Chapter 3: Investigating the Orbits of the Planets in the Solar System

Starry Night allows you to simulate the sky from many different locations and perspectives.  In the image above, you are seeing a view of the Solar System that no human or robot has ever been able to see; the perspective is from a location high above the north pole of the Sun, about four times as far from the Sun as Uranus is located.  From this perspective, you can see the layout of the outer planets and their orbital paths are shown.  This is a common figure in many textbooks and in many picture books for children.  In past research conducted at Penn State, we were surprised to learn that some students have interpreted diagrams like this as indicating that the planets follow physical tracks in space just like trains follow train tracks on Earth.

Investigation Question:

What factors are needed to produce orbits similar to the planets in our Solar System, and why?

In this investigation, we are going to use a different software simulator to allow us to investigate the motion of the planets.  Astronomers have created very sophisticated programs that allow us to simulate how objects move, and in general these are referred to as “N-Body Simulations” as they allow you to, for example, program in 1 million objects and allow them to move as predicted by our understanding of scientific principles.  There is a powerful, but simple, N-body simulator available at phet.colorado.edu called “My Solar System”, which you will use to investigate the motion of a simulated Sun and planets.

To begin this investigation, we first return to Starry Night to allow us to observe the layout and motion of objects in the Solar System.  Your observations of the planets (and any other objects visible in Starry Night) will serve as some preliminary data to guide your investigation.

After observing both the inner Solar System and the outer Solar System in motion for a few moments, discuss in your groups the answers to the following discussion question, and record your thoughts in your notebook:

• How do the orbits of the planets compare to each other; in what ways are they similar and in what ways do they differ?

As stated in the investigation question, your goal is to be able to simulate orbits that are similar to those we observe in the Solar System.  So you need to have a clear idea of what properties of an orbit you consider important for it to be sufficiently similar to how the planets behave.

Familiarizing yourself with the My Solar System n-body simulator

Go to the PhET Interactive Simulation and click play in order to open the simulator program.  The first goal of this investigation is to familiarize yourself with this data collection tool so you understand how it works and what it is showing you.  Play around with all of the controls and see how many different results you can produce by changing various parameters and pressing “Start”.

In this investigation, we are going to build more and more structure into our use of the My Solar System tool in order to address the investigation question.  After you feel familiar with how it operates, our next goal is to start building a more realistic simulation of our Solar System.  In particular, we know that the Sun is much more massive than the planets.  The default preset sets the mass of the yellow body to be 200 in some arbitrary units and the mass of the purple body is 10 in those same units.  This means that the simulated Sun is only 20 times more massive than the simulated planet.  You can simulate a more realistic relationship between the Sun and the planet by increasing this ratio such that the Sun is 100 times more massive than the planet.  To do this, type 2000 in the yellow box under “mass” for body 1 and type 20 in the purple box under “mass” for body 2.  After changing the mass, do the following in your groups:

• While leaving the mass of the two objects constant, change all of the rest of the parameters you can adjust and after each change press “Start” to simulate what happens.
• Try to determine all of the possible outcomes for the planet.  That is, what are all the different ways in which the planet behaves after you change its initial parameters and then press start?
• Determine what your group considers to be the definition of a “stable orbit”.  Try to narrow down what are the best parameters to produce a stable orbit for your purple planet.
• See if you can determine what factors appear to be most important to create orbits that look like Earth’s orbit around the Sun.

Narrowing the investigation question

As we have done in previous investigations, we are now going to narrow the question a bit and have each group focus on a piece of the puzzle.  We are going to focus on the sub-question, “How does one parameter affect a planet’s orbit around its star?”.  Everyone in all groups should start this piece of the investigation by creating a stable orbit that looks like the orbit of the Earth around the Sun.  The masses of the yellow star and purple planet should be set to 2000 and 20 as they were previously.  All of the other parameters you can alter should be set using the results of your previous experimentation with the simulator so that the initial orbit looks as close to Earth’s orbit as seen in Starry Night as your group can accomplish.  Each group will now be assigned a particular parameter to study in depth while leaving all of the other parameters as they were from this initial orbit.  Parameters your group may be assigned are:

• Mass of the star
• Mass of the planet
• Distance between the star and planet
• Magnitude of the velocity of the planet

Each group should complete a significant number of trials that allows you to explore all of the possible behaviors of the system that can occur just by varying your one parameter.  After each group completes this experimentation, you should discuss in your group a claim that answers the sub-question and what evidence from the simulator you will record to support the group claim.  Groups should share their claims and evidence on white boards so that everyone can learn how each specific factor impacts the behavior of the resulting motion of the objects.

