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--- repository:satellite_orbit [2020/02/27 20:37]
porcaro1 [Activity]
+++ repository:satellite_orbit [2020/02/27 21:05]
porcaro1 [Activity]
@@ Line 25: / Line 25: @@
 ==Satellite Orbit==
 **Part 1**\\
+{{ :repository:satellite_orbit.png?nolink&600|}}
 Copy and paste the following [[https://www.glowscript.org/#/user/nrosenmund/folder/Public/program/Newton'sLawOfGravitationandEnergyConservationSTUDENT | GlowScript code]] into your own GlowScript account. Read through the code and predict what might happen during the simulation
   - Run the program, observe and describe what happened and how it differed from your predictions
@@ Line 63: / Line 63: @@
     - Relationship between radius and velocity of the satellite.
   - Respond to the following statements/questions using your prior knowledge and physics concepts
+    - Discuss how changing the parameters and initial conditions (initial momentum, mass, G) affect orbit shape, net force, kinetic energy, potential energy, total mechanical energy, and momentum.
     - Using this simulation and your own experience, how can you explain how the Earth-Moon system could have originated?
     - Why does the satellite remain in orbit without crashing to Earth?
-    - Discuss how changing the parameters and initial conditions (initial momentum, mass, G) affect orbit shape, net force, kinetic energy, potential energy, total mechanical energy, and momentum
 ===Code===
 [[https://www.glowscript.org/#/user/nrosenmund/folder/Public/program/Newton'sLawOfGravitationandEnergyConservationSTUDENT | Link]]
@@ Line 143: / Line 143: @@
 **Part 1** \\
 {{ :repository:satellite_orbit_answer_1.png?nolink&600|}}
-''Monospaced Text''
   - The satellite begins with a velocity pointing away from the Earth. Eventually, the satellite comes to a complete stop, then accelerates towards the Earth until it crashes.
   - Approximately 6 seconds
@@ Line 180: / Line 179: @@
         - $\dfrac{Gm_{1}m_{2}}{(2r)^2}=\dfrac{Gm_{1}m_{2}}{4r^2}=\dfrac{1}{4}F_{g}$
     - Claim: Changing the initial momentum of the satellite changes the shape of the satellite's orbit around the Earth
-      - Support; mass of the satellite affects the size of the orbit, while velocity affects the shape. Therefore, altering the initial momentum, which is mass times velocity, will alter the size and shape of the orbit
+      - Support; mass of the satellite does not affect the orbit, while velocity does affect the shape. Therefore, altering the initial momentum, which is mass times velocity, will alter the size and shape of the orbit
         - At velocities less than circular speed (Part 1 Problem 13b), the orbit is elliptical
         - At velocities exactly at circular speed,  the orbit is circular
@@ Line 188: / Line 187: @@
         - Larger satellite mass results in smaller orbit size
   - Claims + Evidence
-    - Claim:
+    - Claim: The kinetic energy of the satellite increases as its distance to the Earth decreases
+      - Evidence: Based on Newton's Law of Gravitation, as the satellite gets closer to the Earth, the gravitational force acting on the satellite increases. Based on Newton's 2nd Law, force is directly proportional to acceleration, so the satellite will begin to accelerate, or in other words, increase its velocity. A larger velocity corresponds to a greater amount of kinetic energy, as proven by the equation for kinetic energy (Part 1 Problem 10d)
+    - Claim: The potential energy of the satellite increases as its distance from the Earth increases
+      - Evidence: When a satellite orbits a planet, it has negative potential energy and is bounded to the planet. Moving the satellite closer to Earth makes its potential energy become more negative. As the satellite drifts farther away from the Earth, its potential energy will approach zero (see Part 1 Problem 10d)
+    - Claim: The total mechanical energy of the satellite remains constant throughout the orbit of the satellite
