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. 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.

In addition, we will 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.


Constructing the Model

Table 1 gives current measurements for the actual sizes and orbital distances of the planets.

Table 1: Measured Astronomical Distances in Solar System
Object
Radius (km)
semi-major axis (km)
Sun
6.96 x 105
--
Mercury
2.44 x 103
5.83 x 107
Venus
6.05 x 103
1.08 x 108
Earth
6.38 x 103
1.50 x 108
Mars
3.40 x 103
2.27 x 108
Jupiter
7.14 x 104
7.78 x 108
Saturn
6.03 x 104
1.43 x 109
Uranus
2.56 x 104
2.87 x 109
Neptune
2.43 x 104
4.50 x 109

As you can see, 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 this by dividing every number in Table 1 by some constant scale value.  

The scale value should make the planet Mars is 1 mm or 0.001 m in size. Determine what the scale value is in terms of how many km of real distance = how many m of scale distance.

Record the scale value here: _____________________km (in space) = ________________m (in the model)

Your GSI will assign an object to you. Place a star next to your object's name in table 2.

Use the scale factor to calculate the size of your object and the distance of the object from the Sun. Show your work below. Fill in these values on the board and in table 2. Copy the information for the other objects from the board.

 

 

Table 2: Scaled distances
Object Radius (mm) Distance from Sun (m)
Sun    0.0
Mercury    
Venus    
Earth    
Mars
  1  
 
Jupiter    
Saturn    
Uranus    
Neptune    

Using the information from table 2, draw a scale picture of your object on plain white paper. Label the picture.

  1. Alpha Centauri is the closest star system to our solar system, although it is 4x1013 km away. It is a multiple star system, and one of the stars is nearly identical to the Sun.What is the scaled distance to alpha centauri?

When everyone has their picture, you will gather on the diag near the flagpole. The person with the Sun will stand near the flagpole. Each group with a planet less than 75 m from the Sun in our scale should measure from the Sun to their distance, and hold their picture that distance from the Sun. Make sure everyone heads away from the Sun in a different direction, so the solar system is spread out, not in a straight line. Anyone with a planet more than 75 m away from the Sun will have to use the map to estimate the location of their planet. Once everyone is in position, mark the location of each planet on the map. Anyone without a planet, or whose planet is more than 75m away should join one of the groups around on of the other planets. Each member of the group should trade off holding the planet image and wandering around, so everyone gets a chance to observe the model. Answer the following questions before going back inside.

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



  2. Consider the scaled distance to Alpha Centauri. Where would this be in our model?Give a general location (a city or town you think is the right distance away.)




Concluding Questions

Show your work and explain your answers for full credit

  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.)





  2. The Moon is 1.74x103 km in radius and 3.844x105 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.



Last modified: 2/14/11 by SAM with input from CMM

original: MW

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