AP Physics – Virtual Solar System Lab

The purpose of this exercise is to test and reinforce concepts regarding orbital motion such as Kepler’s Laws of Planetary Motion and Newton’s Laws of Motion and Universal Gravitation.  It should be noted that nothing can be proven with a simulation – the program is written based on Newton’s Laws and so it will illustrate them.

Start the program by clicking on the My Solar System link found on the Physics Links page of Mr. Milligan’s World.  Or just go to:  http://phet.colorado.edu/sims/my-solar-system/my-solar-system.swf.

Play with the program a bit to see how it works.  The values for position, mass, time, etc. are in arbitrary units and do not represent numbers of meters, kilograms, seconds, etc.

Part A – Newton’s Laws and Circular Orbits

1. Select Preset: Sun and Planet.  Make checks in the boxes for System Centered, Show Traces, and Show Grid.  Set the slider at halfway between Accurate and Fast.  (But, feel free to change this setting – greater accuracy requires more calculation and hence a slower animation – and more patience!)

2. Enter the following in the Initial Settings boxes and click on Start and observe the result.

3. Experiment with the initial velocity of body 2 until you produce a circular orbit – you may want to use the virtual tape measure to measure the radius, but the grid is also helpful.  Record this speed in the table.

4. Use the timer and Start, Stop, and Reset to determine the period of this circular orbit.  You can turn on or off the Show Traces option or change the accuracy setting in order to change the speed of the simulation.

5. Use the values of this simulated orbit to determine the value of the universal gravitational constant G (in this simulated universe it is not the value we have learned). 

6. Use your value for G to calculate the correct speed for a circular orbit if the initial x-position is changed from 200 to 150.  Use trial and error to see if this value or a different one produces a circular orbit at this radius – record the observed speed that best produces a circle.

7. Change the number of bodies to 3 and for the third body use a mass of 0.001 (1/100^th the body 2’s mass).  Place this body in the same size orbit as body 2 but directly on the opposite side of the “sun”.  Experiment to find the velocity necessary for a counterclockwise circular orbit for body 3.  What does this imply about the effect of a planet’s mass on its own orbit?

Part B – Kepler’s Laws and Elliptical Orbits

8. Change the number of bodies back to 2.  Change the mass of body 1 to 300 and the mass of body 2 to 0.001.  Leave body 1 motionless at the origin and then experiment with body 2 in order to produce a clearly elliptical orbit that occupies a good part of the screen.  Use the “tape measure” tool to measure the major axis and the minor axis of this orbit.  Also measure the perihelion distance (closest approach to the Sun).  If the Sun is located at one focus of an ellipse then the perihelion distance should be given by:    (based on properties of an ellipse).  Perform this calculation and compare to your measured value as a test of Kepler’s 1^st Law of Planetary Motion.

9. For the same elliptical orbit find the speed (a “mouse-over” function) of body 2 at each extreme of its orbit – and its distance farthest from (aphelion) and nearest to (perihelion) the “sun”.  According to Kepler’s 2^nd Law of Planetary Motion the “planet” should “sweep out” equal areas in equal periods of time.  Test this idea by calculating, for each extreme, the area swept out in a unit of time equal to 0.01 (arbitrary units).  For such a small interval of time, the area can be approximated as that of a right triangle (ignoring the curvature of the orbit).

10. Repeat the previous two steps for a different elliptical orbit of your choosing.

11. Create a 4 body “solar system”.  Let body 1 represent “a sun” by using a relatively large mass (say 300 to 400).  Then let bodies 2, 3, 4 represent “planets” by using relatively tiny masses (For example, if mass of Sun = 330 then mass of Earth would be 0.001 and Jupiter would be 0.32.)  Adjust the initial positions and velocities so that all three planets will orbit your sun at various distances and various eccentricities.  Use the tape measure and the timer to measure the major axis and the period of each orbit.  Without changing your sun, adjust your planets to produce three more unique orbits and find the major axis and period of each one.  This gives you data for six orbits around the same “sun”.  According to Kepler’s 3^rd Law of Planetary Motion the ratio of the semi-major axis cubed to the period squared should be constant for these six orbits.  Calculate this ratio for each of the six orbits and compare.  Take the mean value of this constant and use it to solve for G (in the simulated universe).  Compare to your previously determined value for G.

Part C – Two Body Interactions

12. Return the number of bodies to 2.  Up until now, the mass of the central object has been much greater than the mass of the orbiting bodies.  Shown below are values that will mimic the planet Pluto and its moon Charon, which have comparable masses.  Run the simulation and determine the period and the radius of each orbit.

13. Use your mean value of G and the dimensions of the orbits to solve for and calculate the period of the planet and of the moon.  Compare each of these calculated periods to the observed period.  Note: the value of r to be used in Newton’s Law of Universal Gravitation is not the same as the radius of either orbit (but rather it is the separation of the two bodies)!

14. Now try deselecting the System Centered option and run the same simulation shown above.  This is the same motion seen from a different frame of reference.  When using the System Centered option, the frame of reference keeps the system of objects centered in the viewing window.  Without the System Centered frame you can visualize how Pluto and Charon move together through space (orbiting the Sun) while simultaneously orbiting one another.

Part A – Newton’s Laws and Circular Orbits

Mass of Central Body	Radius of Orbit	Observed Speed	Calculated Values:
500	200		G =
500	150		v =

Show work for calculated values:

Does the mass of a satellite have a significant effect on the orbit of that same satellite?  Record observations and explain using physics concepts:

Part B – Kepler’s Laws and Elliptical Orbits

	Elliptical Orbit #1	Elliptical Orbit #2
Major Axis
Minor Axis
Perihelion (Calculated)
Perihelion (Observed)
Speed at Perihelion
Aphelion
Speed at Aphelion
Area “Swept” at Perihelion
Area “Swept” at Aphelion

Show work for calculated values of one orbit:

Simulated “solar system”
Mass of “sun” =
Planet Mass	Major Axis	Semi-Major Axis	Period	R^3/T^2
			Mean:
			G:

Show work for finding G:

Part C – Two Body Interactions

	Planet-Moon System
	Separation of Bodies = 150
	Gravitational Attraction =
	Mass	Orbital Radius	Period (observed)	Period (calculated)
“pluto”
“charon”

Show all work: