# What your satellite’s journey time is and how it compares

NOTICE:
All the helpful documentation and instructions are attached in the additional materials. In those files there is a coursebook, where from page 61 there is a detailed description of this project.
Optional extras are not marked and don’t count towards the assessment for the project.
The project is about orbital motion of the inner planets of the solar system. An n-body numerical integration simulation.
The task is to write an object-oriented PYTHON program to simulate the orbit of the inner planets (Mercury, Venus, Earth, Mars) around the sun. The code should be commented (explaining what each method/function does).
Instructions copied from the coursebook:
The code should:
• Read the planet details and simulation parameters from file.
• Implement the Beeman integration scheme to update the position and velocity of the planets and the sun at each time step.
• Show the orbit of the planets as they move around the sun in a graphical display.
• Calculate and print the orbital periods of the planets in Earth years (you may also write them to file if you wish, but this is not required).
• Regularly write out to a file the total energy of the system, i.e. the sum of kinetic and gravitational potential energy.
Once you have a working code, you should work through the experiments below:
1. Orbital periods
Experiment 1 : Check how closely the orbital periods of the planets in your simulation match their actual orbital periods.
2. Energy conservation
The Beeman algorithm is a symplectic integrator, which means that the total energy of
the system should be conserved over time.
Experiment 2 : Check whether (or not) energy is conserved during your simulation. Illustrate your results graphically.
3. Satellite to Mars
Suppose you wish to launch a satellite from Earth to perform a fly-past of Mars.
Experiment 3 : Search for an initial velocity (or range of velocities) that enables a satellite to get close to Mars. You should
check:
• How close to Mars your satellite gets.
• What your satellite’s journey time is and how it compares
to that of NASA’s Perseverance mission.
• Whether your satellite ever gets back to Earth.
Afterwards, there should be a written report that include:
1. Introduction. A short outline of your project, the experiments that you tackled and the aims of these.
2. Methods. A high-level overview of your program design, along with an explanation of why designed your program and your experiments the way that you did.
3. Results and Discussion. A presentation of the key results from your experiments and a discussion of what they mean.
4. Conclusions. A short recap of the purpose of the project, the extent to which the objectives of your experiments were met and suggestions for future work.
Report should be a maximum of 2,000 words.
The word count should be included at the end of the report.

Pages (275 words)
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