Calculating the Density of a Planet

Quote of the Day

Democracy is the theory that the common people know what they want, and deserve to get it good and hard.

— H. L. Mencken

Introduction

Figure 1: Artist's Impression of the dwarf planet
Eris. (Source)

I have been reading some interviews with Michel Brown, an astronomer that has a book out called "How I Killed Pluto and Why It Had it Coming." His interviews are interesting and I encourage people to read or view them (Example). Michael is the discoverer of the Kuiper Belt object ("dwarf planet") called Eris and its moon Dysnomia (Figure 1). I became intrigued during one of these interviews when it was mentioned that if a moon is found around a planet, we can compute the planet's density. Let's look at Mike's planet Eris and its moon Dysmonia and see if we can compute the density of Eris.

Analysis

You can use Newton's law of gravity, the equation for centripetal acceleration, and the definition of density to determine the density of a planet. I like to use a computer algebra system to experiment with a problem. For this demonstration, I will use the symbolic solver in Mathcad to help me out. All of the data I used in my analysis came from the Wikipedia. The analysis itself is shown in Figure 1.

Figure 1: Determination of a Planet's Density from Satellite Data.

Conclusion

According to my calculations, Eris's density is almost 2.5 gm/cm³. This is in the density range listed in the Wikipedia for Eris. This is a good example of a basic astronomical calculation that can help researchers determine the characteristics of worlds that we can only see as distant objects.

Save