2015 is shaping up to be an interesting year in space exploration. For the first time, we will get up-close views of a dwarf planet. In fact, two different spacecraft will visit two different dwarf planets. The Dawn spacecraft is nearing its second primary target, Ceres, later this week. Later this year, the New Horizons spacecraft will visit Pluto.

Of course, related to all of this is the public controversy over the International Astronomical Union’s (IAU) “demotion” of Pluto from planet status. Regardless of your view on the matter, Pluto is still there, just as it always was, and nothing has changed concerning its existence. It doesn’t really matter what we call it. I won’t go into great detail to explain why Pluto was demoted, but we can use the Wolfram Language to explore some of the primary reasons.

One of the requirements for being labeled a planet according to the IAU definition is that the object must have cleared its orbit of other bodies. Planets have typically either absorbed or thrown out intruders so that they dominate their orbital zones. In the case of Ceres and Pluto, both bodies violate this requirement. Here is a graphic showing the orbit paths of Jupiter and Mars in orange, several large asteroids in blue, and the orbit of Ceres in red. As you can see, Ceres lies in the asteroid belt between Mars and Jupiter, along with many other objects, all classified as dwarf planets, asteroids, minor planets, or small solar system bodies, depending on your preference (or in the case of Ceres, by IAU definition).

A similar analysis can be done for Pluto. In the following example, you can see that all of the planets’ orbits (in orange) are relatively nice and concentric until you get to Pluto (in red), which crosses Neptune’s orbit. In addition, there are a number of other known “Plutoids” (in blue) that cross orbits with Pluto. And in fact, there are many more such objects. So if Pluto is a planet, then all of these objects, and many more, could potentially be declared planets, and that would be a nightmare for educational books to keep up with. The traditional question of “How many planets are there in the solar system?” becomes a large number that keeps growing as more objects are discovered.

Something else that is interesting to explore is size. Many people don’t really comprehend the sizes of Ceres and Pluto. The only size restriction provided by the IAU definition for a planet is that the body must be large enough for gravity to have pulled it into a spherical shape. This seems to be the case for both Ceres and Pluto, but this alone doesn’t make them planets. But it’s still interesting to visualize the sizes of these bodies by comparing them to something we are more familiar with. We can make use of GeoGraphics to put the size of these bodies into perspective. Here is a 2D map of the United States, with Texas highlighted in red. The inner disk represents the size of Ceres projected against Texas, the middle disk represents the size of Pluto, and the outer disk represents the size of our Moon. So the cross-section of Ceres is about the same size as Texas. Both Ceres and Pluto are noticeably smaller than our Moon.

With a bit more exploration, we can move this visualization into three dimensions by using texture mapping to move the above map onto a sphere.

First, we define a couple of geographic entities we will need:

Next, we use GeoGraphics to construct our 2D map and then convert it to an image:

Then we obtain several radius values we need, making sure they are all using the same units:

For positioning things, it’s useful to determine a center point for our map:

We need to position Ceres, Pluto, and the Moon near the center point of the map and offset them to appear as if they are sitting on the surface of Earth at that point:

We can apply the map as a texture on a sphere that represents the Earth using ParametricPlot3D:

Finally, we can combine the pieces and compare the sizes of Ceres, Pluto, and the Moon to the Earth:

In the coming days and weeks, the Dawn spacecraft will provide us with the first close-up views of the dwarf planet Ceres. Later this year when New Horizons passes Pluto, we will get our first close-up views of the more controversial member of this group of objects. Nothing we discover will result in Pluto being reinstated as a planet, as the reasons for its demotion are still there. But we will obtain more data on these small objects than has ever been gathered before, and it will give us a new understanding of these often under-appreciated members of our solar system. Dwarf planets are worthy of study regardless of what they are called.

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