Project 3: Learning goals
- Predict the motion of a system of gravitationally interacting objects analytically and computationally.
- Evaluate the validity of predictions for the motion of gravitationally interacting objects.
- Generate free body diagrams for a system of multiple objects and identify Newton’s 3rd Law force pairs in order to explain physical phenomena.
- Determine the net force acting on a single-particle system using a diagrammatic representation (free-body diagram) and by performing any necessary calculations.
- Explain the motion of single-particle systems using interactions (forces) as the basis for the explanation.
Project 3: Learning Concepts
- Forces cause changes in momentum
- Uniform circular motion
- Newtonian gravitational force
- Iterative prediction of motion
Project 3: Part C: Geostationary orbit
Carver is impressed with your work, but remains unconvinced by your predictions. He has asked you to write a simulation that models the orbit of the satellite. To truly convince Carver, the simulation should include representations of the net force acting on the satellite, which has a mass of $15\times10^3$ kg. Your simulation should be generalized enough to model other types of orbits including elliptical ones.
Conceptual questions:
- What changes can you make to your code in order to put the satellite into an elliptical orbit?
- How does the program demonstrate that mass is inconsequential to the model?
- Can you think of an alternate way of writing the separation vector between the Earth and the satellite?
- In both the Tuesday problem and the Thursday problem we pretend that the moon does not exist - what impact would the moon have in this model?
- What change or changes could you make to the code to create a more accurate model?
Project 3: Part D: Geostationary orbit
While you have continued to impress Carver, he remains unsure about the size of the force acting on the satellite and its distance from Earth. He seems particularly concerned the distance of the satellite from Earth not very more than $\pm$ 1%. Graphs of its distance from Earth and the magnitude of the net force acting on it may convince him.
The syntax you need to work with in order to include a graph involves two lines of code(mass of Earth vs time is given as an example). One outside the while loop and the second inside as the variable being plotted on the vertical axis changes with time:
Outside the while loop, add: graphExample = PhysGraph(numPlots=1)
Inside the while loop, add: graphExample.plot(t, mEarth)
Project 3: Part E: Geostationary orbit
Use Glowscript to generate a single graph, plotting both the x-component of the satellite's momentum and the x-component of the net force acting on the satellite as a function of time. If you were not able to complete part B from last time, hand draw a prediction of these two graphs before constructing these graphs using Glowscript.