Rebecca J. Carlson, Physics and Astronomy
Introduction
Small objects from outer space collide with the earth’s atmosphere every day. Most of these are small enough to burn up completely before hitting the ground. A few, however, reach the earth’s surface as meteorites. On occasion, an asteroid large enough to cause serious darnage impacts the earth. Although impacts large enough to destroy cities only occur once in a thousand years or so, if such an event were to occur there would be great loss of life and damage of property (Rather 1992). Because of this, it is important to develop plans to deter an asteroid on a colllslon course with earth, should one be discovered. If an asteroid is discovered only a short time before Impact, it would be a great benefit if we already knew some things about the dynamics of deflecting asteroids, I have developed a computer code that simulates the deflection of an asteroid one month before Impact. I have found that the direction of deflection Is very important, and that the energy needed to deflect most asteroids between 100 and 500 meters in diameter is small enough that It would be possible, with our present technology, to prevent such an asteroid from impacting.
Possible Deflection Scenarios
Very large asteroids can cause global damage due to the large amounts of dust that would be injected Into the upper atmosphere on impact. The resulting nuclear winter could cause global crop failures for years. But such objects only strike once In a few million years (Rather 1992). With our current search methods, it is very unlikely that an object of this size will be able to impact us. We would find it and alter It’s orbit so that it is no longer a threat well before the impact. Smaller objects are a different story. It is estimated that in the next 25 years, only 10% of objects smaller than 100 meters in radius will be detected (Morrison 1992). Although these objects would not threaten human civilization, they can cause local damage equivalent to that of a moderately sized nuclear bomb (Hills 1993). They also strike about once every millennia. It is possible that an object around 100 meters In diameter could go undetected until it is less than a full orbit before impact. Allowing several months to refine the object’s orbit, prepare a device to deflect it and send the device to intercept the asteroid, it is a realistic possibility that there would only be one month left until impact when the asteroid is reached.
Code Development
The motion of any object in a gravitational field can be described with a second order differential equation. If there are more than two objects present, however, the differential equation cannot be solved exactly. In the simulation, A Runge-Kutta Integration routine was used to make a numerical approximation of the asteroid’s motion. Runge-Kutta, although slower than some other Integration routines, is very accurate and is frequently used in gravitational simulations. Since the earth has a very low eccentricity, I approximated the earth’s motion as a circle to cut down the computation time. For each time step, the program calculated the force on the asteroid due to the earth and the sun, then allowed the asteroid to move as It would under the influence of that force until the start of the next time step when the force was calculated again. Although the theory and equations for this process are simple, writing a computer code that worked correctly took most of the time that I spent on the research project.
Simulations
For the simulations, I defined a coordinate system in which 0 degrees was the point on the earth directly away from the sun. Ninety degrees was pointing in the direction of earth’s motion, while -90 degrees pointed opposite earth’s motion. Each simulation began with the asteroid already on the face of the earth. The location, the impact velocity and the direction of approach was selected. For this project, I chose to concentrate on asteroids that impacted at the earth’s equator at angles nearly perpendicular to the earth’s surface. These asteroids all have moderate to low orbital inclinations, a characteristic of the near earth asteroid population. Next the program ran time backwards until the asteroid was one month away from impact. At this point, the program made an estimation of the asteroid’s orbital parameters. If the asteroid was not in a closed orbit around the sun, the program started over. If the asteroid was in an allowed orbit, the program tested to see if the asteroid would hit the earth again if time ran forward for a month. I used this to test the accuracy of the simulation. Most of the time the asteroid impacted within a degree of latitude or longitude from its original location. If it did not, The time steps were made smaller.
The next step was to change the velocity of the asteroid in six different directions and see which, if any, prevented an impact. Each asteroid was slowed, sped up, deflected towards the sun, deflected away from the sun and lastly deflected above or below its orbital plane. For each change in velocity, the asteroid was run in towards the earth, and the impact location or closest approach was recorded.
Results
It was expected that the best direction to deflect an asteroid would depend mostly on the shape and orientation of the asteroid’s orbit. I found that the solution was simpler than that. In the 40 different asteroid impacts simulated, the direction that required the least energy for deflection depended only on the final approach direction. Very similar orbital characteristics can produce different approach directions, and in all cases the approach direction mattered the most. An asteroid that approached the earth from -135 or 180 degrees could best be deflected towards the sun thirty days before impact. Likewise an asteroid approaching the earth from -45 or 0 degrees should be deflected away from the sun. Asteroids that approached the earth from directly behind, or -90 degrees, should be deflected up relative to their orbital plane if they approach from above the earth, or down if they come from below. Lastly, asteroids that approached the earth from 45 degrees should be sped up. I did not find any allowed orbits that approached the earth at 90 or 135 degrees at low inclination. Direction of deflection is extremely important too. Many of the asteroids simulated would miss the earth by several thousand kilometers if deflected in the right direction, but deflecting them by the same amount in any other direction would not prevent impact.
I found that asteroids impacting the earth on the back are the most difficult to deflect. This was expected, as these asteroids must be traveling faster than the earth, and therefore, have higher energies than the asteroids that approach the earth from other directions. But stlll, the maximum change in velocity needed to deflect any of the asteroids tested would require only 73 tons of TNT for a stony object 100 meters in diameter, an asteroid large enough to destroy the city of Los Angeles. It would take 9 kilotons of TNT for a 500 meter diameter object, an asteroid large enough to destroy a small state like Connecticut (Hllls 1993). This is based on the assumption that an explosion would impart 1% of its energy as kinetic energy to the asteroid (Rather 1992). Explosions of this size are well within our capabilities, as we currently have nuclear explosives that release several megatons of TNT.
Future Plans
I intend to continue working on this project this summer. First, I would like to see if the generalizations made hold for high inclination approach directions. I would like to expand my code so that asteroids can be deflected at more than thirty days before impact. This would require the use of the exact motion of the earth instead of an approximation, as well as greatly reduce the length of time steps in order to retain the necessary accuracy. I want to compare the effect that direction of deflection has on asteroids that are intercepted at different times before impact. I would also like to simulate different methods of deflection. An explosive planted on the surface of an asteroid would impart a change in velocity almost instantaneously, and in a somewhat unpredictable manner. A rocket planted on the surface of an asteroid could push it over an extended period of time, giving us more control over the asteroid’s change in velocity. Some modifications to the computer code would be needed In order to do these things.
Conclusion
A steroids between 100 and 500 meters in diameter that approach the earth at low inclinations can be deflected If intercepted only a month before impact. The effectiveness of the deflection depends greatly on the direction in which the asteroid’s velocity is changed. The optimum direction for deflection at one month to impact depends on the asteroid’s direction of final approach to the earth. With improvements to the computer code and after examining some further simulations, I plan to see if these generalizations continue to hold true for asteroids in high inclination approach directions and for interceptions made more than a month before impact.
References
- Hills, Jack, and P. Gada. “The Fragmentation of Small Asteroids in the Atmosphere,” Astronomical Journal. 1993. 105:1114-1144
- Morrison, David, ed. The Spaceguard Survey: Report of the NASA International Near-Earth-Obiect Detection Workshop. JPL/California Institute of Technology, Pasadena, 1992
- Rather, John D. G .. Chair. Summary Report of the Near-Earth-Object Interception Workshop. JPL/California Institute of Technology, Pasadena, 1992