The Size of the Solar System
• Become familiar with the scale of the planets vs. their distances. • Get an overview of the solar system.
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, for example, onto a turnable page. [pic]
Constructing the Model
Table 1 gives current measurements for the actual sizes and orbital distances of the planets. For moons, the semi-major axis is the distance to the planet. Table 1: Measured Astronomical Distances in Solar System (*KBO radii are not well known) |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 | |Moon |1.74 x 103 |3.84 x 105 | |Mars |3.40 x 103 |2.27 x 108 | |Jupiter |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 | |Saturn |6.03 x 104 |1.43 x 109 | |Titan |2.58 x 103 |1.22 x 106 | |Uranus |2.56 x 104 |2.87 x 109 | |Neptune |2.43 x 104 |4.50 x 109 | |Pluto |1.16 x 103 |5.91 x 109 | |Charon |6.35 x102 |1.96 x104 | |Quaoar* |5.84 x 102 |6.49 x109 | |Sedna* |7.45 x 102 |7.51 x 1010 |
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. Suppose the length of a hallway in the campus in meters is 10 meters. We can choose a scale factor, so that we can fit all the planets from the Sun to Uranus in this hallway. Then, the scale value can be obtained through the following procedure: If 10 meters are assigned to 2.87 x 109 Km
Then the scale factor for distances from the Sun is: 1 meter/2.87 x 108 Km For the size of the planets, we can choose in our scaled model, the radius of the Sun to be 10 centimeters. Then, the scale value can be obtained through the following procedure: If 10 centimeters are assigned to 6.96 x 105 Km
Then the scale factor for radii is: 1 centimeter/6.96 x 104 Km Use the scale factors to calculate the size of your object and the distance of the object from the Sun (round two decimal digits). Fill in these values 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 in table 2....
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