The Carver Media Group is planning the launch of a new communications satellite. Elliot Carver (head of Carver Media Group) is concerned about the launch. This is a $200,000,000 endeavor. In particular, he is worried about the orbital speed necessary to maintain the satellite's geostationary orbit (and if that depends on the launch mass). You were hired as an engineer on the launch team. Carver has asked that you allay his concerns.

Conceptual questions:

1. How do you know you can classify the satellite's orbit as uniform circular motion?
2. If the gravitational force is acting inward, why does the satellite not fall to Earth?
3. What is the difference between the gravitational force, the net force, and the centripetal force ($mv^2/r$) in this case?
4. Is there a force exerted on Earth? If so, why do we ignore it? If not, why not?
5. Explain the difference between mass and weight.

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.

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:

1. What changes can you make to your code in order to put the satellite into an elliptical orbit?
2. How does the program demonstrate that mass is inconsequential to the model?
3. Can you think of an alternate way of writing the separation vector between the Earth and the satellite?
4. 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?
5. What change or changes could you make to the code to create a more accurate model?

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)

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.