James Royston

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Io
Mission Objectives

• James Royston
• Paul Salazar
• Shawn Wheelan
• Diego Hernandez

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Mission Objective

• To find presence of life on Io, one of Jupiters
  moons.
• Their will be both a fly-by of Io, and then the
  satellite will be put into a circular orbit
  around Io, to search for presence of life.

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Home
General
Io facts
Life on Io
Finding radius of orbit
Finding the period
Calculating Gravity on Io
Model of Satellite around Io
Moons orbit model
Finding gravity
Sources
Finding Hyperbolic Flyby
Finding tangential velocity
Finding Centripetal acceleration
Title
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General

• Name Io
• Mass of satellite 5000
• Discovered by Galileo Galilei
• Parent Jupiter

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Io Facts

• Mean Orbital radius 1821.3
• Eccentricity 0.0041
• Periapsis 420,000 km
• Apoapsis 423,400 km
• Revolution period 1.769137786 d (152,853.5047 s)
  
• Orbital circumference 2,649,600 km (0.018 AU)
• Orbital velocity max 17.406 km/s, mean 17.334
  km/s, min 17.263 km/s
• Inclination 2.21 (to the ecliptic) 0.05 (to
  Jupiter's equator)
• Mean diameter 3642.6 km (0.286 Earths)
• (3660.03637.43630.6 km)
• Surface area 41,910,000 km2 (0.082 Earths)
• Volume 2.531010 km3 (0.023 Earths)
• Mass 8.9319e22 (0.015 Earths)
• Mean density 3.528 g/cm3
• Surface gravity 1.79 m/s2 (0.183 g)
• Escape velocity 2.6 km/s
• Rotation period synchronous
• Equatorial rotation velocity 271 km/h
• Axial tilt 0

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Life on IO

• Life on Io is harsh. The atmosphere is floating
  away so therefore there is more radiation. There
  are volcanoes and the molten lava is super hot
  even when dry making the surface very hot. Above
  the surface though it is very cold. There is no
  temperature medium. There is no water on Io.

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Standard Forms

• Circle X2 y2 r2
• Ellipse
• Hyperbola

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First Find Height of Orbit

• Ho (height of orbit) is found by using a ratio of
  Earth satellite's orbits 1/40

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Second Perihelion and Aphelion

• Perihelion Point on the orbit that is closest
  to the sun
• 2.141 AU
• Aphelion Point on the orbit that is farthest
  from the sun
• 3.165 AU
• A Length of semi-major axis
• 2.1413.165 5.306/2 2.653
• B Length of semi-minor axis
• C Distance from center to focus point
• 2.653-2.141 .512

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Finding Radius of the Orbit

• Radius of planet 1821.3 km
• s/r is ratio of the satellite to the radius of
  the planet. For earth, it is about 1/40
• 1/40 Ho/1821.3
• 1821.3 40Ho
• 1821.3/40 Ho 45
• Ro HoRp 451821.3 1866.3
• Distance from foci to center a-c

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Model of Satellite around Io

• This orbit is circular
• X2 y2 1866.32
• (Period is 1.7 hours)
• Function /-sqrt(1866.32 - x2)

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Centripetal Forces relationship with Newtons
First Law

• As the inertia of the satellite is trying to pull
  away from the center the centripetal force is
  keeping the satellite from leaving making it move
  in at a constant speed and leaving it in a stage
  of motion that cant be stop.

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Symbol Explanation

• Fg stands for force gravity.

• Newton's universal gravitational constant

• Mathematical form
• G6.67e-11 e stands for 10

• The masses of the objects.

• This is the symbol for the radius.

• This is acceleration.

• This is centripetal acceleration.

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Finding Gravity

• G6.67xe-11
• M1 5000 kg
• M2 8.9319e22 kg
• R 1821.3 km
• Substitute

Gravity Equation
G6.67x10-11
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Finding Centripetal Acceleration
ac
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Finding Tangential Velocity
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Finding the Period

• We need two equations. C2pr, D RT
• C D
• 2pr RT
• 2pr
• R
• Period 6407 seconds
• 6407 Seconds, 106.7 minutes, 1.77 Hours

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Finding

• Major Axis 423,400
• Minor Axis 420,000
• 423,400/2 Semi-Major Axis211700
• 420,000/2 Semi-Minor Axis210,000

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Moons Orbit Model

• Model of Io around Jupiter
• Most of these orbits look like theyre circular,
  even though they are elliptical
• Function /-sqrt((432242.5)2-x2)

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Finding Hyperbolic Flyby

• In hyperbolas, a2b2c2
• Blue is the path a satellite would follow during
  a flyby of Io

--- Asymptotes --- Orbit of the Satellite ---
C-Circle
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Sources

• http//en.wikipedia.org/wiki/Io_28moon29
• And our very wonderful teachers