Hazardous Asteroids Teacher Guide
Introduction
There are thousands of Solar System objects classified as potentially hazardous asteroids (PHAs), which could hit Earth at some time in the future. Scientists estimate that there are thousands more PHAs yet to be discovered. Rubin Observatory is exceptionally good at discovering faint nearEarth asteroids because of its ability to frequently scan large areas of the sky and to image very dim objects. Over a ten year period, Rubin Observatory is expected to detect more than 80% of all potentially hazardous objects thought to exist.
Students analyze nearEarth asteroids, newly discovered by the Rubin Observatory, to evaluate a specific asteroid’s potential threat to Earth. They come to understand how uncertainty in measurements can cause the perceived threat level of an asteroid to change with time. Students learn how to calculate the size of an asteroid and evaluate the amount of potential damage an impact would cause.
Learning Outcomes
 Students analyze orbits of nearEarth asteroids recently discovered by Rubin Observatory to estimate the likelihood of a serious threat to Earth.
 Students develop an appreciation for how uncertainty in observations of moving Solar System objects affects the predictions of their orbits.
 Students can explain the factors that affect the gravitational interactions between two Solar System objects, and how such interactions can alter the orbits of small Solar System objects.
 Students evaluate how the velocity and mass of an asteroid determines the amount of potential damage if it impacts Earth.
 Students come to understand that Earth impacts are rare events.
Prerequisite Concepts
 Students should be familiar with how to calculate the kinetic energy of an object.
 Students should know the difference between common Solar System bodies: asteroids, meteoroids and comets.
 Students should be familiar with the brightness measurement of magnitude and its scale.
 Students should have been introduced to Newton’s Laws of Motion and gravity.
Where This Fits In Your Teaching
 Solar System
 Earth
 planetary geology
 asteroids
 gravity
 Newton's laws of motion
 orbits
 kinetic energy
 nearEarth objects (NEOs)
 conservation of energy
 asteroid impact
 climate change
 natural hazards
NGSS Storylines
 What is the difference between a near Earth object and a potentially hazardous asteroid?
 Why is it important to continuously monitor known asteroids?
 Can we predict when an asteroid is likely to impact Earth?
 Upon Earth impact, what other forms of energy result from conversion of the kinetic energy of the asteroid?
 What can be done to mitigate the threat of an asteroid impact?
 What changes could an asteroid impact bring about in climate and habitability?
 How could an asteroid impact change the course of human history?
Suggested investigation which could come BEFORE this one:
See Related Rubin Observatory Investigations for more details.
Investigation Timing
Online component: 4080 minutes
Standards
Threedimensional lesson summary for astronomy/physics classes
Students use mathematical and computational representations of the physical and orbital properties of asteroids to reason how gravitational interactions, kinetic energy, and changes to asteroid orbits allow one to determine whether an asteroid will be potentially hazardous for Earth, and the overall damage it may cause.
Building towards:
HSESS14 Use mathematical or computational representations to predict the motion of orbiting objects in the solar system.
Science and Engineering PracticeUsing Mathematics and Computational Thinking 
Use mathematical, computational, and/or algorithmic representations of phenomena to describe and/or support claims and/or explanations. 
Disciplinary Core IdeaHSESS1.B: Earth and the Solar System 
Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun. Orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system. 
Related DCIsHSPS2.B: Types of Interactions

Forces at a distance are explained by gravitational fields permeating space that can transfer energy through space. 
Related DCIsHSPS3.A: Definitions of Energy 
Energy is continually transferred from one object to another and between its various possible forms. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. 
Crosscutting ConceptScale, Proportion, and Quantity 
Students use algebraic thinking to examine scientific data and predict the effect of a change in one variable on another. 
Threedimensional lesson summary for geoscience classes
Students analyze data on the physical and orbital properties of an asteroid to predict whether the asteroid is likely to strike Earth. They calculate the incoming asteroid’s kinetic energy and consider what will happen when kinetic energy converts to other forms of energy on impact. Students then construct an explanation based on evidence of the potential damage and harm to life if the asteroid were to impact Earth.
Building towards:
HSESS31 Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity.
MSESS32 Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their effects.
Science and Engineering PracticeConstructing Explanations and Designing Solutions (HS) 
Construct and revise an explanation based on valid and reliable evidence obtained from a variety of sources (including students’ own investigations, models, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future. 
Science and Engineering PracticeAnalyzing and Interpreting Data (MS) 

