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The James Webb Space Telescope (JWST) is a now space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million fm from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 m in diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see” deeper into space.
The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m. Suppose that a
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- Comet C has an elliptical orbit of eccentricity 0.9393 with the sun at one focus. The greatest distance of the comet from the sun is 2848 million mi. Find the least distance between the comet C and the sun. The least distance between the comet C and the sun is million mi. (Round to the nearest whole number as needed.)arrow_forwardNeptune 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_forward
- The 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_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
- A 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_forwardNeptune moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 4,502,899,800 km, and the eccentricity is 0.0112. Find the maximum distance (aphelion) of Neptune from the sun. Round your answer to the nearest kilometer.arrow_forwardAn artificial satellite to orbit Earth was launched by the Philippines. The orbit was an ellipse with Earth's center as one focus. Tne orbit's highest point from the center of the Earth was 2500 miles, and its lowest point was 2100 miles. Find the eccentricity of the orbit.arrow_forward
- The planet Saturn orbits the Sun in an elliptical path with the Sun at one focus. The eccentricity of the orbit is 0.0565 and the distance between the Sun and Saturn at perihelion (the closest point) is 1.353 × 109km. Determine the distance at aphelion (the farthest point). Round to the nearest million kilometers.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 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_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_forward
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