## Week 7: October 12 - 16

### Kepler-453b: A Real Tatooine?

In August 2015 the discovery of Kepler-453b was announced. Kepler-453b orbits a binary star, like the planet "Tatooine" in "Star Wars". We apply numerical techniques for solving differential equations to explore the possible orbital dynamics of this planet.

### Animation

Animating a graph involves updating the coordinates of drawn objects such as points and lines, then redrawing the objects. We learn how to do this in an IPython notebook.

### Solving Algebraic Equations

Finding the roots of a function - the values where it equates to zero - arises often when solving problems in science and mathematics. Since it is not always possible to find such roots exactly, methods for finding numerical approximations are needed. This week we start to examine such methods and explore their advantages and limitations.

Week 7 Notebook

### Python

• Error handling with try/except.

### Matplotlib

• FuncAnimation
• subplot

## Quiz

There will be no quiz this week.

## Assignment 6: Tatooine

Activity:

• Develop a program which implements the improved Euler method to simulate the dynamics of the Kepler 453b system.
• Generate complete trajectories for the planet under a range of initial conditions to see what kinds of orbits exist.
• Find an orbit as close as possible to the pair of stars that still seems stable.
• Optional: Visualize the trajectory generated by adding animation to the simulation code.
• Optional: Explore some trajectories with unequal masses and see the effect on stability.

Tools:

• Use the code developed in class for the improved Euler method for one star as the basis for your simulation involving two stars.
• Use the animation code from class and the class notes as a template.