Question

= A1. A distant star is determined to have a surface temperature of Tstar - 6000K and a radius of 5.0 x 108 m. A planet named Hydra is detected orbiting this star at a distance of 1.0 x 1011 m and has an albedo of 0.60. [1] (a) At what wavelength is the peak irradiance from this star? [1] (b) What is the total Luminosity of the star? (c) What is the effective temperature of Hydra? (d) The actual surface temperature of Hydra is 800 K. Briefly explaining this ob- servation using the principles of different transmittance of the atmosphere for short-wave photons and long-wave photon. A diagram may be useful. 3

Answer 1

1/4 Te 2.309 X1096) (1-060) 16 Tx(5.67 X10%) x(1x10") ret = 238.6K Csdanned with CamScanner

shock at which (d) The effective temperature is the ideal temp planet precisely re-radiates all of the energy it recieves from the star. So for an idealized black body, it is Te = 14 L 16 TTDO 300 K. But in reality, the planets don't absorb all of the radiations from the star that hits them. Therefore, to know the incoming radiation, we must also consider Albedo, the amount of reflection back into space. Albedo is measured on a scale from ono reflectivity) to I Call light reflected) So considering this, the effective temperature becomes, radiation 000 Te = (ht L (1-2))/4 165 Da Ñ 238 K Now, we also need to consider the surface temperature of the planet g CScanned with CamScanner

ion Cuva The incoming radiation is a shortwave radiat- visible) which gets reflected off clouds. Some gets absorbed by the atmosphere and some passes Horough the planet's surface. The absorbed radiation causes the atmosphere to warm. The heat generated by this absorption long wave radiation (IR). is emitted as N Reflected Incoming Clouds Clouds Absorbed by Atmosphere radiation reflected Surface radiation Surface Mountains Here it is given of as the surface temperature of Hydra is Book. This is much warmer than expected. The difference is because the greenhouse effect, the ability of planetary atmospheres to trap the heat. Whatever fraction of incoming radiation is not reflected by albedo, heats whatever opaque surface absorbs it. The warmed up. result is the atmospheric gases C Scanned with CamScanner