asteroid named Égaré(French for 'stray') was
informally studied in the Rock from the Sky puzzle.
Telescopic observations made before the summer of
2018 predicted its collision with Earth at an
orbital intersection on Thursday July 21,
2022. With a diameter of 100 meters, Égaréis eight times more
massive than the bolide
that produced the Barringer meteor
crater some 50,000 years ago. Égaré, with
a mass mA = 2.4x109 kg,
ranks alongside the meteoroid that caused the Tunguska Event
-- the largest impact in recorded history.
For general audiences, sad
to say, it is customary to describe large
quantities of energy in terms of the explosive
power of TNT.
Accordingly, the energy released that day over
Tunguska has been estimated to be 15 megatons of
TNT (15 MtnTNT),
which is 1,000 times greater than either atomic
bomb dropped in World War II. From here
on, we shall prefer Joule
as our unit of energy from the International
System of Units (SI), according to which 1
MtnTNT = 4.2x1015
1 in the Rock
from the Skypuzzle,
indicates that when Égaré
crosses Earth's orbit, it will be traveling at
V = 39.4 km/s = 39.4x103
m/s. At impact, the asteroid's kinetic
energy will be given by mA V2 /2 ≈ (2.4x109)(39.4x103)2
Depending on the angle that Égaréenters
Earth's atmosphere, much of that energy will be
dissipated in the atmosphere or exploded into
In the Rock from the Skypuzzle, we
discovered that some conventional proposals for
protecting Earth from a collision with a near-coplanar
asteroid do not work. Specifically...
Applying a vectored thrust to
delay or advance the arrival of the
asteroid at an inbound intersection --
with a tangential ∆V in
either the prograde or retrograde
direction -- will change the shape of
its orbit so that the Earth will
likewise arrive earlier or later at the
new location for the inbound
intersection, which can defeat the
continue to be used in our model here in
Deflection puzzle as an informal study
of some of the complexities that
arise in protecting our planet from threats by a
Near Earth Object (NEO) in a near-coplanar
orbit (inclination≈ 0
Worldwide endeavors for
avoiding meteor impacts can be divided into three
of potential threats from NEOs based on their
sizes and orbital parameters.
of the orbital motion of each NEO to ascertain
its likely point of impact.
of the threatening NEO's orbit to avoid
collision with Planet Earth.
puzzle emphasizes Task 3, which comprises the most
of the NEO:Égaréis postulated to be 100
meters in diameter. That is comparable to
the size of the asteroid responsible for the Tunguska Event,
which flattened 2,000 km2.
and Velocity: Assuming a density
of 5 gm/cm3,
a mass of 2.4×109
kg. At each orbital intersection
the velocity of Égaréis
estimated to be V = 39.4 km/s.
Energy: Asteroid Égaré
will have a kinetic energy of 2.0×109
at impact with planet Earth
Joules, equivalent to 444 megatons of TNT.
topics are especially pertinent to the Detection of
Near Earth Asteroids (NEAs). Finding and
cataloging NEAs has been going on since
antiquity. Worldwide efforts received a
significant boost in 1992 by governmental
Based on one discovery in the Astrogating Asteroidspuzzle,
the most important parameter for an NEA
is the inclination
of its orbit with respect to that of
Earth. Nevertheless, inclination seems
to be buried in listings and not
mentioned at all in a key description of
(Minimum Orbital Intersection Distance).
are many projects
and missions now actively participating in
the crucial Detection
business. Today, countless
astronomers, both professional and amateur, are
using advanced instruments and a growing fleet of
robotic telescopes atop remote mountaintops.
They are sharing their findings on worldwide
databases, listing and updating tens of thousands
of entries. Moreover, at this writing, a
total of 875 named entries are being tracked as Large
NEAs (> 1 km in diameter).
mission demands precision in Prediction,
but line-of-sight tracking is limited, which
necessitates placement of a transponder
in orbit around the asteroid.
for Thrust Vectoring:
As sketched below in Figure 1, the transponder
satellite will also provide up-close videos of Égaré
to gauge its features and tumbling motion.
The satellite must relay positioning adjustments
for final deployment of the Deflection
much of its orbit Égaré
is not optically visible from Earth because of
daytime sky-glow. Satellites in Earth orbit,
can track Égaré
optically; however, the demand for frequent
updates and extremes in precision must make use of
a separate transponder
to be put into position as soon as practicable --
but not necessarily landed on the surface.
Typically an asteroid like Égaré is
on its own axis normal to the orbital plane with a
period of two hours. That favors the
placement of the transponder satellite in a
synchronous polar orbit aroundÉgaré,
with its transceiver antenna pointed constantly to
The transponder satellite will have an orbital
period given by...
τS = (rS)3/2
/ (2π G mA)1/2,
satellite's period in seconds rS =
satellite's orbital radius in meters mA =
mass of asteroid Égaré= 2.4×109
G = gravitational constant
For an orbital radius rS = 373
meters, τS≈ 2
Meanwhile, at aphelion (3.0 AU), Égaré can be as far as 4.0 AU
from Earth (600×106 km), so the round-trip
delay at the speed of light (300×103 km/s) will be as long as 2×600×106 / 300×103or more than an
hour. Some solvers may enjoy designing a
protocol for 'go-round' messaging.
