course_planning:183_projects:s23_week_3_geostationary_orbit

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
Next revisionBoth sides next revision
course_planning:183_projects:s23_week_3_geostationary_orbit [2023/01/25 19:34] – hallsteincourse_planning:183_projects:s23_week_3_geostationary_orbit [2023/01/25 20:53] – hallstein
Line 102: Line 102:
   * **Tutor Question:**  If you added in another body, what two forces would constitute the net force acting on the satellite?   * **Tutor Question:**  If you added in another body, what two forces would constitute the net force acting on the satellite?
   * **Expected Answer:**  $\vec{F}_{\rm net}=-GM_{1}m\hat{r}_{1}/r_{1}^{2}-GM_{2}m\hat{r}_{2}/r_{2}^{2}$   * **Expected Answer:**  $\vec{F}_{\rm net}=-GM_{1}m\hat{r}_{1}/r_{1}^{2}-GM_{2}m\hat{r}_{2}/r_{2}^{2}$
- 
-{{course_planning:geostationary_part_1_questions.png}} 
  
 </WRAP> </WRAP>
Line 185: Line 183:
  
 <WRAP alert> <WRAP alert>
-The addition of the non-constant Newtonian force is challenging for students.  If the group is struggling to correctly model it, do not push them to add in a graph. Rather, focus on correctly completing the previous tasks and ask any remaining tutor questions.+The addition of the non-constant Newtonian force is challenging for students.  If the group is struggling to correctly model it, do not push them to add a graph. Rather, focus on correctly completing the previous tasks and ask any remaining tutor questions.
 </WRAP> </WRAP>
  
 <WRAP tip> <WRAP tip>
 ==Tutor Questions:== ==Tutor Questions:==
-  * **Question:**  How can you prove that the orbit is actually circular? +   * **Question:**  Can you simulate other trajectories with your program?
-  * **Expected Answer:**   +
-Aside from just eyeballing it, we can add in a graph of the distance from the center of Earth! (Moved to separate part C of the problem) +
-<code python> +
-#MotionMap/Graph +
-separationGraph = PhysGraph(numPlots=1) +
- +
-#Calculation Loop +
- separationGraph.plot(t,mag(Satellite.pos)) +
-</code> +
- +
-  * **Question:**  Can you simulate other trajectories with your program?+
   * **Expected Answer:**  We can change the initial conditions of radius and velocity to show this.   * **Expected Answer:**  We can change the initial conditions of radius and velocity to show this.
  
Line 210: Line 197:
   * **Expected Answer:**  It is the step in time that passes every loop of the calculation loop.  Increasing the time step makes for a "rougher" approximation to the real world phenomenon.   * **Expected Answer:**  It is the step in time that passes every loop of the calculation loop.  Increasing the time step makes for a "rougher" approximation to the real world phenomenon.
  
-{{course_planning:georobitconceptualq2.png}}+ * **Question:**  How can you prove that the orbit is actually circular? 
 +  * **Expected Answer:**  Aside from just eyeballing it, we can add in a graph of the distance from the center of Earth!  
 +Part C includes adding this graph: 
 + 
 +<code python> 
 +#MotionMap/Graph 
 +separationGraph = PhysGraph(numPlots=1) 
 + 
 +#Calculation Loop 
 + separationGraph.plot(t,mag(Satellite.pos)) 
 +</code>
  
 </WRAP> </WRAP>
Line 218: Line 215:
   * Groups should have developed a working code that models any gravitational orbit around the Earth and be able to explain what and how they did it.   * Groups should have developed a working code that models any gravitational orbit around the Earth and be able to explain what and how they did it.
  
-  * For groups that get through this part (it's tough for many groups), they should check that the orbit is circular and explain that and they should add arrows to represent different physical quantities (i.e., momentum of the satellite, etc.).+  * For groups that get through this part (it's tough for many groups), they should check that the orbit is circular and explain that and they should add arrows to represent different physical quantities (i.e., the momentum of the satellite, etc.).
 </WRAP> </WRAP>
  
Line 284: Line 281:
  
 Changes made to the given code: Changes made to the given code:
 +{{course_planning:project_solutions:project_3_code_b.png}}
  
 ====== Project 3: Part C: Geostationary orbit ====== ====== Project 3: Part C: Geostationary orbit ======
Line 294: Line 292:
  
