Orbits explainedOrbits explained

An asteroid's orbit is a promise kept with remarkable precision. Six numbers describe it completely, and three of them — size, shape and tilt — already tell you where a body lives, how long its year lasts and whether its path ever comes near Earth's.

The orbital elements#

An orbit around the Sun is an ellipse, and the classical orbital elements pin that ellipse down in space and place the asteroid on it at a given moment, called the epoch.

From a and e follow the two distances that matter most:

• Perihelion q = a(1 − e) — the closest approach to the Sun.
• Aphelion Q = a(1 + e) — the farthest point from the Sun.

Kepler's three laws#

Johannes Kepler published three laws of planetary motion in the early seventeenth century. They apply to every asteroid in the catalogue.

1. Orbits are ellipses, with the Sun at one focus. The Sun is not at the centre of the ellipse, which is why perihelion and aphelion differ.
2. Equal areas in equal times. A line from the Sun to the asteroid sweeps out equal areas in equal intervals. An asteroid moves fastest at perihelion and slowest at aphelion.
3. The square of the period is proportional to the cube of the semi-major axis. For a small body orbiting the Sun, with the period P in years and a in AU, P² = a³ — so P = a^1.5.

The third law makes the orbital period a pure consequence of size. Earth, at 1 AU, takes one year; Jupiter, at 5.20 AU, takes about 11.9 years. A useful companion figure is the mean orbital speed, approximately 29.78 / √a km/s, where 29.78 km/s is Earth's own mean speed around the Sun.

Worked example: Vesperine#

Vesperine (ASR-0001) has a = 2.64 AU, e = 0.11 and i = 7.2°. Everything else on its listing follows from those values.

a = 2.64 AU    e = 0.11    i = 7.2°
 
q = a × (1 − e) = 2.64 × 0.89      ≈ 2.35 AU   perihelion
Q = a × (1 + e) = 2.64 × 1.11      ≈ 2.93 AU   aphelion
P = a^1.5       = 2.64 × √2.64     ≈ 4.29 years
v ≈ 29.78 / √a  = 29.78 / 1.625    ≈ 18.3 km/s mean speed
 
2.50 ≤ a < 2.82  → Middle main belt
q ≥ 1.3 AU       → not a near-Earth object

Perihelion q

2.35 AU

a(1 − e)

Aphelion Q

2.93 AU

a(1 + e)

Period P

4.29 yr

a^1.5

Orbit class

Middle belt

Between the 3:1 and 5:2 gaps

Vesperine never comes closer to the Sun than about 2.35 AU — well beyond Mars, whose average distance is 1.52 AU — and never strays past about 2.93 AU. The diagram below draws the orbit to scale, with the Sun at one focus.

Orbit classes#

Every entry is assigned an orbit class automatically from its elements. These are the classes used in the catalogue:

How the classifier decides#

The rules are checked in order, and the first one that matches wins. Earth's perihelion (0.983 AU) and aphelion (1.017 AU) set the near-Earth boundaries.

Ranges include the lower bound and exclude the upper one, except the Trojan, Hilda and outer-belt distances and the Hungaria inclination range, which include both ends.

Near-Earth objects#

A near-Earth object (NEO) is any asteroid — or short-period comet — with a perihelion below 1.3 AU. Near-Earth asteroids fall into four groups, and the catalogue has one of each:

• Atira — orbit entirely inside Earth's: Lumen Ward, with a = 0.74 AU and Q ≈ 0.92 AU.
• Aten — Earth-crossing, smaller than Earth's orbit: Kestrel, with a = 0.93 AU.
• Apollo — Earth-crossing, larger than Earth's orbit: Helion Drift.
• Amor — approaches from outside without crossing: Meridian Thorn, with q ≈ 1.24 AU.

Helion Drift is a clear Apollo. With a = 1.62 AU and e = 0.46, its perihelion is 1.62 × 0.54 ≈ 0.87 AU — inside Earth's orbit — while its aphelion of about 2.37 AU carries it out past Mars. Its year lasts 1.62^1.5 ≈ 2.06 Earth years.

"Near-Earth" describes an orbit, not a danger. A separate label, potentially hazardous asteroid, is reserved for bodies whose orbits pass within 0.05 AU of Earth's orbit and that are bright enough (H of 22 or less, roughly 140 m or larger) to matter. Computing that minimum distance needs the full set of elements, so the catalogue does not assign it.

Kirkwood gaps and resonances#

In 1866 Daniel Kirkwood noticed that asteroids avoid certain distances from the Sun. The gaps sit where an asteroid's period would be a simple fraction of Jupiter's: a mean-motion resonance. A resonance written 3:1 means three asteroid orbits for every one of Jupiter's. Repeated, regularly timed tugs from the giant planet pump up eccentricity until the orbit crosses Mars or Earth and the asteroid is removed. The same mechanism delivers a steady supply of near-Earth asteroids and meteorites.

The locations follow from Kepler's third law: an asteroid completing p orbits for every q of Jupiter's sits at a = 5.20 × (q/p)^(2/3) AU.

Not every resonance clears space. At the 3:2 and 1:1 resonances, the geometry keeps asteroids away from close encounters with Jupiter, and they collect there. Peregrine Ash, a Hilda at a = 3.97 AU, has a period of about 7.91 years; Jupiter's is about 11.87 years — a ratio of almost exactly 3:2.

Absolute magnitude H#

How bright an asteroid looks depends on its distance from the Sun and from us, and on the angle of illumination. Absolute magnitude H removes those effects: it is the brightness the asteroid would have at 1 AU from both the Sun and the observer, seen fully lit. As with all astronomical magnitudes, a smaller number means a brighter object.

Brightness alone cannot give a size, because a dark surface reflects less light than a bright one. With the geometric albedo p, the diameter in kilometres is:

D = 1329 / √p × 10^(−H / 5)

For Vesperine, with a diameter of 3.8 km and an albedo of 0.24, this gives H ≈ 14.27. The table shows why albedo matters so much:

Next steps#