Defining and defying Roche limits

This exercise is a part of Educator Guide: This Dwarf Planet Hosts an Odd Ring / View Guide

Directions for teachers:

Before beginning this lesson, review the basics of force diagrams and planetary gravitational force. The lesson plan “May the force move you” includes a comprehensive overview of forces. Then, students should read the Science News article “The Kuiper Belt’s dwarf planet Quaoar hosts an impossible ring” before discussing the questions below. A version of the article, “This dwarf planet has an odd ring,” appears in the March 11, 2023 issue of Science News.

To review exceptions to scientific rules and moon formation, you can pull questions from the How Earth got its moon and Accepting the exceptions lesson plans.

Ring around the planet

1. What are planetary rings? What planets in our solar system have rings?

Planetary rings are disks that orbit around planets and other astronomical objects. These rings can contain gases, dust, rocks, ice, small meteors and other debris. Saturn, Jupiter, Uranus and Neptune have rings.

2. What are moons, and how do scientists think they formed?

Moons are astronomical bodies that orbit planets, dwarf planets and asteroids. Like planets, moons vary greatly in their size, composition and features. Scientists think that many moons formed from disks of gas and dust that circled planets as the planets formed. Some moons are thought to have originated elsewhere in space but were captured into a planet’s orbit. There are various hypotheses about the origin of Earth’s moon. A commonly accepted hypothesis is that a Mars-sized object struck Earth, and the resulting debris coalesced in orbit to form our moon.

3. Which planets in our solar system have moons?

The planets in our solar system that have moons are Earth (one), Mars (two), Jupiter (92), Saturn (83), Uranus (27) and Neptune (14). Pluto, which is a dwarf planet, has five moons. 

Defining limits

1. Describe what the Roche limit tells you about gravity and the interactions of objects in space. Draw a simple diagram that supports your description.

The Roche limit is an estimated distance from a planet or object in a solar system beyond which the gravitational force of the larger body isn’t typically strong enough to prevent the gravity of smaller particles from forming a moon. Within the Roche limit, the gravitational force of the larger body overcomes the gravitational forces of smaller objects, preventing them from coalescing to form moons.

Student diagrams will vary but should include a planet, a line defining a Roche limit, a moon outside the Roche limit and a ring inside the limit.

2. On your diagram, add force arrows (vectors) to show the relative forces that are present on a moon beyond the Roche limit. Then show the same for forces on the particles on the rings.

Diagrams will vary, but arrows pointing inward for the moon’s own gravitational forces should be longer than the arrows pointing outward, which indicate the gravitational pull from the larger body. The arrows for particles in a ring should have the opposite lengths.

3. Check out the “Far-out ring” illustration in the article. What do you notice about the Roche limits indicated for Haumea, Chariklo and Quaoar? How are the Roche limits for Chariklo and Quaoar similar?

The three objects have different Roche limits. Chariklo and Quaoar both have rings outside their Roche limit.

4. List all factors that you can think of that might impact the predicted Roche limit of a planet.

A planet’s composition, size and proximity to the sun. The composition, size, and spread of the ring or moon may also impact the Roche limit.

Defying limits

1. What does “The dwarf planet Quaoar has a ring that is too big for its metaphorical fingers.” mean?

Quaoar’s ring appears to be well beyond its Roche limit, so the metaphor of a ring on a finger is being used to explain that the ring is bigger than scientists thought it was supposed to be.

2. Why do you think scientists make generalizations and create limits and rules like the Roche limit? What is the downside of generalizing?

Student answers will vary, but will likely include something about how using generalizations and categories simplifies the process of looking at many specific examples. Treating each example as an individual case to memorize or look up would require much more time and effort. The downside of making generalizations is that it may cause us to overlook or minimize the exceptions that are not the norm.

3. How can identifying exceptions to the scientific generalizations or rules help advance scientific knowledge? Explain.

Understanding the limitations of generalizations or rules can help scientists better understand a topic and revise those rules if necessary. It is these exceptions that might open new lines of scientific questioning.