Description
We are going to explore the orbital motion of the five different gravitational systems, A through E, through a virtual simulation provided by PhET. You will fill out the masses of the star and the planet. You will also measure the orbital radius and the period of the system in the Excel worksheet (highlighted area). You will learn about the properties of orbital shape, escape velocity, and Kepler’s third law. View the PhET “Gravity and Orbits” Interactive Simulation at: phet.colorado.edu/sims/html/gravity-and-orbits/latest/gravity-and-orbits_en.html Review the video PhET Gravity & Orbits at: https://c24.page/yy2uzvpr68p259rjdxu56cwp8e to familiarize yourself with the various functions of the simulation before beginning your assignment. Use the attached Excel worksheet for this unit. Save all of your work directly to the worksheet. See the attached instructions to access the details for this activity.
Unit III: Virtual Simulation Assignment Instruction
Open the “Gravity and Orbits” PhET simulation:
Review the video PhET Gravity & Orbits to familiarize yourself with the various functions of the simulation before beginning your assignment.
After opening the simulation website, click on “To Scale”
Step 1: Adjust the mass of the star and that of the planet.
Find the toolbox on the right side of the screen. Make sure that the star mass is 1, that of our sun, and the planet mass is 1, that of our Earth, in the bottom toolbox (see green oval). This is System A.
Record the mass M of the star as 1 and the mass m of the planet as 1 on your Excel worksheet.
Then, the masses of the planet and the star in kilograms will be automatically evaluated. Please note, the mass of the sun is 1.99 x 1030 kg and that of Earth is 5.98 x 1024 kg.
Step 2: Observe the orbital motion of the planet around the star.
Click on “Path,” “Grid,” and “Measuring Tape” in the toolbox (see green oval) to observe the orbital motion of the system.
Press the triangle button to observe the orbital motion of the planet around the star. Be sure to know the starting point so that you do not miss the one cycle of the motion.
To save time, you can click on the “Fast Forward” button at the beginning of the orbital motion; you should click on “Slow Motion” when the planet gets closer to the starting point, though. Pause the button when the planet arrives at the starting point. If you miss the exact moment of the ending, you may click on the orange button on the far right to start the process over.
Step 3: Find the orbital period T of the planet.
If you succeeded in finding one cycle of the motion, read the period of the orbital motion in the unit of Earth’s days (see green oval), and record the number in the table. Then, the period in seconds will be automatically calculated. See the screenshots below.
Step 4: Measure the orbital distances R1 and R2.
Now, grab the ”Measuring Tape,” and measure the distances R1 and R2 from the star to the planet. R1 is the horizontal orbital distance when the planet is located at the right side of the star when you look at the screen. Enter the value of R1 in thousands of miles (k-miles) on your Excel worksheet; then you’ll see the distance converted into meters. See the screenshots below. Please note, your measurement might slightly differ from what is provided due to discrepancies in individual measurement methods.
R2 is the horizontal orbital distance when the planet is located at the left side of the star when you look at the screen. See the screenshot below.
Read the number R2 in thousands of miles (k-miles), and record it in the table on your worksheet.
Then, the distances in meters will be automatically evaluated with the average distance or semi-major axis a, eccentricity e, and escape speed V of the planet. The orbital eccentricity is the difference between the radius at apoapsis (when the planet is farthest from the star) and that at periapsis (when the planet is closest to the star) divided by the sum of these two values, and it determines the shape of the orbits. If e is zero, the orbit is circular. If 0 < e < 1, the orbit is elliptical. If e = 1, the orbit is parabolic. If e > 1, the orbit is hyperbolic.
The escape velocity V of the planet is the minimum speed to overcome the gravitational field of the star. The planet must have greater energy than its gravitational binding energy to escape the star’s gravitational field. If we assume a circular orbit for simplicity, the square of the escape speed is proportional to the mass of the star and is inversely proportional to the orbital radius of the planet.
Step 5: Investigate System B (M = 2, m = 1)
Now, click on the orange button to nullify the condition. This time we will investigate System B. Adjust the mass of the star to be 2 and that of the planet to be 1. Record the mass M of the star as 2 and the mass m of the planet as 1 on your Excel worksheet. Repeat the above process from steps 2 to 4 to record T, R1, and R2 for System B.
Step 6: Investigate System C (M = 0.75 , m = 1)
After entering the data for System B, click on the orange button for the next system. For System C, adjust the mass of the star to be 0.75 and that of the planet to be 1. Record the masses of the star and planet accordingly on your Excel worksheet. Repeat the above process from steps 2 to 4 to record the T, R1, and R2 for System C.
Step 7: Investigate System D (M = 1, m = 2)
For System D, adjust the mass of the star to be 1 and that of the planet to be 2. Record the mass M of the star and the planet accordingly on your Excel worksheet. Repeat the above process from steps 2 to 4 to record T, R1, and R2 for System D.
Step 8: Investigate System E (M = 1, m = 0.5)
For System E, adjust the mass of the star to be 0.5 and that of the planet to be 0.5. Record the mass M of the star and the planet accordingly on your Excel worksheet. Repeat the above process from steps 2 to 4 to record T, R1, and R2 for System E.