Potentially HazardousPotentially HazardousAsteroidsAsteroidsPhilip W. SharpPhilip W. Sharp

Department of MathematicsDepartment of Mathematics

University of AucklandUniversity of Auckland

What is a PHA?What is a PHA?

• Size not used. Instead, use absolute

magnitude, must be at least 22.0.

• The body comes within 0.05 AU of Earth.

1142

Chicxulub ImpactChicxulub Impact

• “Chic-shoo-loob”

• 65 Mya

• Crater is about 180 km in dia, buried beneath the Yucatan Peninsula, Mexico.

• Impactor is thought to have been 10 km across, weighed 3 trillion tonnes, hit at 20 kps, and had the energy equivalent to 60 -100 Tt.

QuizQuiz

1. What were the possible physical effects of the Chicxulub impact?

2. What caused the Tunguska Event in 1908?

3. How many different ways can “Chicxulub” be pronounced?

EffectsEffects

• Earthquakes (11 – 12.4)• Volcanic eruptions• Tsunamis: primary (1km) and secondary• White-hot debris fell back to earth

a) wild firesb) smoke mixed with rain clouds, created acid rain

• Dust high in the atmosphere

TunguskaTunguska

Thought to have been caused byan air burst of a large meteoroidor comet at an altitude of 5-10km.

Impactor is thought to have been afew tens of metres across.

10-15 Mt.

Flattened 80M trees over 2,150square kms.

Photograph taken by 1927 expedition.

In December, 2002, a posting to the dinosaur@usc.edu forum listed 13 possible pronunciations of the word Chicxulub:

SHICK-shah-lube, Chicks-ooh-lub, Cheek-hoo-loob, Chick-shoe-lube, chik-shooloob, tchik-ksooloob, CHICK-shoo-loob, Cheekshooloob, Chich-a-lube, Chicks-a-lub Chicks-a-loob, CHAI-shoo-loob, Chikjulub

Meteor CraterMeteor Crater

50 thousand years ago

Impactor

• 50 m in diameter• 300 thousand tonnes• 12.8 kps

Crater

• 1200 m in diameter• 170 m deep• Rim 45 m high

Tzar BombaTzar Bomba

• 30 October, 1961• Detonated about 4km above the surface• Design yield was 100 Mt• Yield reduced to 50 Mt to stop fall out reaching mainland Russia. 50 Mt is about ¼ of the yield of the 1883 Krakatoa eruption• 210 petaJ in 39 ns = 5.4 yottawatts (1.4% of the Sun’s power)

Mathematical ModellingMathematical Modelling

1. Real Solar System

2. Model of the real Solar System

3. Input to the model

4. Solution of the model for the given input

Modelling the orbitModelling the orbit

1. Detection

Several programs have been set up

* Spacewatch – U of Arizona

* LINEAR – MIT (USAF, NASA)

* Spaceguard Foundation - private

2. Initial orbit (Keplerian)

Assume the body moves in an elliptical

orbit about the Sun, ignore other bodies.

Angular information only• Celebrated method of Gauss• Requires three observations

Distance and velocity information as well• Distance obtained using radar• Velocity using Doppler• Require just two observations

Observational uncertainty

• Can lead to large errors in the initial orbit

• Several techniques to reduce the uncertainty

3. Improved orbit

Use least squares and the best model for

the orbital motion of the large bodies in the

Solar System.

Components of the best model

1. The mass of the asteroids.

2. General relativity.

3. Earth-Moon interactions:

• the oblateness of Earth and the Moon;

• tides raised on Earth by the Moon and vice versa;

• internal structure of Earth.

Yarkovsky Effect

4. Estimating the probability of hitting Earth

• Generate the initial r and v of 1M artificial small bodies. The r and v are chosen from Gaussian distributions (law of errors) centred on the best values for the real body.

• Integrate the motion of the bodies for a few hundred years.

ApophisApophis

• Discovered in 2004.• Exaggerated headlines.• No chance of hitting April 13, 2029.• 1 in 250,000 chance of hitting April 13,

2036.• 3 in one million chance of hitting in 2068.• About 320 metres in diameter.• 510 Mt.