How to deal with impacting bodies
Joachim Köppen Kiel/Strasbourg/Illkirch February 2002
Contents
The DecisionMap Applet gives rough estimates for the warning time and the energy necessary to make a deflection of an approaching body. It computes them in a straight-line approximation, neglecting the effects of the gravitational fields of the Sun and the Earth, but taking into account that the Earth moves with respect to the Sun with about 30 km/s.
When you start up the applet, you hit the Click to Start button, and you see something like the following screen:
The value of the approach angle is 180 degrees, which means that
the asteroid is on a head-on collision course with Earth.
To change this angle, click the text field, enter a new value, and
hit the Enter or
To show the lines of constant impact energy, one clicks on the appropriate large button, which will then change its colour, and then the "Clear & Compute" button. One gets from left to right 1 kT, 1 MT (green), 1 GT, and 1000 GT = 1 TT (Tera-tons).
Adding the lines of constant detection time (at a visual brightness of 20 magnitudes). Note that this calculation takes more computing time. From left to right there are shown: 1 day, 1 week, 1 month, 0.5 years (red), 1 year, and 10 years
Switch off the previous lines by clicking the buttons, and clicking the bottom button. This draws the curves of constant energy necessary for a deflection by 1 lunar orbit radius if we send an interceptor 0.5 years before impact and at a speed of 4 km/s. The curves from left to right refer to 100 kT, 1 MT (blue), 10 MT, 100 MT, and 1GT. This is the change of kinetic energy necessary for the deflection, but the actual energy by impact or by a nuclear explosion must be higher, corresponding to a certain efficiency factor.
To get the next screen, we have simply clicked with the mouse on the black dot, representing probably the asteroid which caused the crater in Arizona, which gives us in the lower left the impact energy, detection time. Then we clicked the button "QuickLaunch" which means that we launch the interceptor right at detection time, and we clicked the Clear & Compute button to redraw the plot. Finally we clicked again on the Arizona locus to get the numerical value for the deflection energy using such an early interceptor:
You'll notice that the curves do not go below a certain velocity: for a head-on collision course there is a minimum impact velocity of about 32 km/s, if a body with no velocity w.r.t. the Sun collides with the Earth, which comes in at its orbital speed of 30 km/s. When you click the mouse in this forbidden area, you also get the appropriate mesage.
Clicking on the button "helioc.interceptor speed" changes over to the "DeltaV from LEO". This means that any entry to the textfield is now being interpreted as the velocity change for the interceptor being launched from a Low Earth parking Orbit. If this entry is too small, you'll be told that it can't escape from Earth orbit, and there will be no blue curves when you request their drawing.
There is something about the conversion of heliocentric speed into DeltaV from LEO which you might find most puzzling: For an approach angle of 180 degrees, enter a helioc. speed smaller than about 30 km/s, say 4 km/s. Clicking the button changes over to show a DeltaV of 26 km/s. Clicking again does not bring back the original 4 km/s but 56 km/s. What's wrong? There is a simple reason: launching the interceptor from LEO with 26 km/s, we could send it in the same direction of the Earth's movement around the Sun giving a heliocentric speed of 56 km/s. But also, we could send it in the other direction giving only 4 km/s, still towards the asteroid! You'll notice that the deflection energy also changes. (mathematically speaking, the conversion from LEO speed to heliocentric speed has two solutions, while the inverse conversion has one). Both approaches could be used, but obviously the faster approach is to be preferred. If you wish to insist on the slower approach, you may do so by entering the heliocentric speed.
Giving the heliocentric speed is useful for comparison with the orbital speed of the asteroid, e.g. from the other applets.
For the Chicxulub crater the head-on collision does not work: the approach from behind does. Here is the complete plot for this situation: one would have had a 3 year warning time, but a deflection would have necessitated a lot of energy!
There is also a page to alter the albedo and the density of the asteroid
as well as a page which gives the estimates for the resulting crater size and measures of the devastation from the impact. The formulae are taken from the JavaScript utility by A.Goddard based on formulae by Eugene Shoemaker.
Another page shows for each mouse click on a situation the orbital parameters of the body, the semimajor axis, the eccentricity, aphelion and perihelion, and the period. This allows to judge which could have been the origin of a body, for instance an asteroid crashing into Earth with almost 70 km/s and almost head-on (160 degree direction) could have been deflected from an orbit just outside Jupiter's orbit into a rather elliptic orbit (eccentricty 73 percent):
By clicking in the plot, one can verify that bodies with impact speeds larger than 72 km/s would need to be head-on crashes with bodies on hyperbolic orbits, while anything with less than 60 km/s must have come from inside the Earth orbit. On the other hand, all collisions "from behind" with speeds larger than 17 km/s are due to bodies on hyperbolic orbits, and bodies on elliptic give impact speeds between 11.5 and 17 km/s.
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