1. Planet A has an orbital period of 12 years and radius that is 0.033 times the radius of the star. Calculate the fractional dip of the star brightness in the case that planet A is transiting. Give the answer as a number. Quote the formula you use and explain any assumptions you have to make.

2. Planet B has an orbital period of 1 year and is located closer to its star than planet A. You succeed in detecting planet B with the radial velocity technique as well! From this measurement you calculate a minimum mass of planet B to be 75% that of the Earth. (a) Since you detect the planet with both transit method and radial velocity method, what do you know about the inclination of the planetary system? (b) Given this inclination, estimate the true mass of planet B (in units of Earth mass). You do not need to do a detailed calculation, just explain the argument.

3. You also measure the radius of planet B to be the same as Earth, one Earth radius. (a) How does the density of planet B compare to Earth: is it bigger or smaller? By how much (write a factor as a whole number or a fraction)? For reference, density = mass / volume, and the volume of a sphere is proportional to the radius cubed. (b) Explain any assumptions you have to make.

4. Given the density of planet B you calculated above, what can you say about its matter composition (rocky/gaseous) relative to Earth? Give supporting arguments based on the composition of planets in the Solar system.

5. You also find that planet B is in the habitable zone, and the star is 10 parsecs away. Planet B appears very close to its star in projected angle on the sky (about 0.1 seconds of arc). You estimate that the reflected light of planet B is about 1,000,000,000 times fainter than the starlight, and its thermal emission about 1,000,000 times fainter than the star at infrared wavelengths. (a) Do you think it would be possible to take an image of planet B, resolving it from its host star and detecting its light using currently available telescopes? (b) Explain your answer qualitatively (no calculations required).

Question

1. Planet A has an orbital period of 12 years and radius that is 0.033 times the radius of the star. Calculate the fractional dip of the star brightness in the case that planet A is transiting. Give the answer as a number. Quote the formula you use and explain any assumptions you have to make.

2. Planet B has an orbital period of 1 year and is located closer to its star than planet A. You succeed in detecting planet B with the radial velocity technique as well! From this measurement you calculate a minimum mass of planet B to be 75% that of the Earth. (a) Since you detect the planet with both transit method and radial velocity method, what do you know about the inclination of the planetary system? (b) Given this inclination, estimate the true mass of planet B (in units of Earth mass). You do not need to do a detailed calculation, just explain the argument.

3. You also measure the radius of planet B to be the same as Earth, one Earth radius. (a) How does the density of planet B compare to Earth: is it bigger or smaller? By how much (write a factor as a whole number or a fraction)? For reference, density = mass / volume, and the volume of a sphere is proportional to the radius cubed. (b) Explain any assumptions you have to make.

4. Given the density of planet B you calculated above, what can you say about its matter composition (rocky/gaseous) relative to Earth? Give supporting arguments based on the composition of planets in the Solar system.

5. You also find that planet B is in the habitable zone, and the star is 10 parsecs away. Planet B appears very close to its star in projected angle on the sky (about 0.1 seconds of arc). You estimate that the reflected light of planet B is about 1,000,000,000 times fainter than the starlight, and its thermal emission about 1,000,000 times fainter than the star at infrared wavelengths. (a) Do you think it would be possible to take an image of planet B, resolving it from its host star and detecting its light using currently available telescopes? (b) Explain your answer qualitatively (no calculations required).

Accepted Answer

“Since you have asked multiple question, we will solve the first question for you. If you want any…

1. Planet A has an orbital period of 12 years and radius that is 0.033 times the radius of the star. Calculate the fractional dip of the star brightness in the case that planet A is transiting.