Bridge to learning: Have students examine the histogram in the investigations that bins the number of asteroid orbits by their eccentricities. Note that although a few orbits approach an eccentricity of zero, they are not in truly circular orbits. Many asteroids and the planets have low eccentricities that make their orbits appear circular. (This tripped up many great minds in astronomy until Kepler came along.) It’s extremely difficult to achieve a circular orbit because of the many complex gravitational interactions in a multi-body system.

Bridge to learning: Some small Solar System objects orbit opposite the direction of most other bodies and planets (a retrograde orbit). Most often these are comets. Students may notice some of these retrograde orbits if they carefully observe the visualizations that are built into this investigation. If at first they don’t see them, advise them to try viewing only the comets. Objects with an inclination of more than 90० have retrograde orbits and are easily distinguished on the inclination histogram.

Retrograde orbits are a result of close encounters of the object with another, more massive body. The orbits of TNOs are more easily altered because they move more slowly in their orbits due to their great distances from the Sun. Main belt asteroids with retrograde orbits may be comets that have been depleted of their volatile components, and had orbits altered by gravitational interactions with Jupiter.

Retrograde orbits should not be confused with retrograde motion, which is when an object appears to move backwards in its orbit, due to the greater orbital speed of Earth relative to the object. Retrograde motion is an apparent (not real) phenomenon, similar to the way a car appears to move backwards, relative to your car, when you pass it.

Bridge to learning: Students will quickly discover through this investigation that asteroids are scattered throughout the planetary orbits. The main belt asteroids are the ones typically described in textbooks, occupying the space from roughly 2 to 3.5 au, placing them between Mars and Jupiter.

Bridge to learning: Asteroids are not that close together and most asteroids are very small, less than 1 km across. If you could make the densest part of the main asteroid belt (from 2.1-3.3 au) into a flat plane, it would have an area of about 6x10¹⁷ km²(and in reality, asteroids deviate far above and below this plane). In this scenario, each asteroid would have more than one million km² of real estate to itself, leaving lots of room for spacecraft to navigate through.

Bridge to learning: How the asteroid belt formed is still an unresolved question. One idea suggests that when Jupiter and Saturn migrated outward to their current positions, they flung most of the asteroids farther out in the Solar System, and the current belt is what is left over. Another hypothesis is that most of the asteroid belt formed after Jupiter and Saturn reached their current positions, and has been filled by both material being flung outwards away from the Sun, and inwards towards the Sun. Jupiter’s gravity has both held the belt in place and prevented it from forming larger objects. (In the same way, Neptune’s gravitational influence stabilizes the orbits of objects in the Kuiper Belt.)

These are due to orbital resonances with Jupiter. More information about this may be found here.

NEOs are defined as small Solar System bodies whose orbit brings them into proximity with Earth’s orbit. Although the majority of these objects are asteroids (NEAs), some are comets.

Since planetary orbits are elliptical, the semi-major axis is used (instead of the radius for a circular orbit). The semi-major axis also more accurately describes the changes in velocity and the orbital position of an object.

Consider, for example, the case of a comet whose orbit extends from beyond Pluto to inside the orbit of Mercury. The time it spends beyond Pluto is much longer than the time it spends near Mercury, due to the the slower velocity at aphelion (its farthest point from the Sun) vs. perihelion (its closest point to the Sun).

It is likely just an observational bias. There are probably lots more TNOs and comets, but it is harder to detect them at such far distances. Another factor is the influence of Jupiter’s gravitational field, which creates a stable reservoir for asteroids.

There are two main groups of comets: long period comets and short period comets (sometimes referred to as Jupiter family comets). The short period comets are as a group less eccentric and inclined than long period comets because they originated from the Kuiper Belt. The long period comets have orbits that are more eccentric because they originated from far distances in the Oort Cloud. They also have a higher range of inclinations, since they originated from a cloud (spherical) distribution instead of from a disk (Kuiper Belt).

The objects in the main asteroid belt can’t form a planet because there isn’t a high enough density for objects to collide and stick together. Even when collisions between asteroids do occur, if their mutual approach speed is too slow, they won’t stick together, and if it’s too fast, they may explode into more fragments, since many asteroids are just “rubble piles” of loosely consolidated materials.

Students may reason that since the Sun's gravity causes an increase in the density of objects nearer the Sun, there should be a lot more asteroids closer to the Sun (like NEOs) instead of in the main reservoir of asteroids between Mars and Jupiter.

There are fewer NEOs compared to MBAs because the “lifetime” of a typical NEO is only a few million years. NEOs orbit in the inner Solar System, where the potential for gravitational interaction with one of the inner planets or the Sun causes their orbits to become unstable. They eventually will either impact a planet or the Sun, or be flung farther out into the Solar System. In fact, there would be few NEOs today if they were not replenished by new arrivals from the main asteroid belt.

Also, NEOs are harder to find as many of them are very small. Another factor is that some NEOs spend most of their time closer to the Sun than Earth, so you would have to look into the Sun’s glare to find them.