The Ein's Place in the Universe

Full Point Deadline: 8 April 2025

The Trapiforms, a.k.a., The Ein's Place in the Universe

YD 649; Location: Earth

The Trapiforms, as we call them, are the inhabitants of the extrasolar Earth-like planet TRAPPIST-1e in orbit around the M-dwarf star TRAPPIST-1. Not being Earthlings, they, of course, do not refer to themselves as the Trapiforms, nor do they know that we call their star TRAPPIST-1, which is named after the Transiting Planets and Planetesimals Small Telescope (TRAPPIST) at the La Sila Obseratory in Chile. 

This civilization refers to themselves as the Ein, and they call their planet, Ein-El, which orbits the star Ur-Set. The Ein are an upcoming galactic civilization that is starting to understand their place in the universe. For our convenience, we will use Yggdrasil standard units, which just so happen to be SI Earth units (how convenient). Recently the Ein successfully measured the full bolometric flux of their star using a satellite that is above their atmosphere. 

Using this information, and a few other known characteristics of Ein-El, let’s go through the process of learning about their planet and planetary system. 

Editorial Note: Once contact and communication between our cultures is established, according to the Transstellar Convention treaty, the names TRAPPIST-1, TRAPPIST-1e, and its people will be officially updated to Ur-Set, Ein-El, and Ein, respectively, to reflect the names of the system’s inhabitants.

Given Properties for Ein-El

• Orbital Period: 6.10 days

• Semi-major axis: 0.0293 AU

• Radius of Ein-El: 5,804 km

• Mass of Ein-El: 4.597 * 10^24 kg  

Part A (+2 Problem Solving)

The Ein measured the bolometric flux from their red M-type star Ur-Set to be F = 1155.0 Watts per meter squared at the top of their atmosphere. What is the bolometric luminosity of the star Ur-Set in Watts and Solar Luminosities?

Part B (+2 Problem Solving)

What is the absolute bolometric magnitude of Ur-Set?

Part C (+4 Problem Solving)

Assuming an albedo of 0.3, what is the thermal equilibrium temperature of Ein?

Part D (+12 Problem Solving)

This star system has a measured parallax of 0.0802 arcsec. From Earth, we measure the visible magnitude of Ur-Set to be V = 18.80.  

Find a bolometric correction for Ur-Set.

Part E (+5 Problem Solving; +5 Connections; +5 to +10 Creativity)

Imagine a social structure that the Ein have that is incredibly alien to how humans do things. Give this a basis in something like their biology, physiology, psychology/neuroscience, etc. Describe what this behavior/custom/tradition/social element is and how it connects to your chosen basis.

Part F (+10 Critical Thinking)

Based on your answer to Part E, discuss how communicating with Ein would be challenging for humans.