Disciplinary Core Idea 

Crosscutting ConceptCause and Effect 

Crosscutting ConceptEnergy and Matter 

Connections to EngineeringInfluence of Science, Engineering, and Technology on Society and the Natural World 
HS: Modern civilization depends on major technological systems. 
Connections to Nature of ScienceScientific Knowledge Assumes an Order and Consistency in Natural Systems 

Science Literacy and Critical Thinking Skills
 Developing and using models
 Analyzing and interpreting data
 Using mathematical and computational thinking
Background
As of February 1, 2020, almost 858,000 small Solar System objects have been discovered, of which only 2044 are classified as potentially hazardous. An estimated 4700 potentially hazardous asteroids (PHAs) are thought to exist. By the end of this investigation, students should understand that while potentially destructive Earth impacts are rare, they do occur, so we need to continue to search for and monitor asteroids.
Potentially Hazardous Asteroids (PHAs) are a subclass of near Earth objects (NEOs). NEOs are asteroids and comets with perihelion distances less than 1.3 au. PHAs 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 U.S Congress Public Law No: 109155 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.
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.
Figure 1: The red trace on the above diagram shows the relative numbers of estimated NEAs by size. The blue trace shows our progress in discovering asteroids of certain sizes. Source: NASA Planetary Defense Coordination Office
In 1908, an object approximately 50 meters in size exploded over Tunguska, Russia with the equivalent of 510 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, it could cause millions of casualties (Figure 2). 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: Equivalent area of destruction for a Tunguskasized asteroid over New York City. Background map imagery from Mapbox; Damage pattern from Boyarkina, A. P., D. V. Demin, I. T. Zotkin, and W. G. Fast. 1964. “Estimation of the blast wave of the Tunguska meteorite from the forest destruction.” Meteoritika 24:112128 (in Russian)
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.
So should students stay awake at night, wondering if they are about to be struck by a killer space rock? No. Potentially Hazardous Asteroids are a very small fraction of the number of asteroids (see graphic below). Statistically, even within the PHA group, impacts are very rare.
Figure 3: Relative numbers of asteroids by designation.
More information may be found on these pages:
The Center for Near Earth Objects Studies
Twenty Years of Tracking NearEarth Objects video
Openstax Astronomy textbook: Potentially Hazardous Asteroids
Links to Videos
These resources are from a teacher workshop on this investigation.
Video: Rob Jedicke, "Killer Asteroids"
Speaker slides
Teacher Notes
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 Earthasteroid distance, its angle of illumination, and, in some cases, its rotation.
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 icecovered 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.
Asteroid mass is also an estimated quantity. Since the composition of most asteroids are 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 of the asteroid equals the mass divided by the volume:
\(\rho = {m \over V}\)
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 below:\(V = {4 \over 3}\pi r^3\)
Where V is the volume and r is the radius of the asteroid.
Combining the two equations above and solving for mass (m), we get:
\(m = 𝜌{4 \over 3}\pi r^3\)
In summary, much of the computation to derive an asteroid’s size, volume and mass are 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, 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 the Earth. Asteroids, the most common type of impactor, strike the 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 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.
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 a water impact. We assume one type of standard hard rock surface for the impact calculator.
Water impacts may produce less damage if in midocean, but the devastating effects of a tsunami along shorelines can be as bad as those experienced with a hard rock impact. Our impact calculator cannot predict the damage of an ocean impact, since many factors are involved.
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 2016 HO3 (a quasistable Earth satellite) are examples.
Figure 4. Locations of the Trojan asteroids along Jupiter’s orbit. Image credit NASA/JPL.
Common Student Ideas

Asteroids never impact Earth (or) asteroids no longer impact Earth.
Bridge to learning: Explore the interactive Earth impact database and map to see the geographic and age distribution of known impact craters. Follow up with discussion: Are all impact craters old? What is the oldest and youngest crater you found?
An impact from a 100meter (328foot) asteroid, the smallest believed capable of causing regional devastation, is estimated to occur about once every 1000 years on average.
An impact from a body the size of the Chelyabinsk meteorite of 2013 (17 meter diameter) is expected to occur once per century.
Common Student Questions

How do we know if we are imaging the same asteroid on two different nights if it has moved?
We detect asteroids because of their motion. By taking measurements of an asteroid’s motion, we can calculate (for the short term) its estimated speed and direction in order to make a fairly reliable prediction of where to see it next, as long as there is a quick follow up observation. We can also confirm whether its magnitude is consistent with the first set of observations.