A change in orbital inclination of 0.1 degree
for asteroid Égaré
requires as much as 173 ×109
Joules of propulsion energy at aphelion where V
= 6.7 km/s.
Mass: To deliver Deflection
tools plus 173 ×109
Joules of energy to a rendezvous with Égaré
requires a spacecraft capable of lifting tonnes of payload to escape velocity.
Distance: The aphelion for Égaré
is located at 3.0 EU = 450 Mkm
from the sun. More than a year must be
allowed for delivery -- with gravity
assist, say, from Mars.
discovered in the Rock
from the Skypuzzle
the preferred avoidance maneuver for Égaré
calls for a vectored thrust of ∆V Normal to
the orbital plane of the asteroid, increasing its
inclination angle by ∆i.
The Right- Hand Rule is reprised here in Figure
3. A most relevant relationship applies the
law of sines...
2) = (∆V /
2) / V; thus... ∆V = 2
V sin (∆i/
∆i = specified
as increase in orbital inclination
required change in the asteroid's velocity V =
orbital velocity of Égaré at
the instant the thrust is applied to
In Figure 1 above, we see that the orbital
intersections are about 0.75 AU (112.4 Mkm) from the major axis
of the Égaré
orbit. The Deflection of
the asteroid when it passes within or beyond
Earth's orbit will be 0.75 sin ∆i. Thus,
if we specify that ∆i
= 1/10 degree, Égaré will
miss Earth by 0.75 sin (1/10) = 0.0013 AU =
262,000 km (163,000 mi) ≈ 120
Earth diameters. Hooray for
The expression derived
above, ∆V = 2 V sin
2), shows that for a specified increase in
orbital inclination angle ∆i, the
directly proportional to the asteroid's
tangential velocity V. At
perihelion V = 80.9 km/s, and at
aphelion V = 6.7 km/s. That
gives us up to a 12-to-1 advantage in producing
∆V if we apply the vectored
thrust at aphelion. For ∆i = 1/10
degree, ∆V = 2×6.7 sin (1/20) =
0.0117 km/s = 11.7 m/s.
change in the velocity of Égaré with
its mass of 2.4×109 kg by ∆V
= 11.7 m/s means a change in kinetic energy of
/2 = 164×109 Joules. Let's do
the most challenging question is left to solvers
of the Orbital
What is your proposal for how the
worldwide community of nations might
deploy requisite resources to deflect
the orbit of asteroid Égaré thereby avoiding its collision
with Planet Earth on Thursday, July 21,
clicking to the Solution page,
you are invited to review the concepts and issues
for avoiding collisions with asteroids on the
worldwide web, starting at this portal.
Any avoidance strategy -- whether by destruction
or deflection -- calls for the delivery by
spacecraft of immense amounts of energy to Égaré.
With no atmosphere surrounding Égaré, the
use of chemical energy would require us to include
a large amount of oxidizer in our Deflection
tool-kit as well as fuel.
Explosives like TNT
come to mind, but -- hey, to deliver 164×109
Joules164 × 109
Joules for a Deflection
strategy, our spacecraft needs to include 390
kilotons of TNT in its payload!
a thermonuclear explosion for Deflection thus
may be the most 'spaceworthy'
choice, inasmuch as
the energy of 164×109 Joules can be
transported in a fission/fusion device weighing
390 kilograms -- that's
one-thousandth of 390 kilotons of
in space -- chemical or nuclear -- are rather
tame. Explosions in space produce heat energy
not mechanical energy. It is mechanical
energy that we really need for Deflection.
Truth be known:
An explosive weapon on Earth makes full
use of surrounding atmospheric mass
Detonation and immense heat cause sudden
over-pressures and winds capable of
destroying structures, while high
temperatures ignite destructive
fires. Indeed, the temperature can
get so high that air itself is
set ablaze (nitrogen + oxygen → NOx) in
a fireball. And a mushroom cloud.
In the vacuum
of space, mechanical energy (some forcef
applied through through
some distancex) is hard to come
by. Think rocketry -- for which one must
expel a huge massm of hot
gases at high speed from a 'nozzle' to produce a
reactive forcef, which we
So, does that mean we
must haul some huge massm
along with immense amounts of energy from Earth
all the way to Égaré in our Deflection tool-kit?
Our objective really
comes down to this: Figure out a way to use part
of the asteroid's own mass to produce the
requisite ∆V Normal of 11.7 m/s.
That won't be easy.
In Figure 4,
we see that a simple surface detonation
will release most of its energy as line-of-sight
radiation directly into space. A small
fraction of the explosive energy may find some
usefulness in heating up a spot on the surface of
Égaré. The sudden high
temperature -- thousands of degrees -- will
dispatch shock waves and heat flows into the
asteroid, blasting and ablating deeper and deeper,
melting metal and fracturing rock. But as
for vectored thrust -- not so much.
The thermal energy will
be 'processed' by physical phenomena acting on
the materials encountered along the way:
conduction & expansion, melting &
vaporization, fracturing & ejection --
something like an inside-out volcano.
on the mass and velocity
of the remedial ejecta, an appropriately
vectored orbital Deflection
may actually be
achieved. If not, mankind will have
succeeded merely in scarring the
surface of the asteroid with a glassy crater,
while temporarily warming the
interior of a near-earth object that is still
predicted to impact Earth on
Thursday, July 21, 2022.