Habitable Hunt
Scientists can learn a lot about planets beyond our solar system by studying their stars. They can calculate an exoplanet’s orbital period by measuring how often its star dims as the planet passes by. They can even find potentially habitable worlds with a few key details. The star’s temperature and luminosity, which are related to its mass, define its habitable zone, the area where liquid water can exist. And the bond albedo, or percentage of light reflected by the exoplanet, helps estimate its temperature.
Scientists recently discovered seven Earth-like planets orbiting the star TRAPPIST-1. Given TRAPPIST-1’s measurements below, what are the inner and outer radii (r), in AU, of its habitable zone? Use the formula below.
TRAPPIST-1 system:
- L* (star luminosity) = 2.0097x1023 watts
- µcb (star gravitational parameter) = 1.06198x1019 m3/s2
- σ (Stefan-Boltzmann constant) = 5.67×10-8 Wm-2K-4
- T (planetary temperature) = 192-295 K
- A (planetary bond albedo) = 0.3
Given the orbital periods (Tp), for TRAPPIST-1’s planets below, which are in the habitable zone? Use Kepler’s third law below to find the semi-major axis of each orbit (ap).
Orbital periods:
- TRAPPIST-1b = 1.51087081 days
- TRAPPIST-1c = 2.4218233 days
- TRAPPIST-1d = 4.049610 days
- TRAPPIST-1e = 6.099615 days
- TRAPPIST-1f = 9.206690 days
- TRAPPIST-1g = 12.35294 days
- TRAPPIST-1h = 20 days
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