SLINGSHOT PROJECT

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SLINGSHOT PROJECT

• By
• Dale Henderson
• Jarly López
• Robert Kemp
• Stacey Cotty
• 
  

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New Horizons

• Our project is based on the New
  Horizons mission. This mission, (to be launched
  in 2006) is going to travel to Pluto. Using the
  gravity and rotation of Jupiter, the probe will
  sling-shot itself towards Pluto.
• With an interactive program you can input the
  space crafts speed, approach angle and planets
  speed. The computer then outputs the resulting
  speed after the swing-by

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Importance of project

• To extend exploration outside our solar system
• Fuel Efficiency
• Position of planets at time of swing by
• Gravity Assist Objectives
• Exploration of Planets
• New Horizons Space Probe

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Voyager I/II Exploration
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Conservation of Energy and Momentum

• Kinetic Energy
• Energy of Motion
• KE ½ x Mass x Velocity2
• Momentum
• Quantity of Motion
• Momentum Mass x Velocity

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How it works..

• Spacecraft gains significant momentum and
  velocity while planet takes minute losses

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Derivation of Velocity Equations

• V2 2U V1
• Velocity after 180 degree turn
• V2 (v1 2u) 1 - 4uv1(1-cos(?))/ (v12u)2 ½
• Velocity considering different angles of approach

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Java code, written in applet form

• import java.awt.Graphics
• import javax.swing.
• public class testaa extends JApplet
• double v2
• public void init()
• String v2b,ss1b,aa1b,ps1b,thetab
• double ss1,aa1,ps1,theta
• ss1b JOptionPane.showInputDialog("Spacecraft
  speeds typically vary between 0 and 100
  Km/s\nPlease input your spacecraft speed ")
• ss1 Double.parseDouble(ss1b)

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code will allows user to interact with world wide
web.

• aa1b JOptionPane.showInputDialog
  ("Approach angle between 0 and 90 degrees\nPlease
  input your approach angle ")
• aa1 Double.parseDouble(aa1b)
• ps1b JOptionPane.showInputDialog("Mercury 47.
  89\nVenus 35.03\nEarth 29.79\nMars 24.13\nJu
  piter 13.06\nSaturn 9.64\nUranus 6.81\nNeptune
  5.43\nPluto 4.74\nPlease input your planet
  speed ")
• ps1 Double.parseDouble(ps1b)

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Final math is fairly simple.

• thetaaa1Math.PI/180
• v2 (ss12ps1)Math.sqrt(1-4ps1ss1(1-Math.c
  os(theta))/((ss12ps1)(ss12ps1)))
• public void paint( Graphics g )
• super.paint( g )
• g.drawRect(15,10,270,20)
• g.drawString("Final speed in Km/s is "
  v2, 25, 25 )

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Triangle equation method, compare results with
different methods

• We know the orbital radius of Jupiter, X1,
  initial velocity towards Jupiter, V1, the orbital
  radius of Pluto, X3 and the time we want to take
  for the mission, t.
• Using law of sines we can find the last side X2,
  and X1X2 d, then d/t Va, average speed.
• Rewriting, Va (V1V2)/2 d/t.
• Thus, V2 2d/t V1

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Compare results
Using the same inputs for both the sling equation
and the triangle equation we have a V2 of 31.6
Km/s for the sling compared a V2 of 31.4 Km/s for
the triangle.
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Validation

• The triangle equation yields the same results as
  the slingshot equation, however the triangle
  equation requires more calculations and is very
  static, not very malleable for other applications
• The slingshot equation has much greater
  applications and is more amendable to parametric
  and vector calculations.
• Furthermore, the slingshot method fits directly
  into other celestial mechanic equations.