Space Voyage Part 3

     This lab will address a few purposes. The first and foremost purpose will be to look at the potential and kinetic energies in a system involving the earth, moon and a orbiting satellite. The second purpose of this lab will be to examine more limitations with program design.

Orbit and graphs of the different types of energy.

 The following is the working code of the program and a video of the potential/kinetic energy graphs for the satellite. A video of the orbit corresponding to the graphs will also be included.

#Physics 4A Lab: Space Voyage Lab Part 1
#April 12th 2012
#Chris Cosio
#This is the first part to a space voyage simulation.
from __future__ import division
from visual import*
from visual.graph import*

scene.y=400
scene.width =800
scene.height = 800

#CONSTANTS
G = 6.7e-11
mEarth = 6.7e24
mcraft = 15e3
mMoon = 7e22
deltat = 390
#OBJECTS AND INITIAL VALUES
Earth = sphere(pos=vector(0,0,0), radius=6.4e6, color=color.cyan)
Moon = sphere(pos=vector(4e8,0,0), radius=1.75e6, color=color.white)
craft = sphere(pos=vector(-5*Earth.radius, 0,0), radius=1e6, color=color.yellow)
trail = curve(color=craft.color)    ## for leaving a trail behind the craft
pvector = arrow(color=color.red)
vcraft = vector(0,5077.5,0)
#3050 is a good velocity for an elliptical orbit
pcraft = vcraft*mcraft
t = 0
Kgraph = gcurve(color=color.yellow)
Ugraph = gcurve(color=color.red)
KplusUgraph = gcurve(color=color.cyan)

#CALCULATION LOOP: ALL REPEATED CALCULATIONS GO INSIDE THE LOOP
while t < 10*365*24*60*60:
   rate(1000000) ## slow down motion to make animation look nicer
   pvector.pos = craft.pos # momentum arrow
   r_E = craft.pos-Earth.pos # Earth-Craft position vector
   r_Emag = mag(r_E)# magnitude of Earth-Craft position Vector
   rhat_E = norm(r_E) # unit vector for r in Earth-Craft direction
   F_grav_mag_E=G*mcraft*mEarth/(r_Emag**2)# magnitude of gravitational force from Earth-Craft system
   F_Egrav=-F_grav_mag_E*rhat_E # gravitational force from Earth-Craft system,
   r_M = craft.pos-Moon.pos # Moon-Craft position vector
   r_Mmag = mag(r_M)# magnitude of Moon-Craft position vector r
   rhat_M = norm(r_M) # unit vector for r in Moon-Craft direction
   F_grav_mag_M=G*mcraft*mMoon/(r_Mmag**2)# magnitude of gravitational force from Moon-Craft system
   F_Mgrav=-F_grav_mag_M*rhat_M # gravitational force from Moon-Craft system
   vcraft = vcraft+(F_Egrav/mcraft)*deltat+(F_Mgrav/mcraft)*deltat # craft velocity
   pcraft = pcraft+F_Egrav*deltat+F_Mgrav*deltat # craft momentum
   pvector.axis = 1*pcraft
   craft.pos = craft.pos + (pcraft/mcraft)*deltat
   trail.append(pos=craft.pos) ## this leaves a trail behind the spacecraft
   K = 0.5*mcraft*mag(vcraft)**2 #Kinetic Energy
   U = F_grav_mag_E*r_Emag+F_grav_mag_M*r_Mmag #Potential Energy
   Kgraph.plot(pos=(t,K)) #Kinetic Energy plot
   Ugraph.plot(pos=(t,U)) #Potential Energy Plot
   KplusUgraph.plot(pos=(t,K+U)) #Total Mechanical Energy Plot
   t = t+deltat
  

     The graphs depict total energy (blue), kinetic energy (yellow), and potential energy from the earth/moon (red). As the satellite gets closer to the earth the gravitational potential increases with the acceleration increase; however, there is a trade off with the distance between the satellite and the earth/moon where being too close would eventually cause a decrease in potential energy. As the satellite reaches a three fourths point between the earth and moon, the kinetic energy becomes relatively low as well as the potential energies. This is due to the net forces acting on the satellite at this point being very small. The graph depicts a few local maximums when it is closes to the moon, and one absolute maximum when it is closest to the earth. If the time interval is changed past a certain value to speed up the program, the orbit becomes inaccurate and the program can even fail. The program failing is evident by the earth or moon sling shooting the satellite away at an escape velocity.