kirkwood: Asteroid Orbital Axis Showing Kirkwood Gaps

In Dimodal: Spacing Tests for Multi-Modality

Asteroid Orbital Axis Showing Kirkwood Gaps

Description

The distance of asteroids from the sun is multi-modal, with modes corresponding to asteroid families and anti-modes to the Kirkwood gaps.

Usage

data(kirkwood)

Format

kirkwood is a numeric vector of 2093 values representing the semi-major axis of an asteroid in Astronomical Units (A.U.).

Details

The axis is stored in column 18 of the original data file. We keep only those asteroids within the orbit of Jupiter, with an axis below 5 A.U. We further keep only those asteroids whose diameter is known or not blank, in column 7 of the data file.

Source

Lowell Observatory maintains the asteroid ephemeris website at https://asteroid.lowell.edu/astorb/ The kirkwood dataset is a subset of the "astorb.txt.gz" static copy of the ephemeris, downloaded on 1 May 25. The full file contains more than 1.4 million entries, and is growing daily. Lowell Observatory provides a query builder for downloading up-to-date values at https://asteroid.lowell.edu/query-builder

The ephemeris is supported by grants from NASA and the Lowell Observatory; details are found on the website. Further distribution of the data requires acknowledging these funding sources.

References

N. Moskovitz, L. Wasserman, B. Burt, R. Schottland, E. Bowell, M. Bailen, M. Granvik, The ⁠astorb⁠ database at Lowell Observatory, Astronomy and Computing, 41, Oct 2022, pp. 100661.

Examples

## Load data.
data(kirkwood, package="Dimodal")

## Start from scratch.
## Normally you would not need to save the results of the call, but
## this clutters up the screen.
opt <- Diopt(NULL)

## Set up the analysis.
## This is a large data set so spacing in features is small but
## smooth, which allows tighter detector parameters.  Values depend
## on the range of the spacing and are found by trial and error.
## Set RNG seeds for repeatability.
## Using bars to mark flats is easier to read with dense data.
opt1 <- Diopt(peak.fht=0.015, flat.fripple=0.0075, analysis=c("lp", "diw"),
              excur.seed=3, perm.seed=5, mark.flat="bar")

## Use Ditrack to see where passing features (filled in dots) appear.
## Interval spacing is the same cut-off.  Wrapped in \donttest because of
## the run time.
trk <- Ditrack(kirkwood, "lp")
dev.new(width=8,height=4) ; plot(trk)
opt1 <- c(opt1, Diopt(lp.window=0.05, diw.window=0.05))

## Run analysis.
m <- Dimodal(kirkwood)

## Summarize the data and spacing.
m$data

## Print features that exist in both low-pass and interval spacing.
## Allow large distance between peaks because  of data set size.
mtch <- match.features(m, near=30)

## Gap distance (in AU), dropping the extra LP peak.
## There are gaps at 2.30, 2.48, 2.86, 2.93, and 3.06 AU.
a_gap <- (select.peaks(m$lp.peaks)$x[-3L] + select.peaks(m$diw.peaks)$x) / 2
a_gap

## Orbital resonance with Jupiter, which has orbital axis of
## 5.201 AU, from Kepler's third law.  The corresponding
## resonance is 3.40 (ratio 7:2 or 10:3), 3.04 (3:1),  2.46 (5:2),
## 2.36 (7:3), and 2.22 (9:4).  Simulations confirm all but the
## first and last.
resonance <- (5.201 / a_gap) ^ (3/2)
resonance

## The flats include families of asteroids, although other
## considerations must be taken into account to find true
## family members (composition of asteroid, orbital
## eccentricity and inclination).
## The second range at 2.76 AU includes the Ceres family,
## the third at 3.13 AU the Themis.  The first range at
## 2.64 AU includes the Eunomia and Prosperina families.
m$diw.flats

## 3 graphs side-by-side with results.
dev.new(width=12, height=4) ; plot(m)

## The full test results of the low-pass peaks.
m$lp.peaks

## In the Ditrack plot there are two peaks in the very lower right
## corner.  We need smaller filter kernels/intervals to find these.
## The parameters already set will still apply.
opt3 <- Diopt(lp.window=0.015, diw.window=0.015, peak.fht=0.025, peak.frelht=0.10)
## Running Dimodal with such small windows will generate warnings
## about the model tests being pushed out of bounds.
## This adds gaps at 1.93 (2:1) and 1.74 (7:4), both expected
## from simulations.  The 2:1 gap position shifts because the
## spacing is so large that there is data point to anchor the
## value and a second, smaller increase pulls the peak to 1.93.
m2 <- Dimodal(kirkwood) ; mtch <- match.features(m2, near=30)
dev.new(width=12, height=4) ; plot(m2)

## Restore default.
opt <- Diopt(opt)

Dimodal documentation built on May 2, 2026, 1:06 a.m.