Science Homework Help

Feynman on the Cavendish Experiment

Cavendish Experiment Set up Demo

For this week’s lab we will continue with our exploration of the applications of the free scientific computing software Mathematica. Last time we explored one dimensional free fall motion. Here we will generalize to two dimensional orbital motion of the international space station.

Instruction how to do the part 2 of the assignment: 

Open a new file in Mathematica (create a Mathematica account if you didn’t have one yet. IT’S FREE. Watch this video if you don’t know how to create a Mathematica account) and call it Orbital Mechanics 1.

Enter in 2+2,  then hit the enter button 5 times to create some space for the cell and then hit shift enter. 

Erase the 2+2 so that you have a blank cell of five lines.

Copy the code in the doc file “Code of Lab #5” (below)

Place your cursor in the blank Mathematica cell and press Ctrl +V  and wait for the code to load

Press Ctrl+S to save the code in your Orbital Mechanics 1 file

Press  Shift + Enter  to run the code. It should result in the orbital diagram that was shown in class. 

Save a copy of this working program so that if you make adjustments and it stops working you can copy using the Ctrl+C  to copy the highlighted material in Mathematica and then Ctrl+V to paste it. 

Assignment:

Part 1:

Read from “The Feynman Lectures on Physics” sections 7-4 to 7-8 and 9-3 to 9-7 on numerical simulation of orbits. Comment a few sentences about the reading.

Part 2:

Run the code multiple times changing the value on n to 50, 100, 300, 500, 700, 1000, 3000, 5000, and 10000. Describe how the final position changes ? Would going to 100000 change things much more? Don’t try it as your system will run away. 

Use your results in set 1 to predict the number of hours and minutes it takes for the International Space Station to orbit the Earth.

Observe how close the ISS is to the Earth. The atmosphere on this scale is thinner than the black line representing the Earth.

Set v0x=2000 and v0y=4000,  and set n=5000. Notice that you will get an incomplete ellipse. Now change n to the following values, n=10000, 20000,30000 and notice how the ellipse become more defined 

Take a screenshot of your images and post them to the discussion board.  Notice that the top of the ellipse is the same as the projectile motion that was studied earlier. 

Notice how sensitive the orbit is to changes in the initial conditions. This phenomenon,  called chaos theory,  was first formally studied in orbital mechanics and is an active area of research. Our exploration of it, particularly regarding gas behavior, will lead to an idea called statistical mechanics that we will investigate more later.