SLINGSHOT
PROJECT
By
Dale Henderson
Jarly López
Robert Kemp
Stacey Cotty
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 craft’s speed, approach angle
and planet’s speed. The computer then
outputs the resulting speed after the swingby
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
Voyager I/II Exploration
Conservation of Energy and
Momentum
• Kinetic
Energy
• Energy
– KE = ½ x
of Motion
Mass x Velocity2
• Momentum
• Quantity of
– Momentum = Mass x Velocity
Motion
How it works…..
• Spacecraft gains significant momentum
and velocity while planet takes minute
losses
Derivation of Velocity Equations
• V2 = 2U + V1
• Velocity after 180 degree turn
• V2 = (v1 + 2u) [ 1 - 4uv1(1-cos(θ))/
(v1+2u)2 ]½
• Velocity considering different angles of
approach
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);
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\nJupiter:
13.06\nSaturn:9.64\nUranus:
6.81\nNeptune:
5.43\nPluto: 4.74\nPlease input your
planet speed: ");
ps1 = Double.parseDouble(ps1b);
Final math is fairly simple.
theta=aa1*Math.PI/180;
v2 = (ss1+2*ps1)*Math.sqrt(1-4*ps1*ss1*(1Math.cos(theta))/((ss1+2*ps1)*(ss1+2*ps1)));
}
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 );
}
}
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 X1+X2 = d, then d/t = Va, average speed.
•Rewriting, Va = (V1+V2)/2 = d/t.
•Thus, V2 = 2d/t – V1
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.
Initial V1,
and radius 
of Jupiter
X1
Solved
distance
X2, and
unknown
V2
Radius of
Pluto, X3
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.