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The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly
The primary mirror when pieced together will function as a parabolic mirror with a focal length of
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- Neptune orbits the Sun in an elliptical path with the Sun at one focus. At aphelion, Neptune is farthest from the Sun at 4.546 × 109 km. If the eccentricity of the orbit is 0.0113, determine the distance at perihelion (closest point between Neptune and the Sun). Round to the nearest million km.arrow_forwardJupiter orbits the Sun in an elliptical path with the Sun at one focus. At perihelion, Jupiter is closest to the Sun at 7.4052 × 108 km. If the eccentricity of the orbit is 0.0489, determine the distance at aphelion (farthest point between Jupiter and the Sun). Round to the nearest million km.arrow_forwardHalley’s Comet and the comet Hale-Bopp both orbit the Sun in elliptical paths with the Sun at one focus. The eccentricity of Halley’s Comet’s orbit is 0.967 and the eccentricity of comet Hale-Bopp’s orbit is 0.995. Which comet has a more elongated orbit?arrow_forward
- On January 31, 1958, the United States launched the research satellite Explorer 1. Its low and high points above the surface of Earth were 220 miles and 1563 miles. Find the eccentricity of its elliptical orbit. (Use 4000 miles as the radius of Earth.)arrow_forwardThe first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957). Its highest point above Earth's surface was 939 kilometers, and its lowest point was 215 kilometers (see figure). The center of Earth was at one focus of the elliptical orbit. Find the eccentricity of the orbit. (Assume the radius of Earth is 6378 kilometers. (Round to three decimal places)arrow_forwardNabil is writing a science fiction novel that takes place in anothergalaxy. In her galaxy, all the planets travel in an elliptical orbitaround their star. The majority of the plot of Nabil’s story takesplace on the planet Tanus which orbits a star named Ini. Thelength of Tanus’ major axis is 150 million miles and the length ofits minor axis is 75 million miles. The star Ini is located at afocus of the elliptical orbit. Write an equation that models the movement of Tanus around its star. Explain how youdetermined your equation and show your work . Create a graph of Tanus’ movement around Ini using your equation from question 1. Labelyour graph with the position of the star and the planet. Suppose that Nabil would like to create a model that shows the path of Tanus’ orbit aroundIni. For ease of programming, Nabil would like Ini to be located at the coordinates (0, 0). Writean equation that models the movement of Tanus around Ini, where Ini is located at (0, 0). Explainthe changes to your…arrow_forward
- Earth moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the minimum distance ( perihelion) and the maximum distance (aphelion) of Earth from the sun.arrow_forwardA planet moves in an elliptical orbit with a star at one of the foci. The perihelion (the smallest distance from the planet to the star) is 128.94 millions of miles and the aphelion (the largest distance from the planet to the star) is 153.64 millions of miles. Find an equation of the planet's orbit around the star. [Hint: Set up a coordinate system with the star at one focus and the major axis lying on the x-axis as in the figure. Calculate a from the equation 2a = aphelion + perihelion. Calculate c from the Aphelion Perihelion (0,0) Star equation c=a - perihelion. Calculate b' from the equation 2 b2 = a? - c?. Write the equation 1.] %3D 2 a 2. What is the equation of the planet's orbit (distances are in millions of miles) about the star? Choose the correct answer below. x2 y? x? В. 19,810.3416 = 1 19,962.8641 + = 1 152.5225 19,810.3416 y? = 1 152.5225 y? OC. = 1 + + 19,962.8641 19,962.8641 19,810.3416arrow_forwardA planet moves in an elliptical orbit with a star at one of the foci. The perihelion (the smallest distance from the planet to the star) is k 132.17 millions of miles and the aphelion (the largest distance from the planet to the star) is 157.53 millions of miles. Find an equation of the planet's orbit around the star. [Hint: Set up a coordinate system with the star at one focus and the major axis lying on the x-axis as in the figure. Calculate a from the equation 2a = aphelion + perihelion. Calculate c from the Aphelion Perihelion (0,0) Star equation c= a - perihelion. Calculate b' from the equation 2 2 b2 = a? - x y = 1.] - c. Write the equation + 2 b- a What is the equation of the planet's orbit (distances are in millions of miles) about the star? Choose the correct answer below. x? x? y? O A. 20,981.5225 В. 20,981.5225 = 1 + 160.7824 = 1 20,820.7401 x? y? y? OC. D. 20,820.7401 = 1 = 1 20,981.5225 + 160.7824 20,820.7401arrow_forward
- Halley’s Comet and the Earth both orbit the Sun in elliptical paths with the Sun at one focus. The eccentricity of the comet’s orbit is 0.967 and the eccentricity of the Earth’s orbit is 0.0167. The eccentricity for the Earth is close to zero, whereas the eccentricity for Halley’s Comet is close to 1. Based on this information, how do the orbits compare?arrow_forwardThe major axis of the elliptical path in which the earth moves around the sun is approximately 186,.000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth O 94,550,000 miles O 94,550,500 miles O 95,550,000 miles O 944,550,000 miles O 94,500,000 miles O 4,550,000 miles O 294,550,000 miles O 94,650,000 miles O 194,550,000 miles O 9,550,000 milesarrow_forwardPluto travels around the sun in an elliptical path with eccen- tricity e = 0.25 with the sun at one focus. The minor axis of its orbit is 10,000,000,000 km. Find the distance between Pluto and the sun at perihelion, the vertex closest to the sun. Then find the distance between Pluto and the sun at aphelion, the further vertex from the sun.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage