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PHY 150 - Astronomy Homework Assignment #3 October 9, 2007 1) Explain some of the advantages of reflecting telescopes over refracting telescopes. Refracting telescopes have a number of serious difficulties. 1) Chromatic aberration of light through an objective lens places the image of an object at different distances from the objective lens for different colors. 2) The objective lens actually absorbs some of the light (completely for some frequencies), thus restricting the light gathering power of the telescope. 3) Defects in the objective lens serve to scatter light and blur the image. 4) Large apertures require large objective lens which, because of their weight, sag and distort the image. Reflecting telescopes do not have the problems mentioned above, in particular, they can be made with very large diameters. But they do have problems of their own. 1) To reduce spherical aberration and produce a sharp focus, the reflecting mirror must be ground to a parabolic shape. This type of mirror only accepts parallel rays, thus, the field of view is limited. 2) Images off axis suffer a defect called coma which affects the image off the central axis of the telescope. 2) Why are radio telescopes so large? All telescopes have diffraction-limited angular resolutions where the minimum resolution is given by θ = 2.5 × 105 λ D where λ is the wavelength and D is the diameter of the entrance aperture of the telescope objective. Radio waves have much longer wavelengths than optical light; therefore, much larger aperture are needed to minimize angular resolution. 3) What would be the diffraction-limited resolution of a telescope with a 50-meter objective mirror be for yellow light with a wavelength of 500 nm? According to the formula given above, this resolution would be −8 500 × 10−9 m 5 50 × 10 θ = 2.5 × 10 = 2.5 × 10 = 2.5 × 10−3 radians 50m 50 5 4) If hydrogen and helium account for 98% of the mass of all the material in the universe, why aren’t the Earth and Moon composed primarily of these two gases? Hydrogen and helium were present when the Earth and Moon formed but were in the form of vapor. As the temperature of the nebular surrounding the newly formed sun decreased the heavier, refractive elements condensed out first. The gaseous hydrogen and helium in the early atmosphere escaped with time. What techniques are used to detect planets orbiting other stars? Why are these techniques unable to detect planets like Earth? There are essentially two techniques for detecting planets about other stars: 1) visual wobble of the star, and 2) spectroscopic Doppler shift of radiation from the star. Both of these techniques work if the planet is big enough to cause measurable wobble of the star. The Earth is relatively small compared to the sun and causes little wobble. 5) The inner core of the Earth is at a higher temperature than the outer core. Why, then, is the inner core solid and the outer core molten instead of the other way around? Seismographic data give us an indication of the chemical composition of the Earth's interior as a function of depth. From this data we are able to calculate the density of the Earth as a function of depth and thus the pressure as a function of depth. These data also allow us to infer the temperature as a function of depth. The core is separated into two parts, an inner solid iron core and a molten outer iron core. The inner core is solid because the pressures found at the center of the Earth do not allow the iron to melt, even at the relatively high core temperatures. 6) What techniques are used to detect planets orbiting other stars? Why are these techniques not very effective in detecting planets like the Earth? Planets revolving around far away stars cannot be resolved from the star by any telescope. However, their existence can be inferred from several techniques, among them: 1) If the star is close enough to Earth then it might be observed to optically wobble in its orbit over time,. This would indicate a planetary companion, and 2) iIf the light from the star is observed to exhibit a timedependent Doppler shifted this too would also indicated a planetary companion. 7) Describe the process of plate tectonics. Give specific examples of geographic features created by plate tectonics. Plate tectonics is the movement of large portions of the crust. These plates ride on the semi-molten asthenosphere. The movement is caused by magma squeezing out along mid-oceanic ridges pushing the plates apart in a process called sea-floor spreading. Where these plates collide they can cause appreciable deformation of the plate edges. Some geographical features created by plate tectonics are mountain ranges, submarine trenches, and volcanoes. 8) Draw a cross-sectional picture of the Earth. Describe the different regions of the Earth and their differences. What process led to these distinct regions? The inner core is composed of a solid iron-nickel mixture. The outer coil has much the same composition but is a molten slush. Outside of the core is the mantle which is composed of high density rock. This is surrounded by a lowerdensity rock mantle. Near the outer limit of the outer mantle is a thin layer of semi-molten rock called the asthenosphere. On top of this layer riders several large crustal pieces called tectonic plates. 9) Africa and South America are separating at a rate of about 3 centimeters per year, as explained in the text. Assuming that this rate has been constant, calculate when these two continents must have been in contact. Today the two continents are 6600 km apart. We can calculate: 1 year 100 cm 1000 meter x x x 6600 km = 2.2 x10 8 years 3 cm meter kilometer This is comparable to the value of 2 x 108 years deduced by Wegener in 1924. 10) Starry Night exercise 7-44. Mercury - At this magnification you can clearly see craters and fault lines. I jumped ahead a few days to get a clear picture. Venus - You only see yellow clouds with some bands in them. The surface cannot be seen. Earth - You can clearly see continents and water even with a partial cloud cover. Mars - I could see the polar ice cap, some craters, but no sharp features. Ceres - I had to work a little to find Ceres. When I did I zoomed in and was clearly able to see craters. Of course, there is no atmosphere on this asteroid.