Expanding the simulation to study three objects

In the prior part of this investigation, you were studying only two objects (a star and planet) and focusing on one parameter in particular.  The real Solar System is much more complicated, as it consists of many more objects which are moving in three spatial dimensions, rather than two.  The next step in our investigation is to bring the simulation closer to the real Solar System by increasing its complexity.  You are going to add a second planet by clicking on the button next to “3” for the number of bodies under the Initial Settings.  This will add a second planet in blue next to the purple planet.  Your goal for this part of the investigation is to try to make the orbits of the two planets appear similar to Venus and Earth, Earth and Mars, or Jupiter and Saturn.  To better reflect the true properties of our Solar System, you are also going to set the mass of the planets to the correct ratio for one of these sets of two planets.  Before beginning this new set of trials, each group should choose one of the following options and set the masses as indicated:

1. Sun:  mass = 2000, Venus:  mass = 0.005, Earth:  mass = 0.006
2. Sun:  mass = 2000, Earth:  mass = 0.006, Mars:  mass = 0.0006
3. Sun:  mass = 2000, Jupiter:  mass = 2, Mars:  mass = 0.6

As before, complete as many trials as necessary by adjusting the other parameters until you reproduce orbits that look similar to what you have seen for these two planets in your observations with Starry Night.  When you have completed your trials, look for any patterns in the properties of the other parameters.  In particular, how does the velocity of the planets relate to their distance from the Sun?

Making predictions to begin building your reasoning for the investigation

Now that you have completed many different trials with many different variations on the parameters available to you in this simulation, you should have built some intuition for how objects will move if you were to vary any factor such as mass of the star, mass of the planet, distance between the objects, and the velocity of the objects.  To begin building your reasoning, we recommend holding a discussion to make some predictions that you can test with the simulation.  In your groups, discuss the following questions:

• If you set up the simulation using the parameters you determined to give you the best Solar System-like orbits for the pair of planets you selected above, but then you increased the mass of the Sun dramatically, how would the outcome of the simulation change?  What if you decreased the mass of the Sun dramatically?
• If you set up the simulation using the parameters you determined to give you the best Solar System-like orbits for the pair of planets you selected above, but then you increased the mass of the inner planet dramatically, how would the outcome of the simulation change?  What if you decreased the mass of the inner planet dramatically?

Building a model of the nature of gravity

In this investigation, you likely have already been discussing in your groups some of your initial thoughts for why the objects in the simulation behave the way that they do.  To fully explain the simulation, you need to understand gravity, so we begin our reasoning work for this investigation with a discussion of gravity.  In your groups, you should discuss what you know about gravity, and then share out with the whole class.  The class understanding of the nature of gravity can be used as the basis to build your reasoning for this investigation, but there are several additional questions to consider in order to build understanding.  The first set of related questions to consider in your group are:

• Is there gravity on the Moon?
• How would we know?

As part of our class exploration of this question, we watch the video of Astronaut Dave Scott doing an experiment on the Moon.  We recommend you pause the video after he introduces the experiment, make a prediction for what will happen, and then hold a class debrief after watching the short experiment.

The next set of questions to consider are:

• Returning to the My Solar System simulator, is there anywhere you could place a planet in the simulator such that it would not feel a force of gravity from the Sun?
  • Similarly, is there someplace you could place an object above the surface of the Earth so it would not feel a pull from the Earth?  What about the Moon?
• Is there gravity in space?

Given your experiments with the simulator and your answers about gravity on the Moon, above the Earth, above the Moon, and in space, can you answer:

• What factors determine the strength of the force of gravity on an object?
• Can you explain, using mathematical reasoning, how the force of gravity changes as you manipulate these factors in the simulation?

Building a model for the nature of orbits using your understanding of gravity

The types of questions you considered in the previous section are exactly the types of questions scientists considered as they unraveled the nature of gravity.  Many of the stories you are likely to have heard about gravity are about Isaac Newton, and he conducted “thought experiments” specifically to explain the nature of orbits.  To continue building a model to explain the nature of planetary orbits, we are going to follow some of the reasoning done by Newton using a new tool built to mimic his thought experiments.  Tools of this sort are called “Newton’s Cannon”.  Using this Newton’s Cannon simulator, your instructor will demonstrate what happens in several trials of the simulator.  In your groups, you should discuss and share out your answers to the following discussion questions:

• What happens when the cannon is fired with low velocities?  What role is gravity playing?  How would you describe what is happening to the cannonball?
• What happens when the cannon is fired with a velocity of approximately 7500 m/s?  What role is gravity playing?  How would you describe what is happening to the cannonball?
• If you could somehow launch this cannonball from a cannon that was nowhere near the Earth, what would the path of the cannonball look like?  What would have to happen to change the path of the cannonball in this case?

To complete the model, we introduce a definition of some physics terminology that needs to be understood and used in this context.  Physicists refer to the property of an object that quantifies its tendency to remain at rest or in constant, straight-line motion as “inertia“.  You should discuss in your group how to incorporate the definition of inertia into your reasoning for this investigation.

Resources for further investigation

N-body simulators like My Solar System can be “gamified”, that is, turned into tools that you can use to compete for points.  A free, on-line game called “Super Planet Crash” is one example of a gamified N-body simulator you can play.  See if you can use your knowledge from this investigation to earn a high score!

Astronomers have built software that combines N-body simulators with other scientific principles, like the behavior of gas in the Universe, in order to study phenomena like the formation of Solar Systems and galaxies.  Just like Super Planet Crash, a team has built a video game that allows you to play around with the Universe itself, called “Universe Sandbox“.  This is a commercial game you can purchase, but they do have an educator’s version available through Teacher Gaming Store.

Understanding the nature of the idea of inertia is a challenging one for younger students.  If you would like to conduct some additional experiments to understand inertia, the education team from the NASA Swift satellite has created an activity guide on this concept.