Theory Play Share & Discuss

Lesson Preview

Teach Roche Limit and Orbits
with Gravity Simulator

This is a printable preview of one of our lessons. Subscribe to gain access to this and 180+ other lessons using 35+ games, and track your students' progression in real time! Learn More

This is a printable preview of one of our lessons. Subscribe for more great content! Learn More

Theory

Roche Limits and Orbits

Get to know the concept of the Roche Limit! Learn more about orbits!

Teacher Resources

This lesson provides more information on orbits, including the related concept Roche Limit. The next slide provides a review of the last lesson’s concepts on matter.

  • Theory: This lesson is about advanced orbit concepts, including the Roche Limit.
  • Play: Students complete tasks that focus on understanding orbital mechanics.
  • Share & Discuss: These slides focus on tasks that concern our solar system and orbits.

Review: Astrophysical Concepts

  1. Universe
Show Notes

All of time and space and its content, which includes planets, moons, minor planets, stars, galaxies, the contents of intergalactic space and all matter and energy.

  1. Galaxy
Show Notes

A gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter.

  1. Solar System
Show Notes

Our planetary system: a group of planets that circle (in this case) a single star.

  1. Star System
Show Notes

(or stellar system) is a small number of stars that orbit each other.

  1. Planetary System
Show Notes

A set of gravitationally bound non-stellar objects in orbit around a star or star system.

Teacher Resources

It’s a good idea to have the students work as pairs and have a few moments to think about these questions before you ask for the answers. Below are the answers, but for clarity and review, the next slide also includes the answers for the students.

For your convenience and as a recap for the students, the next slide features all of these concepts and their explanations, so you can use the answers below while quizzing the students and then go through the answers together with the next slide so everyone can both see and hear them.

Review: Groups in Space

Remember these concepts?

The Solar System is our Sun and the objects that orbit it, including Earth.

A Star System or Stellar System is a small number of stars that orbit each other.

A Planetary System is a set of gravitationally bound non-stellar objects in orbit around a star or star system.

A Galaxy is a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter.

The Universe is all of time and space and its content, which includes planets, moons, minor planets, stars, galaxies, the contents of intergalactic space and all matter and energy.

Game screenshot.

Roche Limit

  • The Roche Limit is the distance within which the gravitational field of a large body is strong enough to prevent any smaller body from being held together by gravity.
  • Inside the Roche limit, orbiting material disperses and forms rings whereas outside the limit material tends to coalesce.
  • Objects that are held together by stronger bonds than just gravity can survive within a Roche limit: for example, satellites built by humans are not automatically destroyed by the Roche limit.

Teacher Resources

Use the sources below and your own to teach the students the concept of the Roche limit.

Additionally, tell the students: The Roche limit is not the only factor that causes comets to break apart. Splitting by thermal stress, internal gas pressure and rotational splitting are other ways for a comet to split under stress. (source)

READ:

WATCH:

Play

Task One: Orbits

  1. Load the code “Orbits”.
  2. Click on the different planets and look at their stats. What do you notice?
  3. Why are the planets moving the way they do? What would happen if they were moving at a different speed? Try it out !

Gameplay screenshot.

Teacher Resources

The core idea of this exercise is to notice the following:

The planets and their speed: planets that are closer to the sun must move faster to maintain their orbit, because the star’s gravity is much more potent when the planet is closer.
Planetary movement causes: This movement is caused by two things: the planet’s velocity and the star’s gravity.
Changing a planet’s speed: If you change the velocity of a planet, its orbit is immediately altered (but the simulator will still keep varying the speed based on how close the planet is to the star). If you slow the planet down sufficiently, it will crash into the star (the simulator does not depict the Roche limit, which would be relevant here). If you speed up the planet sufficiently, it will break away from its orbit and fly away from the star, ultimately reaching so far that the star’s gravity will have no significant effect on it.

How to Play

Gravity Simulator main screen.

After you’ve launched Gravity Simulator, this is the main screen. Your students should select the load from code option, but below are descriptions for each option for your convenience.

  • Build: Start the simulation with nothing in it. Useful for experiments when you want to work on something specific.
  • Load from code: Loads up a ready-to-go simulation. Quickly gets you started and is the easiest way to learn how the simulator works.
  • Toggle fullscreen: This lets you play the simulator in a window or in fullscreen mode. This is a purely personal preference and has no effect on the simulation itself.
  • Exit the universe: Stop playing and close the program.

Task Two: Changing Physics

  1. Load the earlier Solar System code that we used before.
  2. Find the physics settings.
  3. Try inputting the different f (r) values that the game suggests. Remember to reset the simulation when you want to change values! What changes do you notice?

