# Planetary Motion and Kepler's Laws Lab

## General Instructions

• Open up the lab in Chrome to get started. Adjust window size to avoid overlaps.
• After resizing window, reload page to synchronize graphics with the new aspect ratio.
• When you change an initial value, you must Reset and Start again for the changes to take effect.
• Zoom and Move around with the controls in the top right corner.
• To find the position, velocity, and time of a given image, click on the image and read the data in the Controller (image will turn white).
• To make images more frequent, decrease the Frames/Image in the Controller. For example, to find where the planet intersects the x-axis, decrease the Frames/Image and click on the image closest to the x-axis
• Before you begin a simulation, you must input the equation for universal gravitation, with the symbols G, M, m, and r. There is no special syntax for equations, so G(mr) is the same as G*m*r; both are acceptable.
• Click the Start button to begin the simulation. Pause, Play, and Reset as needed.
• To print or save a data table, click the "Printable" button above the data table on the right. Then fill in your names and class and click print.
• To print or save a graphical simulation, use ⌘-P. For a black background, check the box for "Background Colors and Images."

## Challenge 1 Procedure

1. Set initial coordinates of Planet=(100, 0) meters.
2. Set initial Vx of Planet=0 m/sec.
3. Set initial Vy of Planet=23 m/sec.
4. Check to ensure that the mass of Planet=100 kilograms.
5. With the above data an eccentricity greater than 0.2 will be produced.
6. To find the position, velocity, and time of a given image, click on the image and read the data in the top right corner (image will turn white).
7. Now you will modify the initial conditions of the planet's motion to…
• Change the initial velocity or planet x-position to make the orbit less elliptical.
• Record the values of X1 and X2 from your simulation on scratch paper. Calculate the eccentricity of your new orbit from these values. Note that X2 is GREATER than X1, even if your simulation does have the sun on the left focus, as in the figure on page 2.
• Continue to modify the orbit and calculate the eccentricity until you achieve an eccentricity of 0.10 or less.
• Record your final data for challenge 1, including all SF, in the table below.
• Show a clear calculation of the eccentricity of the final orbit (with units) in the labeled space, below your data.
8. Save your simulation and data table as PDFs. Then print one copy of each PDF for your lab group to include in your report. Label it with your names and Challenge 1.
9. By clicking on planet images, find the highest and lowest velocities of the planet. On the printout show where the highest and lowest velocities occur by drawing a directional arrow representing velocity vectors, labeling each with their magnitude.

## Challenge 2 Procedure

1. Choose any mass, starting position, and starting velocity of the comet. Vary conditions to make the orbit more eccentric and calculate the eccentricity on scratch paper.
2. Vary the starting conditions of your comet until you…
• Record the data for the final comet orbit for Challenge 2, below.
• Write a clear calculation of the eccentricity of the comet's orbit (must be greater than 0.80 to be acceptable). Show this calculation in the labeled space, below your data.
• Change image frequency to maximize data points.