Question

Kepler 1606b is an exoplanet: a planet orbiting a star different than our own. Named for the star it orbits (Kepler 1606, a star about 3000 light-years away), it was discovered in the year 2016 by the Kepler space telescope.

Kepler 1606b orbits its star a little bit closer than the Earth's orbit to the Sun, at a distance of 0.64⋅rearth, where rearth=1.50×1011 m is the radius of Earth's orbit. The star Kepler 1606 is bit cooler than our Sun, with a temperature of 5422 K, and is a bit smaller than our Sun, with a radius of 0.86⋅Rsun, where Rsun=7.00×108 m is the radius of the Sun.

Note: In the following, do not confuse the planet Kepler 1606b with the star Kepler 1606. (Unfortunately for us, the naming system used for exoplanets just adds a letter to the star's name, and can make it hard to distinguish planet from star.)

(a) If Kepler 1606b has no atmosphere and an albedo similar to the Earth's (albedo of 0.3), what would the equilibrium average temperature of the planet be? Give your answer in ∘C.

(b) If we include a thin atmosphere for the planet Kepler 1606b, with an atmospheric emissivity of e=1, what would the surface temperature of the planet be? Give your answer in ∘C.

(c) What is the equilibrium temperature of the thin atmosphere? Give your answer in ∘C.

Answer 1