[Paper Review] Asteroids in the Inner Solar System II - Observable Properties

N. W. Evans, Serge Tabachnik|May 19, 2000

Astro and Planetary Science1 references4 citations

TL;DR

This paper simulates long-lived coorbiting asteroids around Mercury, Venus, Earth, and Mars using orbital integrations to predict their observable properties—such as sky position, proper motion, and brightness—for guiding future surveys. It finds that stable populations concentrate near but not exactly at classical Lagrange points, with broad velocity distributions and non-traditional peak locations, especially for Mercury, and identifies optimal search strategies using wide-field CCD, GAIA, and infrared surveys to detect objects as small as 0.8 km in radius.

ABSTRACT

This paper presents synthetic observations of long-lived, coorbiting asteroids of Mercury, Venus, the Earth and Mars. Our sample is constructed by taking the limiting semimajor axes, differential longitudes and inclinations for long-lived stability provided by simulations. The intervals are randomly populated with values to create initial conditions. These orbits are re-simulated to check that they are stable and then re-sampled every 2.5 years for 1 million years. The Mercurian sample contains only horseshoe orbits, the Martian sample only tadpoles. For both Venus and the Earth, the greatest concentration of objects on the sky occurs close to the classical Lagrange points at heliocentric ecliptic longitudes of 60 and 300 degrees. The distributions are broad especially if horseshoes are present in the sample. The full-width half maximum (FWHM) in heliocentric longitude for Venus is 325 degrees and for the Earth is 328 degrees. The mean and most common velocity of these coorbiting satellites coincides with the mean motion of the parent planet, but again the spread is wide with a FWHM for Venus of 27.8 arcsec/hr and for the Earth of 21.0 arcsec/hr. For Mars, the greatest concentration on the sky occurs at heliocentric ecliptic latitudes of 12 degrees. The peak of the velocity distribution occurs at 65 arcsec/hr, significantly less than the Martian mean motion, while its FWHM is 32.3 arcsec/hr. The case of Mercury is the hardest of all, as the greatest concentration occurs at heliocentric longitudes close to the Sun.

Motivation & Objective

• To model the synthetic observable properties of long-lived coorbiting asteroids in the inner Solar System.
• To identify optimal search strategies for detecting these elusive objects using current and upcoming observational technologies.
• To quantify the spatial distribution, proper motion, and detectability thresholds for asteroids near the Lagrange points of Mercury, Venus, Earth, and Mars.
• To assess the limitations of past searches and the potential of future missions like GAIA and SDSS in discovering these populations.

Proposed method

• Numerical N-body integrations of test particles over 1 million years to identify stable coorbiting orbits around Mercury, Venus, Earth, and Mars.
• Initial conditions are drawn from uniformly distributed ranges of semimajor axis, inclination, and differential longitude based on stability limits from prior 100 Myr simulations.
• Orbits are re-simulated and sampled every 2.5 years to generate synthetic observational data on sky position, proper motion, and brightness.
• Probability density contours on the sky and velocity distributions are computed from surviving test particles to model detectability.
• Search strategies are evaluated based on field-of-view, exposure time, tracking methods, and sensitivity thresholds for different instruments.
• Sensitivity estimates are derived for GAIA, SDSS, wide-field CCD, and infrared coronagraphs, using magnitude adjustments at regions of highest concentration.

Experimental results

Research questions

• RQ1 Where are the most likely sky positions for detecting coorbiting asteroids around Venus, Earth, Mars, and Mercury, and how do they deviate from classical Lagrange points?
• RQ2 What are the expected proper motion distributions of these coorbiting asteroids, and how broad are they in terms of full width at half maximum (FWHM)?
• RQ3 What are the detectability limits for coorbiting asteroids using current and upcoming surveys such as GAIA, SDSS, and wide-field CCD imaging?
• RQ4 Why are only certain types of orbits (e.g., horseshoes or tadpoles) stable for each planet, and how does this affect search strategies?
• RQ5 How do observational constraints from past surveys compare to the predicted detectability of coorbiting populations?

Key findings

• For Venus, the greatest concentration of coorbiting asteroids occurs at heliocentric ecliptic longitudes of 60° and 300°, with a full width at half maximum (FWHM) of 325° in longitude.
• For Earth, the sky distribution peaks at 60° and 300° with a FWHM of 328°, and the most common proper motion is 21.0 arcsec hr⁻¹, with a FWHM of 21.0 arcsec hr⁻¹.
• For Mars, the peak sky concentration occurs at heliocentric ecliptic latitudes of ±12°, and the most likely proper motion is 65 arcsec hr⁻¹, with a FWHM of 32.3 arcsec hr⁻¹.
• For Mercury, the most likely locations are at heliocentric longitudes of 16.0° and 348.5°, significantly offset from the classical 60° and 300° points, due to orbital eccentricity.
• The most common proper motion for Mercury coorbiting objects is 459 arcsec hr⁻¹, though velocities can exceed 1000 arcsec hr⁻¹, indicating high-speed detection challenges.
• GAIA is expected to detect coorbiting Venusian asteroids with radii ≥0.8 km and terrestrial ones with radii ≥1 km, while Martian Trojans with radii ≥1.9 km are detectable by GAIA.