The Size of the Solar System
Overview
• Become familiar with the scale of the planets vs. their distances.
• Get an overview of the solar
... [Show More] system.
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 (*Kuiper Belt Object 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 (avg. distance from Earth)
Mars 3.40 x 103 2.27 x 108
Ceres 4.73 X 102 4.14 X 108
Jupiter 7.14 x 104 7.78 x 108
Io 1.82 x 103 4.22 x 105 (avg. distance from Jupiter)
Ganymede 2.63 x 103 1.07 x 106 (avg. distance from Jupiter)
Saturn 6.03 x 104 1.43 x 109
Titan 2.58 x 103 1.22 x 106
(average distance from Saturn)
Uranus 2.56 x 104 2.87 x 109
Neptune 2.43 x 104 4.50 x 109
Pluto 1.19 x 103 5.91 x 109
Charon
(moon of
Pluto) 6.35 x102 1.96 x104 (avg. distance from Pluto)
Quaoar* 5.84 X 102 6.49 X 109
Eris* 1.16 X 103 1.02 X 1010
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 Earthbound 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: [Show Less]