Planets Around An Ultra-Cool Dwarf Star

Quote of the Day

Mistakes are a great educator when one is honest enough to admit them and willing to learn from them.

— Alexander Solzhenitsyn


Figure 1: Artist's Conception of the Trappist-1 System.

Figure 1: Artist's Conception of the Trappist-1 System.

I have been interested in the possibility of their being habitable regions around stars that are smaller and dimmer than the Earth. I saw an article this week on a solar system about a star, Trappist-1, that is  not much larger than Jupiter and that is quite cool for a star (2550K).

My plan here is to look at some measured data for Trappist-1 and see if I can derive some of the other parameters for this star and its system. I will use information available from the Wikipedia and the Open Exoplanet Catalog.

Planetary scientists have discovered three planets around Trappist 1 (Figure 1), and I think I can duplicate their estimates of the planet's orbital radius and solar insolation. I will add an estimate for their effective temperature.



Insolation is the solar radiation striking Earth or another planet. It is the rate of delivery of solar radiation per unit of horizontal surface (Source).
Brown Dwarf
A brown dwarf is a substellar object not massive enough to ever fuse hydrogen into helium, but still massive enough to fuse deuterium—less than about 0.08 solar masses and more than about 13 Jupiter masses (Source).
Ultra-Cool Dwarf
A dwarf star of spectral type M7 or later – the warmest kind of brown dwarf. These stars are at the high-mass, high-temperature end of the brown dwarf scale (Source).

Exoplanet Background

The exoplanet background for this post is covered in an earlier post.


My Mathcad source and its PDF are included here.

Star Characteristics

Figure 2 summarizes my

  • Analysis setup
  • Trappist-1's measured star characteristics (light green highlight)
  • My comparison of Trappist-1 with Jupiter in terms of diameter and mass (yellow highlight).
    • Trappist-1's diameter is only 13% larger than Jupiter
    • Trappist-1's mass is 83.8 times that of Jupiter.
Figure 2: Definitions and Star Characteristics.

Figure 2: Definitions and Star Characteristics.

Planet Orbital and Insolation Characteristics

Figure 3 shows my application of Kepler's 3rd law to determine each planet' orbital radius. I also determine the insolation of each planet by Trappist-1. Two of the planets are much warmer than the Earth. The data for the 3rd planet had a wide range of values – for computational ease, I chose the shortest possible orbital period. Using the shortest period means that I am assuming that the planet's radius is the minimum possible consistent with the observations.

In Figure 3, measured period data has a light green highlight, while my derived characteristic are highlighted in yellow.

Figure 3: Planet Orbit and Insolation Characteristics.

Figure 3: Planet Orbit and Insolation Characteristics.

Estimated Planetary Temperatures

Figure 4 shows my estimates for the planet temperatures. One of the planets has an effective temperature similar to that of Earth (-21 °C), and the others are much hotter.

Figure 4: Estimate Planet Temperatures.

Figure 4: Estimate of Planet Temperatures.


I find these small stars and their planets interesting. Even though these stars are relatively cool, it is possible to have a planets close enough to these stars to receive significant heat.

In this case, the star is close to the Earth (~40 light-years). I hope we will be able to gather more data about this planetary system in the near future.

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