For each problem, neatly show your work i ncluding equations used -- numerical answers only will not get full credit. Also, be sure to i nclude diagrams/sketches when requested. For numerical answers, i n general use 3 significant digits as you carry out your calculation. Also, for l arge (>1000) or small (<0.001) numbers, please use scientific notation and/or metric prefix. For example, i nstead of 0.0000103 meters, either report 1.03 x 10- 5 m, or 10.3 micro-meters (microns).
4. The following question will help us understand the concept of the Habitable Zone coming up i n Chapter 10. In the absence of clouds and greenhouse gases, we can approximate the surface temperature of a planet using the following
equation: TK = 300K (Lsun1/4 ) / (Rau1/2 ), where T k is the temperature (in Kelvin) around a star with luminosity Lsun (in solar luminosities) at a distance Rau (in astronomical units).
a. [2pts] Imagine living on an Earth-like planet around a Brown Dwarf with only 1/1000 x the luminosity of the Sun. How CLOSE (in au) would your planet need to be to this star to have the same temperature as Earth around the Sun? (you can use the above equation to do the comparison).
b. [3pts] In about 5 billion years, the Sun will be a red giant and have 1000x higher luminosity! What will the equilibrium temperature of Earth be then? What will be the equilibrium temperatures of Jupiter's moon Europa and Saturn's moon Titan then?
c. [1pt] Do you think l ife might be possible i n our solar system when the Sun is a red giant, and i f so, which planets/moons? Justify your answer.
For each problem, neatly show your work i ncluding equations used -- numerical answers only will not get full credit. Also, be sure to i nclude diagrams/sketches when requested. For numerical answers, i n general use 3 significant digits as you carry out your calculation. Also, for l arge (>1000) or small (<0.001) numbers, please use scientific notation and/or metric prefix. For example, i nstead of 0.0000103 meters, either report 1.03 x 10- 5 m, or 10.3 micro-meters (microns).
4. The following question will help us understand the concept of the Habitable Zone coming up i n Chapter 10. In the absence of clouds and greenhouse gases, we can approximate the surface temperature of a planet using the following
equation: TK = 300K (Lsun1/4 ) / (Rau1/2 ), where T k is the temperature (in Kelvin) around a star with luminosity Lsun (in solar luminosities) at a distance Rau (in astronomical units).
a. [2pts] Imagine living on an Earth-like planet around a Brown Dwarf with only 1/1000 x the luminosity of the Sun. How CLOSE (in au) would your planet need to be to this star to have the same temperature as Earth around the Sun? (you can use the above equation to do the comparison).
b. [3pts] In about 5 billion years, the Sun will be a red giant and have 1000x higher luminosity! What will the equilibrium temperature of Earth be then? What will be the equilibrium temperatures of Jupiter's moon Europa and Saturn's moon Titan then?
c. [1pt] Do you think l ife might be possible i n our solar system when the Sun is a red giant, and i f so, which planets/moons? Justify your answer.
