# Background and Notes

## Background

Potentially Hazardous Asteroids are a subclass of near Earth objects (NEOs). NEOs are asteroids and comets with perihelion distances less than 1.3 au. The vast majority of NEOs are asteroids, so this group is often referred to as Near-Earth Asteroids (NEAs).

NEAs are divided into four groups (Atira, Aten, Apollo and Amor) according to their perihelion distance (q), aphelion distance (Q), and their semi-major axis (a). Each of these measurements are illustrated on Figure 1 below:

Figure 1. Measurements of an ellipse. Credit Rubin Observatory.

More background about the four classes may be found here.

Potentially Hazardous Asteroids (PHAs) are defined based on parameters that measure the asteroid's potential to make a threateningly close approach to Earth. To be classified as a PHA, the asteroid must have an Earth Minimum Orbit Intersection Distance (MOID) of 0.05 au or less, and a minimum diameter of 140 meters. Objects of this size or larger are capable of causing serious damage if they strike Earth.

This is not to say that an Earth impact from an object less than 140 meters in diameter is inconsequential. The graphic below illustrates the relative amount of damage caused as a function of asteroid size. Even an asteroid 25 meters in diameter is capable of devastating a city.

In 1908, an object approximately 50 meters in size exploded over Tunguska, Russia with the equivalent of 5-10 megatons of TNT (hundreds of times greater than the first atomic bombs), leveling over 2,000 square kilometers of forest. This is also the approximate diameter of the impactor that made Meteor Crater in Arizona. If a similar event occurred over a major metropolitan area today, it could cause millions of casualties. NASA estimates there are over 300,000 objects larger than 40 meters that could pose an impact hazard and would be very challenging to detect more than a few days in advance.

Figure 2. NEO Discovery statistics as of May, 2023. Credit NASA-JPL Center for Near-Earth Object Studies.

Objects smaller than 25 meters vaporize in the atmosphere and fragment into small pieces that drift slowly down to Earth’s surface without making any crater. On a daily basis, about one hundred tons of interplanetary material accumulates on Earth’s surface.

The U.S Congress Public Law No: 109-155 of 2005 directed that NASA should find, track, and characterize at least 90 percent of the predicted number of NEOs that are 140 meters and larger in size by 2020. That goal was not realized. By 2020, less than half of the estimated 25,000 NEOs that are 140 meters and larger in size were detected.

Rubin Observatory’s efforts over the first ten years of operation combined with other initiatives should raise the detection of PHAs to 80% of the predicted number by 2032.

So should you stay awake at night, wondering if you are about to be struck by a killer space rock? No. Potentially Hazardous Asteroids are a very small fraction of the number of asteroids. Statistically, even within the PHA group, Earth impacts are very rare.

More information may be found on these pages:

The Center for Near Earth Objects Studies

NASA Planetary Defense Coordination Office - NEOs

OpenStax Astronomy textbook links:

## Teacher Notes

- Our investigations are designed so that students cannot proceed to the next page without answering each question. If you would like to quickly preview the entire investigation, you can use “educator mode” on the Start page. Enter the passphrase:
**3ducatorMod3**to activate it. - Absolute magnitude (H) used in this investigation has a different definition than the absolute magnitude (M) of stars. Asteroids generate no light of their own, instead they reflect sunlight. The brightness of the reflected sunlight from an asteroid varies as a function of the Earth-asteroid distance. An asteroid’s absolute magnitude has been arbitrarily defined as
*the visual magnitude an observer would record if the asteroid were placed 1 Astronomical Unit (au) away from the observer and 1 au from the Sun,**and**viewed at an angle that would place the object in opposition and on the ecliptic.*(Note that this geometry is physically impossible.) - The albedo of an object is also needed in order to calculate its size from absolute magnitude. A certain brightness might be due to a small object that is highly reflective or a large object that is much less reflective. Albedo also varies with the amount of surface roughness. An ice-covered surface may be smoother and reflect light more efficiently. The albedo for most asteroids cannot be directly measured. Since the majority of small Solar System objects are silicates, we assume an approximate albedo of 0.15 to use with H when calculating the size of objects on plots.
- Asteroid mass is also an estimated quantity. Since the composition of most asteroids is unknown, we assume a rocky asteroid (the most common type) with a density of ~2500 kg/m3. Mass can be computed from the asteroid density if its volume is known:

- The density (𝜌) of the asteroid equals the mass (m) divided by the volume (V): 𝜌 = m/V

- Since we do not know the shape of the asteroid, we assume it is spherical in shape.The volume of this asteroid can be then be calculated by using the formula for a sphere, where V is the volume and r is the*radius*of the asteroid: V = 4/3 𝝅 r^3

- Combining the two equations above and solving for mass (m), we get: m = (4/3 𝝅 r^3)/𝜌

In summary, much of the computation to derive an asteroid’s size, volume, and mass is based on assumptions about average albedo and density. Only absolute magnitude is a direct measurement, so there is a considerable degree of uncertainty involved. - The kinetic energy of an incoming asteroid is based on an estimated mass and approach velocity, so this too is an estimate and not a directly measured quantity. The approach velocity can be approximated based on measurements of the orbital speed of both Earth and the asteroid, and the angle at which they approach each other. The minimum velocity of objects impacting the Earth is about 11,200 m/s, which is equivalent to the escape velocity of Earth. Asteroids, the most common type of impactor, strike Earth at an average velocity of 18,000 m/s. The most energetic asteroid impacts are around 25,000 m/s. If the impactor is a comet, the velocities are higher, averaging 30,000 m/s, up to a maximum of 53,000 m/s for the greatest velocity ever recorded. Another factor that affects the kinetic energy delivered to the Earth’s surface on impact is the angle at which an asteroid enters the atmosphere. In this investigation, a 45° angle is assumed for all calculations.

- Not all large asteroids that cross the orbit of a planet are potentially hazardous. Some asteroids share the orbit of a planet but are locked in stable orbital resonances so that they will never come close to the planet. The Trojan asteroids of Jupiter or asteroid 469219 Kamoʻoalewa (a quasi-stable Earth satellite) are examples.
- The amount of damage, including the estimated crater diameter and depth, varies depending on what type of surface is encountered: hard bedrock, soft sedimentary rock, or water. We assume one type of standard hard rock surface for the impact calculator. Water impacts may produce less damage if the impact is in the middle of the ocean, but the devastating effects of a tsunami along shorelines can be as great as those experienced with a hard rock impact. Our impact calculator cannot predict the damage of an ocean impact, since many factors are involved.