io-volcanos-report (1)

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Florida International University *

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1002L

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Geography

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Jan 9, 2024

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docx

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Name: Sachintha Peiris (6216473) AST1002L RVC RVF RVD RVE 1238 Io’s Volcanos While hunting for volcanic plumes on Io, the NASA/ESA Hubble Space Telescope captured this image of the volatile moon sweeping across the face of Jupiter. ~ NASA Theory: From the height of the volcano's plume, you can approximate the velocity that the material left the volcano using these equations: v height = ( velocity ) 2 2 ×g v velocity = √ 2 ×g× ( height ∈ meters ) where the height is measured in meters, the velocity in meters per second, and g is the acceleration due to gravity for the surface of Io in meters per second square. Values of g are given for a few solar system worlds in Table 1. Also given in this table is the escape velocity ( V escape ) of the planetary object. Objects moving faster than V escape can escape the gravitational pull of that object. Table 1: Values of g for some solar system objects. Object g ( m / s 2 ) V escape ( km / s ) Vesta 0.23 0.35

Name: Sachintha Peiris (6216473) AST1002L RVC RVF RVD RVE 1238 Io 1.81 2.6 Earth 9.81 11.2 Show All work: You can print this report, complete it, and upload it back to the submission page. Or you can use the Picture Format of Microsoft Word to take the measurements of the pictures or place a ruler on your computer screen to measure the volcanoes' plumes and radiuses, then convert your values into millimeters. Do not zoom in on the pictures to take data; leave the page zoom at 150%. 1. The first image that follows was taken by Voyager 2 of the volcano Prometheus. The second image is of the Tvashtar volcano taken by the New Horizons spacecraft. For each of the images determine the maximum height of the volcano above the surface of Io. To do this, you must first calculate the image scale. The radius of Io is 1820 km. For the image of Prometheus, you may assume that 1/4 of the disk is being shown. Your task is much easier and more accurate for Tvashtar as most of the disk of Io is displayed. Show all work. (14 pts) Prometheus Create a system of two equations using: r Io , r plume , r image , to find h Prometheus r Io -------- r image h -------- r plume a) Find the height of Prometheus? Height: 80.778 miles, 5 mm x 1820 km = 9100

Name: Sachintha Peiris (6216473) AST1002L RVC RVF RVD RVE 1238 9100/70 mm = 130 km H= 130km ----> H= 80.7m b) Using the information from the preceding theory, determine the velocity of the material ejected from Prometheus? V= sqrt (2 x 1.81 x 130) V=sqrt (2 x 1.81 x 130,000) V = sqrt (470.6) V=sqrt (470,600) V= 21.69 km/s or V= 686 m/s Tvashtar Create a system of two equations using: r Io , r plume , r image , to find h Tvashtar c) Find the height of Tvashtar? Height: 565.448 miles, 45 mm x 1820 km = 81,900 81,900/90 mm = 910 km H = 910 km -----> 910,000 m

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