit on the map, describe the landmarks that can be used to identify its orbit.
  2. Answer the Model Questions below.

Outside Version:

  1. When your GSI tells you to, go outside to the flagpole The group with the Sun should stand at the flag pole and hold up their picture. Groups with planets whose orbits will fit on the map should pick a spot along the orbit where they can see the flag pole, stand at that spot, and hold up their picture. Groups whose orbits are too far should gather near the flag pole and hold up their pictures.
  2. Look around for the other planets, and mark their positions on your map. Include labels.
  3. Write down which planets you can actually see the drawing of from where you are, and how big the Sun looks.


  4. When your GSI waves you over, gather at the flag pole. Check your labels with the other groups and add any that you didn't get. Take a look at the sketches of the other planets, then answer the questions below.

Model Questions

  1. Can you tell the difference between Jupiter and Neptune from the pictures? How about Neptune and Uranus? Earth and Mars? Explain your answers.



  2. The difference between Earth's semi-major axis and Venus' semi-major axis in the model is 12.4 m. Does this represent the average distance between Earth and Venus, the minimum distance, or the maximum distance (assume the orbits are actually circular)? Explain, using the model as an example.





Concluding Questions

Show your work and explain your answers for full credit. You should also turn in the map and sketch for the group, so make sure you have the names of your group members at the start of this activity.

  1. If you placed the drawing of Jupiter at the scaled distance of alpha Centauri, could you see it while standing at the picture of Earth (assuming you had a clear line of sight: no trees, buildings, etc.)? What does this tell you about searching for planets orbiting other stars?





  2. The Moon is 1.7x103 km in radius and 3.8x105 km from Earth. The International Space Station obits at about 300 km above the Earth's surface. Using the same scale as the model, sketch a picture of the Earth, Moon and ISS (use an X or some other symbol for the ISS since it is too small to actually be visible on this scale.) Show your calculations indicating how you determined the size of the moon and the relative distances of the ISS and Moon from Earth. Does your picture surprise you at all?


Last modified: 12/21/2011 by SAM based on previous version by CMM

original: MW

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