Earth and Space Science > Activities > Modeling the Earth-Moon Orbital System

# Modeling the Earth-Moon Orbital System

#### Summary

Students will create a physical model of the Earth-Moon system that demonstrates that both bodies revolve around their common center of mass (barycenter) and that the Moon does not really orbit the Earth.

## Learning Goals

Students will understand that for most planetary and stellar systems, though one object appears to revolve around the other, in actuality, the systems are much more complex. In a simple two-body system the location of the focus can be easily demonstrated and computed. For more complex systems (such as our solar system), the barycenter wanders around and is not easily calculated.

## Context for Use

This is an intermediary unit. It is intended to come after students have seen that all orbits are actually ellipses with various degrees of eccentricity (though they often can be treated as almost circular). After students see that stars wobble because of the gravitational forces of the planets that orbit them we will work on a project to have students compute the orbital periods of exoplanets based on the radial velocity of the stars they orbit.

## Description and Teaching Materials

The following will be made available to the students:

• Rods of various lengths (meter sticks can be used).
• String.
• Tape.
• Clay.
• Balls of various sizes and masses.
• Paper.
• Scales.
• Rulers.

In addition, students will be provided with facts about the Earth-Moon system that may or may not be useful to them including mass, diameters, densities, distances apart, etc. Depending on the group, these could be in actual units or in relative sizes or percentages where Earth=1.

## Teaching Notes and Tips

After students have learned that orbits are ellipses and that the orbital period of an object is related to its orbital distance the teacher will inform them that "the Moon does not really orbit the Earth and the Earth does not really orbit the Sun." This abrupt apparent overturning of what they have learned will provoke them to explore their belief systems more fully during the activity.

The teacher will explain that, working in groups of three to four students, they are to use the materials provided (or anything else they want to add) to create a working model of the Earth-Moon system. They should make it to scale (and they can interpret "scale" however they want). The model should rotate when suspended.

Potentially useful information about the Earth, Moon, and their relationship should be on the board. This information should include more things than they need (for instance, masses are necessary but volumes and circumferences are not). As noted above, this information may be provided with units (Mass of Moon: 7.347 x 1022 kg) or comparisons (Mass of Moon: 1.2% Earth's mass) or both.

Some students should end up with models where both the Earth and Moon revolve around a point that is near the surface of the Earth. Because the mass of the supporting rod or stick they are attached to is not being taken into account, the true Earth-Moon barycenter will not be accurately replicated. A thorough discussion of the limitations of the models, what things were able to be scaled accurately, and what things needed to be included for this to be a fair representation of the real Earth-Moon system should be carried out with the class. Students should come to see that the center of mass of both objects is what they both revolve around. Depending on the level of the group, the equation for calculating the equation can be given and solved for the Earth-Moon system.

If a projector is available, animations of this should be shown. Students will likely ask about planets around stars. What they have learned should be extended to the solar system. Ask them where they think the barycenter of the solar system is. They should realize that this is a much more difficult question because of the multiple bodies involved. After sufficient discussion, a graphic showing the way it wanders around the vicinity of the Sun can be shown and discussed.

## Assessment

No summative assessment is associated with this activity. Students will debrief after the lab to discuss the pros and cons of the various models they created.

## References and Resources

The following sites and resources may be useful for gaining a deeper background understanding of the material.

http://cseligman.com/text/moons/earthmoongravity.htm

http://scienceprojectideasforkids.com/2010/barycenter-of-the-earth-moon-system/

http://calgary.rasc.ca/barycenter.htm

http://en.wikipedia.org/wiki/Center_of_mass#Barycenter_in_astrophysics_and_astronomy

NASA activity that shows a similar type of model: NASA Math of Extrasolar Planets Activity (Acrobat (PDF) 112kB Jul23 11)

## Modeling the Earth-Moon Orbital System --Discussion

Hello Mike –

I appreciate your aim to help kids understand more about the complexity of the actual systems they are studying. I also appreciate that your students will both create and use a model, and get to think about the issues that models present. Your activity is designed to give you a good window on students’ thinking (and its complexity), and that is equally important.

The fact that you will include more information on the board than students need is one of the ways you keep students in “figuring out mode.” I’ll be interested to hear what the models they create are like, and about the thinking/decisions that go into them. Alert us if you post some news about that as you carry this out! (And include some of it in the teacher notes if you post a public version - which I hope you will.)

When you tell the kids that the Moon does not really orbit the Earth, a way to put it that is in keeping with the spirit of your activity might be “I’m convinced that the Moon doesn’t really orbit the Earth….” (or “Scientists think that….”). I think that phrasing implies that you have reached a conclusion for reasons, and invites the students to join you (and scientists) in thinking about all this. It might also invite them to keep asking, as they read science texts, how the reported information was attained , and to see it all as a work in progress….

Ellen

5414:18316

Mike, I love the open-endedness of this unit. Please do let us know how it goes.

I also wonder about the wording. I think it's still correct to say the Moon orbits the Earth -- it's not correct to say that the Moon orbits the Earth's center of mass, or center of figure. Better to say, perhaps, the Earth and the Moon together orbit a point between their centers.

thanks again, keep in touch -

Lindy

5414:18335