+      - Evidence: If you were to calculate the kinetic and potential energy of the satellite at any point during its orbit, you will find that the sum will always be the same negative value (negative because it is bounded, as explained above). The total energy does not change because no work is being done on the system: only a transfer of internal energies. You can also see this in the graphs displayed below your code; the line or bar representing total mechanical energy will remain fixed
+    - Claim: The net force acting on the Earth and the satellite are equal and opposite
+        - Evidence: According to Newton's 3rd Law of Motion, every action has an equal and opposite reaction. That means that the gravitational force from the Earth acting on the satellite is equal in magnitude and opposite in direction to the force from the satellite acting on the Earth
+      - Claim: The mass of the satellite does not affect the orbital shape
+        - Evidence: We discovered earlier that the shape of the orbit is dependent on the speed of the satellite, not the mass (Part 2 Problem 1eI). You can test this by changing the values of "mSatellite" in your code (line 17), and you will find the shape of the orbit stays the same regardless
+      - Claim: The larger the radius between the satellite and the Earth, the smaller the velocity
+          - Evidence: This has already be thoroughly discussed in Part a of this problem
+===Code===
+[[https://www.glowscript.org/#/user/nrosenmund/folder/Public/program/Newton'sLawOfGravitationandEnergyConservationTEACHER | Link]]
+<code Python [enable_line_numbers="true", highlight_lines_extra="18,24,34,56,66,69"]>
+GlowScript 2.7 VPython
+get_library('https://rawgit.com/perlatmsu/physutil/master/js/physutil.js')
+rom __future__ import division
+from visual import *
+from visual.graph import *
+#Window setup
+scene.range = 7e7
+scene.width = 1024
+scene.height = 760
+#Objects
+Earth = sphere(pos=vector(0,0,0), radius=6.4e6, texture=textures.earth)
+Satellite = sphere(pos=vector(6.6*Earth.radius, 0,0), radius=1e6, color=color.orange, make_trail=True)
+#Parameters and Initial Conditions
+mSatellite = 1000
+pSatellite = vector(-1500*mSatellite,2598*mSatellite,0)
+G = 6.67e-11
+mEarth = 5.98e24
+r = (Earth.pos - Satellite.pos)
+g1 = gcurve(color=color.cyan,label="kinetic energy")
+g2 = gcurve(color=color.red,label="gravitational energy")
+g3 = gcurve(color=color.green,label="total mechanical energy")
+#Time and time step
+t = 0
+tf = 60*60*24*10
+dt = 1
+graphv = gdisplay(xmin=-0.25, xmax=1.25, ymin=-12e10, ymax=12e10, ytitle="Energy")
+g4 = gvbars(gdisplay = graphv, color = color.red, delta = 0.2, label = "Kinetic Energy")
+g5 = gvbars(gdisplay = graphv, color = color.blue, delta = 0.2, label = "Potential Energy")
+g6 = gvbars(gdisplay = graphv, color = color.green, delta = 0.2, label = "Total Energy")
+#MotionMap/Graph
+FSatelliteMotionMap = MotionMap(Satellite, tf, 200, markerScale=4000, labelMarkerOrder=False)
+pSatelliteMotionMap = MotionMap(Satellite, tf, 200, markerScale=0.2, markerColor=color.blue, labelMarkerOrder=False)
+#Calculation Loop
+ev = scene.waitfor('click')
+while t < tf:
+    rate(6000)
+    g4.delete()
+    g5.delete()
+    g6.delete()
+    Fnet = vector(0,0,0)
+    r = (Earth.pos - Satellite.pos)
+    Fnet = vector(G*mEarth*mSatellite/(mag(r)**2)*(r/mag(r)))
+    pSatellite = pSatellite + Fnet*dt
+    Satellite.pos = Satellite.pos + (pSatellite/mSatellite)*dt
+    if mag(Satellite.pos) < Earth.radius:
+        text(text='You Crashed!!', pos=vec(0, 4e7, 0), color = color.red, depth=1, height= 7e6)
+        break
+    FSatelliteMotionMap.update(t, Fnet)
+    pSatelliteMotionMap.update(t, pSatellite)
+    t = t + dt
+    KE = 1/2*mSatellite*mag(pSatellite/mSatellite)**2
+    PE = G*mSatellite*mEarth/mag(r)
+    g1.plot(t, KE)
+    g2.plot(t, PE)
+    g3.plot(t, KE+PE)
+    g4.plot(0, KE)
+    g5.plot(0.5, PE)
+    g6.plot(1.0, KE+PE)
+    #Earth Rotation (IGNORE)
+    theta = 7.29e-5*dt
+    Earth.rotate(angle=theta, axis=vector(0,0,1), origin=Earth.pos)</code>
+----
+====See Also===