Kirkwood gap

Key takeaways

Kirkwood gap belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Kirkwood gap to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Kirkwood gap from memory before moving on to harder problems.

Reference excerpt

A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter. The gaps were first noticed in 1866 by Daniel Kirkwood, who also correctly explained their origin in the orbital resonances with Jupiter. For example, there are very few asteroids with semimajor axis near 2.50 AU, period 3.95 years, which would make three orbits for each orbit of Jupiter (hence, called the 3:1 orbital resonance). Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiter's. The weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family (see List of asteroid families). Most of the Kirkwood gaps are depleted, unlike the mean-motion resonances (MMR) of Neptune or Jupiter's 3:2 resonance, that retain objects captured during the giant planet migration of the Nice model. The loss of objects from the Kirkwood gaps is due to the overlapping of the ν5 and ν6 secular resonances within the mean-motion resonances. The orbital elements of the asteroids vary chaotically as a result and evolve onto planet-crossing orbits within a few million years. The 2:1 MMR has a few relatively stable islands within the resonance, however. These islands are depleted due to slow diffusion onto less stable orbits. This process, which has been linked to Jupiter and Saturn being near a 5:2 resonance, may have been more rapid when Jupiter's and Saturn's orbits were closer together. More recently, a relatively small number of asteroids have been found to possess high eccentricity orbits which do lie within the Kirkwood gaps. Examples include the Alinda and Griqua groups. These orbits slowly increase their eccentricity on a timescale of tens of millions of years, and will eventually break out of the resonance due to close encounters with a major planet. This is why asteroids are rarely found in the Kirkwood gaps.

Main gaps The most prominent Kirkwood gaps are located at mean orbital radii of:

1.780 AU (5:1 resonance) 2.065 AU (4:1 resonance) 2.502 AU (3:1 resonance), home to the Alinda group of asteroids 2.825 AU (5:2 resonance) 2.958 AU (7:3 resonance) 3.279 AU (2:1 resonance), Hecuba gap, home to the Griqua group of asteroids. 3.972 AU (3:2 resonance), home to the Hilda asteroids. 4.296 AU (4:3 resonance), home to the Thule group of asteroids. Weaker and/or narrower gaps are also found at:

1.909 AU (9:2 resonance) 2.258 AU (7:2 resonance) 2.332 AU (10:3 resonance) 2.706 AU (8:3 resonance) 3.031 AU (9:4 resonance) 3.077 AU (11:5 resonance) 3.474 AU (11:6 resonance) 3.517 AU (9:5 resonance) 3.584 AU (7:4 resonance) 3.702 AU (5:3 resonance).

Asteroid zones The gaps are not seen in a simple snapshot of the locations of the asteroids at any one time because asteroid orbits are elliptical, and many asteroids still cross through the radii corresponding to the gaps. The actual spatial density of asteroids in these gaps does not differ significantly from the neighboring regions. The main gaps occur at the 3:1, 5:2, 7:3, and 2:1 mean-motion resonances with Jupiter. An asteroid in the 3:1 Kirkwood gap would orbit the Sun three times for each Jovian orbit, for instance. Weaker resonances occur at other semi-major axis values, with fewer asteroids found than nearby. (For example, an 8:3 resonance for asteroids with a semi-major axis of 2.71 AU). The main or core population of the asteroid belt may be divided into the inner and outer zones, separated by the 3:1 Kirkwood gap at 2.5 AU, and the outer zone may be further divided into middle and outer zones by the 5:2 gap at 2.82 AU:

4:1 resonance (2.06 AU) Zone I population (inner zone) 3:1 resonance (2.5 AU) Zone II population (middle zone) 5:2 resonance gap (2.82 AU) Zone III population (outer zone) 2:1 resonance gap (3.28 AU) 4 Vesta is the largest asteroid in the inner zone, 1 Ceres and 2 Pallas in the middle zone, and 10 Hygiea in the outer zone. 87 Sylvia is probably the largest Main Belt asteroid beyond the outer zone.

See also Orbital resonance Alinda group Cybele group Griqua group

References

External links

Article on Kirkwood gaps at Wolfram's scienceworld

Illustrations

Worked examples

Example 1 — a first encounter with Kirkwood gap

Start with the simplest possible case. Write down what Kirkwood gap claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kirkwood gap before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kirkwood gap ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kirkwood gap

In research: Kirkwood gap appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Kirkwood gap in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Kirkwood gap is common in secondary-school and first-year university syllabi. It links to neighbouring topics Asteroids, Resonance with Jupiter, so understanding it makes those chapters shorter.
In everyday life: Look for Kirkwood gap outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Kirkwood gap in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kirkwood gap means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Kirkwood gap out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kirkwood gap in simple terms?

A Kirkwood gap is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods) of the orbits of main-belt asteroids. They correspond to the locations of orbital resonances with Jupiter.

Why does Kirkwood gap matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kirkwood gap?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kirkwood gap.