Gameplay screenshot.

Teacher Resources

Important: Emphasize to the students that they must reset the tutorial with the rewind button every time they want to enter a new value into the physics box.
Warning: This task is challenging and may take the students some time. It is very likely they will not understand the equations, but this is all right: all they need to do is follow the instructions - input the equations into the physics tab - and notice what is happening. As you are going through the answers together, you can explain what the equation truly means, although keep in mind that the core lesson is to make sure the students understand the importance of mass and distance when it comes to gravity.
Note: If some of your students do not have the Solar System code from before, it’s provided in full for your convenience on the next slide. It needs to be copied to the “load from code” window to be utilized.

The core idea of this exercise is to notice the following:

The nature of gravity: Although this equation - F = GMm / r*2 - can appear a little intimidating, its reality is quite easily observed in the simulator itself: when two objects have more mass (the letters M and m in this equation), the force of gravity is stronger between them (the letter F), and the farther away they are from each other (r stands for distance between the two objects) the weaker the gravity is. The G stands for the gravitational constant, an unchanging value that applies to all instances of gravity.

1/r^2: The default setting: since the equation is then “F = GMm*1/r^2”, it is the true equation for gravity. With this setting the simulation behaves realistically.

1/r^2.5: This weakens gravity further with distance, making the equation “F = GMm*1/r^2.5”. This will cause some of the planets to begin “wander off”, because the gravity is suddenly too weak to maintain the orbits at their current distances from the Sun.

1/r: This greatly strengthens gravity: though distance still weakens it, the planets start to gravitate toward the Sun because the gravity is that much stronger.

r^2: This means that gravity greatly increases the further away the two masses are, causing planets that are further away to shoot straight into the Sun with extreme speed, and closer planets to feel far lesser effects than the distant planets.

Note: It is not necessary to try out the the tan(r) function, and it is quite complex to explain.

The Solar System Code

Use this code:

https://goo.gl/PRmCKg

Teacher Resources

This is the code that allows students to use the Solar System simulation if they haven’t saved it from before.

/Gravity fun at TestTubeGames\ _settings(gravity: r^-2, x: -216.9865, y: 6.899657, zoom: 4.717124, name: Solar System);
_type0(m: 1000, col: 2, lcol: 3, d: 0.05828428, noGrav);
_type1(m: 0, col: 4, lcol: 3);
_type2(m: 0, col: 4, lcol: 3);
_type3(m: 0, col: 4, lcol: 3);
_type4(m: 0, col: 4, lcol: 3);
_type5(m: 0, col: 4, lcol: 3, rObj: 20);
_type6(m: 0, col: 4, lcol: 3, rObj: 20);
_type7(m: 0, col: 4, lcol: 3, rObj: 20);
_type8(m: 0, col: 4, lcol: 3,);
_type9(m: 0, col: 4, lcol: 3, rObj: 20);
_add(type: 0, x: 0, y: 0);
_add(type: 1, x: 80, y: 0, vy: 3.535534);
_add(type: 2, x: 160, y: 0, vy: 2.5);
_add(type: 3, x: 220, y: 0, vy: 2.132007);
_add(type: 4, x: 320, y: 0, vy: 1.767767);
_add(type: 5, x: 1120, y: 0, vy: 0.9449112);
_add(type: 6, x: 2060, y: 0, vy: 0.696733);
_add(type: 7, x: 4120, y: 0, vy: 0.4926646);
_add(type: 8, x: 8500, y: 0, vx: 0.004034842, vy: 0.3429616);
_add(type: 9, x: 6460, y: 0, vx: 0.006089382, vy: 0.3933741);

Share & Discuss

Share & Discuss

  • Did you understand the equations? If you didn’t, what was hard about them?
  • What was most fun about this lesson?
  • Was there something you wanted to do in the simulator but didn’t know how to? What was it?

Tasks after Playing

What is the Roche limit?

Show Notes

The Roche Limit is the distance within which the gravitational field of a large body is strong enough to prevent any smaller body from being held together by gravity.

How does gravity work? What are the two variables that determine the magnitude of gravity between two objects?

Show Notes

The distance between the bodies (the square of the distance is inversely proportional to the magnitude of gravity) and the multiplied result of the masses of the two bodies determines how strong the force of gravity is.

What would happen if gravity worked in a different way? Use examples from the task.

Show Notes

These changes would range from minor to severe. As demonstrated in the simulation, making gravity stronger with distance often causes planets to crash into the Sun