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.  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.  This is exactly the same principle employed by map makers so that they can fit Texas onto a turnable page.


Constructing the Model

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

To determine the scale value you'll need to know how much space you have. Measure the length of the hallway in meters: ____________.
Choose a scale factor so that you can fit all the planets from the Sun to Uranus in the hallway. The entire class will need to use the same scale factor.

Record it 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. Fill in these values on the board and in table 2. To make it easier to make the model, find the distance from the previous object to the current object. Again, record the distance on the board and in table 2. Copy the information for the other objects from the board.

Table 2: Scaled distances
Object Radius Distance from Sun Distance from Previous
Sun    0.0 0.0
Mercury      
Venus      
Earth      
Mars      
Jupiter      
Saturn      
Uranus      
Neptune      

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

The person/group with the Sun will decide which end of the hallway to start at. Tape the picture of the Sun to the wall. The person/group with Mercury should measure from the wall and place Mercury on the floor at the appropriate distance. The person/group with Venus can then measure from Mercury to Venus and tape Venus to the floor. Continue until all 8 planets are taped to the floor. The people/groups with Neptune and Pluto should figure out how many times longer the hallway would have to be to fit their planet in using this scale (i.e. it would have to be 1.5 times longer, twice as long, 10 times longer...) Note that distance on the picture and tape the pictures to the wall opposite the Sun.


Observations from the Model

  1. Look at the pictures of the planets, and at table 2. Are all the pictures the right size? Can you tell the difference between Jupiter and Neptune from the pictures? Can you tell the difference between Earth and Mars? Explain your answers.








Stand at the position of Earth and hold a ruler at arm's length. Close one eye and measure the size the Sun appears to be. Enter this into table 3. Stand at the position of Mercury and Saturn and measure the size again. Enter these values into table 3. Calculate the ratio of the size of the Sun at that planet to the size of the Sun at Earth.

Table 3: Sun Size
Standing at Apparent Size Compared to Earth
Earth   1
Mercury    
Saturn    

Questions

Show your work and explain your answers for full credit

  1. Solar power is a great way to power a spacecraft in orbit around Earth. Would it also be useful around Mercury and Saturn? Explain.





  2. Are there any problems with this model? How would you solve those problems? What would be the problems with the new model?





  3. The nearest star is alpha centauri, 4.3 light-years away. How far away is that from the Sun in this model? Where would you have to go to post its picture (hint, the hallway points north)?





  4. Alpha Centauri is actually a multiple star system, but one of the stars is nearly identical to the Sun. If you included a picture of a planet the size of Earth with your picture of alpha Centauri, would you be able to see your picture of the other planet while standing at the picture of Earth (assuming you had a clear line of sight: no trees, buildings, or Earth in the way)?





  5. 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: 2/11/08 by SAM

First version: MW

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