Trying to Get Hit: The Physics of Deep Impact

All Solar System objects undergo collisions. This fundamental fact, recognized only in this century, now underlies much of our knowledge of planetary geology.

It's popular, too, as a disaster scenario for movies and other media. Hollywood actioneers taking shots at Earth have included the 1998 films Deep Impact and Armageddon. A couple of generations earlier, When Worlds Collide (1951) featured a runaway planet on a collision course with Earth. Books include the recent novel Lucifer's Hammer, wherein Earth is pounded by comets.

Of course, the theme goes way back in the science fiction genre. Consider Jules Verne's Off On A Comet, written last century!

When I was child, I read these stories and also factual tales of such things as astroblemes by authors like Dietz. As a eight-year-old, my favorite birthday gift was a tektite. A two-inch glassy-black rock from Indochina, it looked a lot like the obsidian I already knew from volcanic regions around my childhood home in New Mexico. Later delvings went deeper and earlier: Ernst Opik's pioneering thoughts on asteroid and comet collisions in the Solar System were particularly intriguing.

The modern scientific popularizers of collisions as a major force in the evolution of planets built on these earlier ideas. It's amazing to think that the famous meteor crater in Arizona was believed to be of volcanic origin within living memory. Shoemaker and others of this group helped prove that Barringer Crater and other similar craters on the earth had an impact origin.

Even though my life and the exclusive culture of professional astronomy have taken divergent paths, I'm still fascinated with the idea of planets as targets. In July of 1994, I watched as craters were punched in Jupiter's atmosphere by Comet Shoemaker-Levy 9. The impact sites of the comet fragments K, H, Q, etc. were easily visible with a 10cm reflector telescope from my backyard in Wichita. They looked like black holes. I followed them as the impacts were still occurring, and then through July 1995. At that time, the Jovian latitudes around 45 degrees south still looked dusky.

Earlier, the 1968 close approach to the earth by 1566 Icarus and the 1973 fireball over the western U.S. were things I remember that got me thinking about impact parameters and related topics.

When I read about the meteorite grazes on the pampas of Argentina, I wanted to know the conditions leading to these unusual collisions.
 
 

The general circumstance of a comet or other object approaching the earth from a great distance is described as a hyperbolic encounter between the two. 

The law of gravitation says two objects will move about each other in four types of curves: hyperbola, parabola, ellipse and circle--the famous conic sections of astrodynamics. You can think of it terms of speed as well as shape. Something in an open-curved hyperbolic orbit will approach the earth with some speed, no matter how far away it is. Also moving on an open curve, a parabolic projectile will start out at zero speed at infinity, then speed up as it closes with the earth. An elliptically orbiting satellite will always move alternately towards and away from the earth in a cigar-shaped closed path, the speed alternately increasing and decreasing, too. And a circularly orbiting satellite is always at the same distance from the earth, always moving at the same speed.

Our comet's path will be a hyperbola whose size and shape will depend on two things. The first one is how fast the comet's moving when it enters the earth's sphere of influence. This region is a ball about a million kilometers in radius and it is roughly where the earth's gravitational effects or influence substantially equal or exceed the sun's influence on an object. The earth's gravity is first "felt" by our comet at this distance, and its path is deflected or bent towards the earth.

The second item is the miss distance: how close the comet would have come to the earth if the earth had no effect on the comet's path. The technical name for this distance is actually very appropriate: impact parameter.

Greater speed means less time in the stronger part of earth's gravitational field, and less deflection. Same with distance--a bigger impact parameter means less effect from earth's gravity.

Putting it all together, at a given speed, going too close will mean that even though the miss distance is larger than an earth radius, the deflection will be great enough that there will be a collision. The effective target size is bigger than the planet. It's as if the earth is trying to get hit because gravity focuses comets and other solar system objects onto a planet.

A grazing collision like the one that happened in prehistoric Argentina occurs at the perigee of the hyperbolic orbit, tangent to the earth's surface and the orbit. Inside the effective target radius, impacts will occur along other parts of the incoming orbit, and impact at angles above the horizontal. The blanketing effect of a beam of particles filling the entire collision cross-section is greatest for those at and just inside the effective target radius and for low approach speeds. The turning angle (deflection) is equal to the blanket angle for an impact and can be as great as 180 degrees. You can be on the far side of the earth from the comet's approach and still get hit!

Where will it hit? That depends on the orientation of the orbit in the solar system relative to the earth, as does the radiant--the apparent direction of the comet's approach. Timing is everything and the position of the comet in its orbit will determine the longitude of impact. If broken up and stung out along the orbit, then the string of pearls will hit repeatedly in a pattern like that seen for Shoemaker-Levy 9's Jupiter impacts.
 

So, for energy input, volcanoes as catastrophes dominate short time spans, perhaps up to 100 million years. Over the one billion-year span, impacts become the most energetic explosive mechanism affecting the earth. Sixty-five million years ago, the Chixulub collision was definitely a bad day for every life form on the earth.

The long-term danger warrants attention by human beings, but can hardly be used to justify a major program at the present time to protect us from earth impacts. It would be more effective zoning islands with active volcanoes off limits.