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Satellite Orbit
Activity Information
Learning Goals
- Use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to describe and predict the gravitational and electrostatic forces between objects HS-PS2-4] * Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motion of particles (objects) and energy and associated with the relative positions [[https://www.nextgenscience.org/pe/hs-ps3-2-energy | HS-PS3-2
Prior Knowledge Required
- Kinematics
- Conservation of Energy
- Newton's 2nd Law
- Net Force
- Momentum
- Newton's Law of Gravitation
- $F_{g}=\dfrac{Gm_{1}m_{2}}{r^2}$
Code Manipulation
- Interpret code and relate to physics concepts
- Copy and paste code
- Replicate motion maps
- Add variables to premade graph
Activity
Handout
Satellite Orbit
Part 1 Copy and paste the following GlowScript code. 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
- How long does the simulation run for?
- What is the initial momentum of the satellite? Which direction?
- Which line of code indicates Newton's Law of Gravitation?
- How far way is the satellite from the Earth initially?
- What is the mass of the satellite? What is the mass of the Earth?
- What does the following line of code mean in physics terms? What does it do?
- “pSatellite = pSatellite + Fnet*dt” (line 48)
- How is velocity represented in the code?
- Modify the code in order to make the satellite orbit the Earth. What changes did you make?
- Qualitatively and quantitatively described the orbit of your satellite in terms of the following, and provide a sketch:
- Shape:
- Net Force:
- Velocity:
- Kinetic Energy:
- Potential Energy:
- Total Energy:
- Add a net force vector to your satellite
- Add a bar graph for the total mechanical energy
- Challenge: modify the code to make the orbit of the satellite circular. What evidence do you have that it is circular (besides visual inspection)?
Part 2 Conceptual Physics Claim, Evidence, and Reasoning (C.E.R.):
- Do you support or refute the following claims? Provide evidence and reasoning:
- Energy is not conserved in the Earth-satellite system.
- The magnitude of the satellite's velocity is constant.
- Changing the mass of the Earth and/or the satellite changes the force of gravity involved in this system.
- If the distance between the Earth and the satellite is doubled, the force between the Earth and the satellite is halved.
- Changing the initial momentum of the satellite changes the shape of the satellite's orbit around the Earth.
- For the following concepts, create a claim, cite your evidence, and provide your reasoning for each prompt:
- The kinetic energy of the satellite.
- The potential energy of the satellite.
- The total mechanical energy of the system.
- Relationship between the net force on the Earth and net force on satellite.
- Relationship between the mass of the satellite and the shape of the orbit.
- 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?
Code
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 * ## ## ## DO NOT CHANGE ## #Window setup ## Window Setup ## scene.range = 7e7 ## or ## scene.width = 1024 ## Objects ## 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 = 15000 pSatellite = vector(30000000,0,0) 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") #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") g3 = gvbars(gdisplay = graphv, color = color.red, delta = 0.2, label = "Kinetic Energy") g4 = gvbars(gdisplay = graphv, color = color.blue, delta = 0.2, label = "Potential Energy") #MotionMap/Graph pSatelliteMotionMap = MotionMap(Satellite, tf, 200, markerScale=0.2, markerColor=color.blue, labelMarkerOrder=False) #Calculation Loop ev = scene.waitfor('click') while t < tf: rate(6000) g3.delete() g4.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 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(0, KE) g4.plot(0.5, PE) #Earth Rotation (IGNORE) theta = 7.29e-5*dt Earth.rotate(angle=theta, axis=vector(0,0,1), origin=Earth.pos)