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UA PTYS 206 - PTYS 206 Homework 2

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PTYS/ASTR 206 – Section 3 – Homework 2 – Assigned 2/5/09NAME:______________________________________________(PRINT CLEARLY)- Homework is due in class on Thursday February 12th.- Late homeworks can be turned in class on Tuesday February 17th for 50% credit.- Homeworks turned in later than this receive 0%.- Students are encouraged to discuss approaches to solving homework problemswith each other; however, all work submitted must be the student’s own. Do notturn in identical homeworks! See the syllabus for more information.______________________________________________________________________Hint: Each of these questions should be quick to answer. If you find yourself engagedin a long chain of complicated reasoning or more than a few lines of math thensomething is probably wrong! Make sure to start this early and talk to the TA or myselfwith any questions.Another hint: Some questions require you to calculate the volume of a sphere. Asimplified version of the formula to calculate the volume of a sphere, with a radius r, is:4.19 * r3Question 1: Craters on AsteroidsThe mass of the asteroid Ceres (the largest asteroid) was just measured at 9.04*1020Kg and its radius is 476 km. Assume that Ceres is a sphere and calculate its volume.What is the average density of this object? Is it closer to ice (1000 kg m-3) or rock (3000kg m-3)?PTYS/ASTR 206 – Section 3 – Homework 2 – Assigned 2/5/09Given its mass and radius, the gravitational acceleration at the surface is 0.27 ms-2.Rock and cold water ice are both quite strong (assume a strength of 2*108 Pascal). Usethe formula in the lecture on cratering to figure out at what diameter craters on Cereswill transition from simple to complex.Compare this crater size to the size of Ceres. The Dawn mission will visit Ceres in a fewyears; do you expect us to find many complex craters there? Why?Question 2: Wavelengths of light emission?The Earth’s surface and lower atmosphere have a temperature of about 300K andradiate like a blackbody. What wavelength of the spectrum do they radiate most at? UseWien’s law from the lecture notes.At this wavelength, is the Earth or the Sun radiating more energy from each squaremeter? Why?PTYS/ASTR 206 – Section 3 – Homework 2 – Assigned 2/5/09Why can’t we observe astronomical objects at a wavelength of 10-11 microns? What dowe ‘see’ if we try that?Question 3: Energy in vs. energy outThe solar power at 1AU is 1370 W m-2. The Moon absorbs 90% of the radiation that hitsit. When the sun is directly over a patch of the lunar surface how much energy is eachsquare meter absorbing? The temperature of this patch is 350K, how much energy is each square meteremitting? (Use the formula in the lecture notes). Is this patch of surface warming up orcooling down?PTYS/ASTR 206 – Section 3 – Homework 2 – Assigned 2/5/09When the emitted and absorbed radiations are the same then the temperature of thesurface isn’t changing. What is this ‘equilibrium temperature’ in this situation?Question 4: SpectraWe observe two patches of gas, their spectra are shown below. One of these patchesis in front of the sun and the other is off to one side. Which is which? Why? A BWhen we measure absorption lines in the light reflected from a planet’s surface, what are the three locations where that absorption could be taking place?PTYS/ASTR 206 – Section 3 – Homework 2 – Assigned 2/5/09A grey body reflects all wavelengths equally. What visible color would a body like thathave if it were orbiting a star that radiated mostly in the ultraviolet? Would it change ifthe star radiated mostly in the infrared? Why?Question 5: Asteroid EnergiesMeteor crater was created by an iron meteorite 50m in diameter, traveling at about 12km s-1 (lower than once thought!). Calculate the energy of such an impact? Assume theasteroid is spherical and that its density is 6000 kg m-3.The asteroid that finished off the dinosaurs and created the crater Chicxulub was 10kmacross and traveling at 20 km s-1 with a rocky composition (density of 3000 kg m-3).How much energy does this correspond to? How many meteor-crater events add up toone Chicxulub event?Under what conditions will an asteroid break up in the atmosphere? If we double thespeed of the impact does that increase or decrease the likelihood of an atmosphericbreakup? Why?PTYS/ASTR 206 – Section 3 – Homework 2 – Assigned


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UA PTYS 206 - PTYS 206 Homework 2

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