Impactors and Their Possible Explosive Effects on the Earth: Part 1
August 2006 :
SPEED AND DIRECTION (I.E., VELOCITY)
Human civilization on Earth and possibly the Earth itself will be destroyed by fire next time [1] or so our scientists, theologians, and fiction writers would have us believe. This may occur in several ways many of which may well be related. I will, however, discuss only the possibilities surrounding an impact from space and its direct results.So, how do scientists, fiction writers, and movies moguls come up with the numbers surrounding their chosen impact disaster? The numbers we see and hear fall into several categories: The inherent speed of the impactor, the innate speed of the earth, and the speed imbued by the mutual attraction between the Earth and the impactor. The summation of these various speeds along the line of motion of the impactor converts these speeds to an effective velocity and hence the violence of the impact. The direction effects depend on the orbital parameters of the incoming object relative to the Earth, i.e., is it prograde or retrograde (i.e., moving counterclockwise or clockwise, respectively) and the angle at which the object is going to enter our atmosphere and possibly hit the Earth’s surface, among others. Besides the above speed and directional parameters of the colliding bodies the destructiveness of impacts also depends on the composition of the impactor (i.e., is it made of ices, stone, metal, or some combination thereof). As you can see this is a pretty complex subject and besides the length of the articles is one of the reasons I choose to present this subject in three articles instead of one.
I will keep the arithmetic as simple as possible, but some will be required. The first of these math problems will be to determine how fast the Earth is going around the sun in its orbit. The Earth’s orbit is nearly a circle around the Sun with its center at the center of the Sun some 149,500,000 kilometers [2] away (about 92,900,000 million miles or one astronomical unit). So given the fact that the Earth’s revolution about the Sun takes about 365.26 days we may readily compute its speed in this assumed nearly circular orbit as: The Earth’s orbital circumference divided by the hours in a year or 2πr/(365.26x24) or in kilometers (2x3.14159x149,500,000)/(365.26x24) or roughly 107,154 km/hr (66,582 mph). In other words the Earth is moving at one hefty speed and hitting any large object, even one standing dead still would make a big splash.
However, the objects that we may hit (or that may hit us) are not standing dead still. These objects are in fact moving at quite some speed of their own relative to the Earth. They are usually headed for or returning from a pass around the Sun (perihelion) where the impactor’s speed may be as much as 600 km/sec if it approaches the Sun closely enough. In addition to the speed of the Earth and the gravitationally generated speed acquired from the Sun an object falling from sufficiently far away, starting at zero speed, on a collision course with an object such as the Earth or the Sun will acquire the escape velocity of the body it is going to hit. The Earth’s escape velocity from its surface is 11.2 km/ sec [3] (6.955 mps) and the Sun’s escape velocity from its surface is 618 km/sec [4] (384.09 mps). So, as the impactor falls past Earth’s orbit it has acquired a respectable percentage of the Sun’s escape velocity, roughly 42 km/sec, because it is falling toward the sun (or is returning from a near encounter with the Sun) [4]. If the object falls directly into the Earth causing all these speeds to be additive, which isn’t very likely as we shall see in a few paragraphs, it would hit the Earth with a relative speed (all values are rounded off) at the surface of about 298,000 km/hr [107,000 km/hr (earth’s orbital speed) + 40,000 km/hr (Earth’s gravitationally imparted speed) + 151,000 km/hr (the Sun’s gravitationally imparted speed)]. So this thing could have an effective velocity of close to 300,000 km/hr (186,000 mph) when it hits Earth’s surface if everything is absolutely right, or wrong, depending on your perspective.
But things are not always as they seem. To achieve the above maximum speed the object must be moving in a retrograde motion (i.e., clockwise with respect to the Sun). Note that all the Sun’s planets including Earth and the asteroid belt minor planets move in a prograde direction (i.e., counterclockwise around the Sun when viewed from above the Sun’s North pole). In addition our impactor must be moving in the ecliptic (i.e., dead flat with respect to the Earth’s orbit) in order to gain the maximum impact speed. Lastly, the impactor’s trajectory must ensure full effect of the Earth’s gravitational attraction.
Almost all these factors will be reduced from their maximum potential due exclusively to the improbability of all of them occurring at the same time. In other words it’s possible to maximize the velocity but it isn’t likely. For example, few of the short period Earth crossers move in retrograde fashion [5, page 96], Halley’s Comet being a famous exception [6, page 186]. If the object is short period (i.e., with an orbital period of less than 200 years) it would probably hit the earth at some other angle than head-on. If the object is prograde then it would have to play catch-up and a very large percentage of its maximum possible impact speed would be lost.
Long period Earth orbit crossers, however, generally come from outside the orbit of the gas giants and could arrive from any direction [5, pages 198-199], even straight down on the North or South Pole. But, before I move on to calculation of the impact results themselves I need to talk about one more factor, the composition of the impacting body and its contribution to the object’s kinetic energy. The discussion of composition and kinetic energy is the subject of next month’s article.
