According to the map, we've only gone about four inches
-- -Harry ("Dumb and Dumber," New Line Cinema, 1994)
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.
Table 1 gives current measurements for the actual sizes and orbital distances of the nine planets.Table 1: Measured Astronomical Distances in Solar System (*KBO radii are not well known)
||semi-major axis (km)
||6.96 x 105
||2.44 x 103
||5.83 x 107
||6.05 x 103
||1.08 x 108
||6.38 x 103
||1.50 x 108
|Moon||1.74 x 103||3.84 x 105|
||3.40 x 103
||2.27 x 108
||7.14 x 104
||7.78 x 108
|Io||1.82 x 103||4.22 x 105|
|Ganymede||2.63 x 103||1.07 x 106|
||6.03 x 104
||1.43 x 109
|Titan||2.58 x 103||1.22 x 106|
||2.56 x 104
||2.87 x 109
||2.43 x 104
||4.50 x 109
||1.16 x 103
||5.91 x 109
|Charon||6.35 x102||1.96 x104|
|Quaoar*||5.84 x 102||6.49 x1012|
|Sedna*||7.45 x 102||7.51 x 1013|
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. Record your scale value and describe how you arrived at it here:
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.
|Object||Radius||Distance from Sun||Distance from Previous|
Using the information from table 2, draw a scale picture of your object on plain white paper. If you have the Sun, you may need to tape some paper together. If your object is a moon, you should include your sketch on the same paper as the planet it orbits. 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 planet pictures are taped to the floor.
The people/groups with Neptune, Pluto, Quaoar and Sedna should figure out how many times longer the hallway would have to be to fit their object 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.
Stand at the position of Earth and hold a ruler at arms 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.
|Standing at||Apparent Size||Compared to Earth|
Show your work and explain your answers for full credit1.
Last modified: 6/16/05 by SAM, original by MWCopyright Regents of the University of Michigan.