 Inside the while loop, add: graphExample.plot(t, mEarth) Inside the while loop, add: graphExample.plot(t, mEarth)
 +
 +<WRAP tip>
 +== Tutor Questions ==
 +  * **Question:** The plotted distance is varying with time.  Is this a concern?  WHy is this?
 +  * **Expected Answer:**  It is not a concern.  We inputted given values to a couple of significant figures and the variations are just a small fraction of the distance...
 +</WRAP>
 +
 +
  
 ====== Project 3: Part D: Geostationary orbit ====== ====== Project 3: Part D: Geostationary orbit ======
Line 299: Line 305:
 On a single graph, plot both the x-component of the satellite's momentum and the x-component of the net force acting on the satellite. On a single graph, plot both the x-component of the satellite's momentum and the x-component of the net force acting on the satellite.
  
 +<WRAP tip> 
 +== Tutor Questions == 
 +  * **Question:** Why does it seem as though the net force is zero? 
 +  * **Expected Answer:**  It looks that way because the size of the force plotted by Python is several orders of magnitude smaller than the size of the plotted momentum.  We fixed this by adding a scale and plotting the force in units of $10^4$ N 
 +  * **Question** From the plotted graph, what is the relationship between Fnet,x and p,x? 
 +  * **Expected Answer** When Fnet,x is at an extreme value, p,x is zero; when Fnet,x is zero, p,x is at an extreme value. 
 +</WRAP>
 Solution code for parts C and D Solution code for parts C and D
  
Line 330: Line 342:
 SatelliteMotionMap = MotionMap(Satellite, tf, 20, markerScale=2000, labelMarkerOrder=False) SatelliteMotionMap = MotionMap(Satellite, tf, 20, markerScale=2000, labelMarkerOrder=False)
 FnetMotionMap = MotionMap(Satellite, tf, 20, markerScale=2000, labelMarkerOrder=False)   # add Fnet force arrows - also need to add in loop) FnetMotionMap = MotionMap(Satellite, tf, 20, markerScale=2000, labelMarkerOrder=False)   # add Fnet force arrows - also need to add in loop)
-#separationGraph = PhysGraph(numPlots=1) 
-graphSatellite = PhysGraph(numPlot=1) 
-graphFnet = PhysGraph(numPlots=1) 
  
-graphpF = PhysGraph(numPlots=2)+graphSeparation = PhysGraph(numPlot=1)   # initialize the magnitude of the separation vector vs time plot 
 +graphFnet = PhysGraph(numPlots=1)   # initialize the magnitude of the net force vs time plot 
 + 
 +graphpF = PhysGraph(numPlots=2)   # initialize the x componets of p and Fnet vs time plot
  
    
Line 352: Line 364:
     FnetMotionMap.update(t, Fnet)  # Add Fnet vector arrows     FnetMotionMap.update(t, Fnet)  # Add Fnet vector arrows
     #separationGraph.plot(t,mag(mSatellite))     #separationGraph.plot(t,mag(mSatellite))
-    graphSatellite.plot(t,mag(Satellite.pos)) +    graphSeparation.plot(t,mag(Satellite.pos))  # update magnitude of sep vector vs time plot 
-    graphFnet.plot(t,mag(Fnet))+    graphFnet.plot(t,mag(Fnet))    # update magnitude of Fnet vs time plot
     scale=1.0E4   # add scale to make fluctuations in Fx visible (units of 10^-4 N)     scale=1.0E4   # add scale to make fluctuations in Fx visible (units of 10^-4 N)
-    graphpF.plot(t,pSatellite.x,scale*Fnet.x)+    graphpF.plot(t,pSatellite.x,scale*Fnet.x)   # update x-components of Fnet and p vs time
    
     t = t + dt     t = t + dt
Line 362: Line 374:
     theta = 7.29e-5*dt     theta = 7.29e-5*dt
     Earth.rotate(angle=theta, axis=vector(0,0,1), origin=Earth.pos)     Earth.rotate(angle=theta, axis=vector(0,0,1), origin=Earth.pos)
-</code>+</code>    
  
 Modification of solution to part B to get |r| vs t, |Fnet| vs t and Fnet,x and P,x vs t: Modification of solution to part B to get |r| vs t, |Fnet| vs t and Fnet,x and P,x vs t:
  
 +{{course_planning:project_solutions:project_3_code_cd.png}}
  
  • course_planning/183_projects/s23_week_3_geostationary_orbit.txt
  • Last modified: 2023/10/18 01:20
  • by hallstein