What’s the difference between an asteroid and a meteoroid?
Both asteroids and meteoroids are space rocks that orbit the Sun. They could be primordial material left over from the formation of the Solar System, or remnants from comets. Meteoroids can also be ejected from the surface of other planets during large asteroid impacts. Some Earth meteorites have been identified as originating from the Moon or Mars.
The general distinction is size: Objects less than one meter in diameter are considered meteoroids. The smallest asteroid ever studied was 2015 TC25, which was observed when it made a close flyby of Earth in October 2015. Its diameter was two meters.

What are the most dangerous asteroids known at this time?
The Sentry Earth Impact Monitoring program maintains an impact risk table of the most interesting potential future impact threats based on current observations. Note that based on this analysis, the asteroid with the highest impact probability has only a 0.012% chance of Earth impact.

If we found an asteroid on a collision course with Earth, what could we do about it?
There isn’t a single answer to this question, because many variables must be taken into account: the time until impact, the orbit and speed of the asteroid, and the size and composition of the asteroid. Most techniques fall into two categories:
 Delaying the asteroid’s arrival time or deflecting its orbit, or
 Fragmenting the asteroid into many small pieces that would not cause significant damage if they impacted Earth
It is critically important that asteroids are detected as early as possible, because there is no way to deflect or destroy an asteroid that’s detected hours before impact. No known weapon system could intercept the asteroid because of the velocity at which it travels–an average of 12 miles per second.
More information may be found at the NASA Planetary Defense Coordination Office.

How do we know the shape of an asteroid? Are asteroids spherical?
Almost all asteroids have irregular shapes. Their masses are so low that gravitational forces have not been able to pull them into spherical shapes like the planets.
Only a very small fraction of known asteroids have been studied in enough detail to determine their shapes. One way to determine an asteroid’s shape is by mapping its surface with radar. Another way is to use two or more telescopes to observe the asteroid simultaneously, a technique called interferometry. Some space probes have flown to asteroids and imaged them. Finally, a rough idea of an asteroid shape may be possible to determine from analyzing light curves of its rotation. But all of these techniques can be used to study only the largest asteroids. Since shapes for most asteroids are unknown, a sphere is used as a general model for determining the volume of an asteroid. The derived sizes are not actual measurements but estimates, since they are computed with some assumed values.

Why does the probability of impact for a newlydiscovered asteroid often increase with additional observations before decreasing?
The initial set of possible orbits have a large range of positions due to uncertainties. As additional observations are made, some of the possible orbits are eliminated (many of which do not pose a risk of Earth impact). But if the small set of possible orbits that are potential Earth impactors are not ruled out, the probability of impact will increase.
For more information about this idea, check our Phil Plait’s blog post on this topic.

How do scientists make an estimate of the total number of asteroids when all of them have not yet been discovered?
The estimate is based on a fragmentation model. Think about this: If you struck a rock with a hammer, it would break into pieces. Some of the pieces would be larger, but the number of smaller pieces would be greater by a certain predictable amount. Applying this to asteroids, we have found with a high degree of certainty all of the larger asteroids. We can apply our model to predict the total number of smaller sizes of asteroids that are likely to be there.
Differentiation
Students use an interactive tool—the orbit visualizer—to examine orbits of Solar System objects in three dimensions in order to evaluate the possible impact threat of an asteroid to Earth. They engage in the process of determining the orbit of a newlydiscovered asteroid by predicting when and where to make the next observation of it, then get feedback on their choices. After reflection, they have the opportunity to modify their observing plan.
At multiple places in the investigation, students must incorporate crosscurricular connections to consider and explain how their results would change if they altered one variable.
The impact visualizer provides an alternate modality to determine the scale of the damage for an asteroid that impacts Earth.
The “Reflect and Discuss” questions encourage students to consider the complex ethical and subjective factors associated with the nature of science and its relationship to society.
The last section, “Putting it all Together”, can be assigned as an individual or group project. The option of a group project allows students to choose specific tasks and work collaboratively.
Ideas for Further Study
Planetary scientists have determined that an asteroid may be considered potentially hazardous if it comes within 0.05 au of Earth. No such number exists for other planets, because the absence of life means there is no “hazard.” But, in the future, humans may inhabit Mars. If you were to calculate a minimum hazard distance for Mars, would it be more or less than 0.05 au? Explain what factors you considered in making your decision.
NEAs are divided into four groups (Atira, Aten, Apollo and Amor). Do more PHAs seem to originate from a certain class of NEOs, such as Amors, Apollos, etc.? What distribution of PHAs belong to each of the four classes of NEOs? Can you develop explanations for any patterns you detect? More information about the four classes of NEOs may be found here.