Find the toolbox on the right-hand side of the screen. Make sure that the star mass is one, that of our sun, and the planet mass is one, that of our Earth, in the bottom toolbox (see green oval). This is System A.
Record the mass M of the star as one and the mass m of the planet as one 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 1.99×1030 kg and that of Earth is 5.98×1024 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 km on your excel work sheet then you’ll see the distance converted into meters. See the screenshots below. Please note, your measurement might slightly differ from what I have 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 km 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 two and that of the planet to be one. Record the mass M of the star as two and the mass m of the planet as one 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 finishing 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 one. 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 one and that of the planet to be two. 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 1 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.