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Homework 5 1. Transit of HD209548. The star HD209548, which has a transiting planet, is roughly the same size as our Sun, which has a radius of about 700,000 kilometers. The planetary transits block 1.7% of the star’s light a. Calculate the radius of the transiting planet. i. 1.7% of the total area of the star will give us the area of the planet: ii. 0.017*pi*(700000)^2=pi*(r)^2 this gives us r=sqrt(0.017)*700000=91,268.8 km b. The mass of the planet is approximately 0.6 times the mass of Jupiter, and Jupiter’s mass is about 1.9*10^27 kg. Calculate the average density of the planet. Give your answer in grams per cubic centimeter. Compare this density to the average densities of Saturn (0.7 g/cm^3) and Earth (5.5 g/cm^3) i. Density=p=M/V=0.6*1.9*10^27/(4/3*pi*91268.8^3)=3.58*10^11 kg/km^3 ii. P(in kg/km^3)*(1000g/1kg)*(1km/10^5cm)^3= 0.358 g/cm^3 iii. This is about 51% of Saturn’s density and about 7% of Earth’s density. It is most likely a gas planet given its overall size and density. 2. The amount of Doppler shift for light or radio waves can be calculated from this formula: Wavelength shift/rest wavelength = v/c The rest wavelength is the wavelength of a particular spectral line in an object that is not moving (relative to us), v is the velocity of the star from which we observe a wavelength shift, and c is the speed of light Suppose that, in a particular star, a spectral line with a rest wavelength of 600 nm is found to be shifted by 0.1 nm (toward the blue). How fast is that star moving toward us, in meters per second? a. C=3*10^8 m/s 0.1*c/600=v=50,000 m/s 3. Future Mission. A wealthy benefactor has just given you a large grant to search for Earth-­‐like planets around other stars. What would you do? Explain. a. There are many correct answers to this question. One could think of launching in space a giant infrared Kepler-­‐like telescope to search for Earth-­‐like planets using the transit method. This telescope would be large enough to also obtain the spectra of these planets and look for signs of life in their atmospheres (water, carbon dioxide, oxygen, organics, red edge and green bump of chlorophyll, etc). 4. Describe a few physiological and sociological factors that might influence whether an intelligent species can develop technology for interstellar communication. a. There are many physiological and sociological factors that would help an intelligent species to develop technology capable of interstellar communication. Some physiological factors are: opposable thumbs that enable humans to create tools and manipulate them to create wondrous items, such as telescopes; and being able to sense electromagnetic radiation, i.e. light, may be critical for interstellar communication. Some sociological factors are: the ability to come together as a species and work towards a common goal; and the curiosity necessary to pursue science as a whole.