Astronmy HW 1

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Sam Houston State University *

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1404

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Astronomy

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Jan 9, 2024

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docx

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Homework 1 question 1 1a. Light from the closest star to the Sun, Proxima Centauri, takes 4.24 years to reach Earth. Calculate the distance to Proxima Centauri. Write your answer longhand (not in scientific notation) and then show how to put your answer into scientific notation One light year is 6.32x10^4 x 4.24 267968 is the distance Scientific Notation: 2.68x10^5 Au 1b. As Earth revolves around the Sun every 12 months, we view the night sky from a slightly different point of view than we had 6 months earlier. For the closest stars to the Sun, we can measure a very small shift in nearby stars' positions compared to more distant stars in the background. This phenomenon, which we'll revisit later in the semester, is called parallax. The farther away a star is, the smaller the shift is. P= 57.3 / d P=57.3 / 2.68x10^5 P= 0.000213831502 Scientific Notation: 2138x10^-4 1c. Because Proxima Centauri is the closest star to the Sun, it will show the largest parallax of any star in the sky (other than the Sun). The human eye can see angles as small as approximately 0.0167°, where the ° symbol means degrees. Calculate how many times larger this angle is compared to Proxima Centauri's parallax. 57.3 / 0.000213831502 = 267,968 The parallax is 267968 x greater AC’s more. 1d. Having established that stars show no visible parallax and must be much farther away than anything in the Solar System is, let's turn our attention to the Sun and the Moon. Suppose you observe that you can see exactly half of the illuminated side of the Moon, implying that the Sun is at a 90° angle from Earth as seen from the Moon. (See the figure below.) Suppose you measure the angle between the Sun and the Moon to be 89.8°. This means that of the three angles in the Earth-Moon-Sun triangle, you know the values of two of the angles. Given that the three angles in every triangle add up to 180°, what is the value of the third angle in this scenario? Your answer should have units of degrees. 180-90-89.8=0.2 degrees 1e. Calculate the distance from Earth to the Moon. Write your answer longhand and then show how to put your answer into scientific notation. M= 1.75x10^-2 x sun’s angle M= 1.75x10^-2 x 0.2 degrees = 0.0035 Au (3.5x10^-3) Au 1f. How would this underestimate of the angle between the Sun and the Moon affect our calculation of the distance from Earth to the Moon? Would we have calculated a smaller distance to the Moon, the same

distance, or a larger distance? Use the equation from part 1E to explain your answer. It would have resulted in a Gogus, large numbers overestimations for the moon’s distance. If 180-90-87=3, then 1.75x10^-2 x 1 x 3 = 0.0525 Au Homework 1 question 2 2a.You observe that at a particular time of day on a particular day of the year, the Sun is directly overhead in Syene, a city in Egypt (which was part of ancient Greece). But at the same time in Alexandria, another Egyptian city almost due north, the Sun is 7.14° away from being directly overhead. What fraction of a full 360° circle is this angle? 7.14 / 360 = 119 degrees / 6000 = 0.01983 2b. What is the circumference of Earth? Write your answer longhand (not in scientific notation) and then show how to put your answer into scientific notation. 493 miles / 0.019833 = 24857.1486 miles Scientific Notation: 2.49x10^4 2c. Suppose you take a vacation from Egypt to Quito, a city in Ecuador very close to Earth's Equator. Compared to someone standing at Earth's North Pole, who spins in place due to Earth's daily rotation, how fast are you traveling through space simply by being on Earth at the Equator? Write your answer longhand and then show how to put your answer into scientific notation. 2.4857.1486 / 24 = 1035.714286 mph Scientific Notation: 1.036x10^3 mph 2d. What is Earth's diameter in miles? Write your answer longhand and then show how to put your answer into scientific notation. The Earth’s diameter in miles is D= c / 3.14 D= 24857.14286 / 3.14 = 7916.287534 miles Scientific Notation: 7.91629x10^3 miles 2e. What is Earth's volume? Use scientific notation. V= 0.524xD^3 0.524 x 7916.2875^3 = 259953675000 miles^3 Scientific Notation: 2.59953675x10^11 miles^3 2f. The volume of the Sun is 3.38 x 10 17 mi 3 . How many Earths would fit inside the Sun? Sol / Terma V = 1300231.666 earth’s per sol. Homework 1 question 3 3a. Why was Pluto reclassified? Is Pluto any different now than it was before? Pluto was reclassified as a dwarf planet by the (IAU) in 2006 because it did not meet the three

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