we derived a simple model for the surface temperature (Tsurf) of a planet: Tour 5 =...

  

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we derived a simple model for the surface temperature (Tsurf) of a planet: Tour 5 = [(1 - A) Splanct] ² 40 sb (1) where oso is the Stefan-Boltzmann constant (5.6705 x 10-8 kgs-³K-4), A is the planet's albedo and Splanet is the solar constant for each planet (under "irradiation" in Table 1). This simple model was also used in the Nature paper. Question A) Assuming an Earth-like albedo of 0.306, calculate the surface tempera- ture of each of the seven planets. It is highly recommended to use a spreadsheet and equations to calculate these answers. You are doing it wrong if you get temperatures lower than 100 kelvin (K), or more than 500 K. B) Discuss why the surface temperature model (Eq. 1) does not work very well for Earth and Venus. C) Discuss why setting A = 0 (as is done in the Nature manuscript) might yield more realistic surface temperature estimates. D) Based on your calculations, discuss which planet(s) orbiting TRAPPIST- 1 could support liquid water. As a hint towards your answer, it might be helpful to to compute the temperature for Earth using Eq. 1. Table 1: Data important for the TRAPPIST-1 system. AU: Astronomical unit or 149.6 × 106 km, Mo: one solar mass (2 × 10³0 kg), Searth: the solar constant at Earth (1361 W/m²). Body Mass Distance Temperature Sun Sun-Earth Mo 1 Sun-Mercury TRAPPIST-1 0.0802 Planet 1b Planet 1c Planet 1d Planet le Planet lf Planet 1g Planet 1h (AU) 1 0.387 0.01111 0.01521 0.02144 0.02817 0.0371 0.0451 0.063 (K) 5772 K 2559 K Irradiation (Splanet) W/m² 1 x Searth 6.674 × Searth 4.25 × Searth 2.27 × Searth 1.143 × Searth 0.662 × Searth 0.382 × Searth 0.258 × Searth 0.131 x Searth we derived a simple model for the surface temperature (Tsurf) of a planet: Tour 5 = [(1 - A) Splanct] ² 40 sb (1) where oso is the Stefan-Boltzmann constant (5.6705 x 10-8 kgs-³K-4), A is the planet's albedo and Splanet is the solar constant for each planet (under "irradiation" in Table 1). This simple model was also used in the Nature paper. Question A) Assuming an Earth-like albedo of 0.306, calculate the surface tempera- ture of each of the seven planets. It is highly recommended to use a spreadsheet and equations to calculate these answers. You are doing it wrong if you get temperatures lower than 100 kelvin (K), or more than 500 K. B) Discuss why the surface temperature model (Eq. 1) does not work very well for Earth and Venus. C) Discuss why setting A = 0 (as is done in the Nature manuscript) might yield more realistic surface temperature estimates. D) Based on your calculations, discuss which planet(s) orbiting TRAPPIST- 1 could support liquid water. As a hint towards your answer, it might be helpful to to compute the temperature for Earth using Eq. 1. Table 1: Data important for the TRAPPIST-1 system. AU: Astronomical unit or 149.6 × 106 km, Mo: one solar mass (2 × 10³0 kg), Searth: the solar constant at Earth (1361 W/m²). Body Mass Distance Temperature Sun Sun-Earth Mo 1 Sun-Mercury TRAPPIST-1 0.0802 Planet 1b Planet 1c Planet 1d Planet le Planet lf Planet 1g Planet 1h (AU) 1 0.387 0.01111 0.01521 0.02144 0.02817 0.0371 0.0451 0.063 (K) 5772 K 2559 K Irradiation (Splanet) W/m² 1 x Searth 6.674 × Searth 4.25 × Searth 2.27 × Searth 1.143 × Searth 0.662 × Searth 0.382 × Searth 0.258 × Searth 0.131 x Searth

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To calculate the surface temperature of each planet using the given equation Eq 1 we can substitute the values of the StefanBoltzmann constant the albedo A and the solar constant Splanet for each plan... View the full answer