Introduction
The collision of an asteroid with a member of the solar system (such as Mars) has the potential to release large quantities of energy. The purpose of this project is to determine the effects of an asteroid colliding with Mars. An energy release resulting from the collision of the asteroid with Mars is calculated in terms of joules which is then converted to TNT equivalent from which comparisons can be made to the detonation of a nuclear weapon. In order to determine the required energies, the physical characteristics (diameter, density, and mass) of the asteroid, the velocity of the asteroid, the gravitational pull of Mars and the atmosphere of Mars are determined.
The physical characteristics of both the asteroid and Mars are evaluated and the values for these parameters are included for this program:
1.2 Computer Program
The program that we will be using is a C++ program to solve the problem.
2.0 Problem Statement
2.1 Problem Statement
The destruction of Mars, by impact of an asteroid could have devastating effects on Earth and possibly effect the whole solar system. The effects of the resultant explosion are estimated to be:
In order to accomplish the calculation this computer program takes into consideration these factors:
Also, to simplify matters in the computer program, it is assumed the collision is a direct head-on encounter and that the asteroid is spherical in shape and uniform.
3.0 Method of Solution
The computer calculation uses C++ language to develop the program. The program calculates the amount of energy resulting from the collision between the asteroid and Mars. The "for loops" were used to input different asteroid masses to evaluate the different effects. The second "for loop" was used to find the gravitational pull between the two objects.
The program developed to solve the energies of collision requires the use of selected input information for the asteroids and Mars, and from this data the program calculates the momentum of both objects and the kinetic energy of the asteroid prior to the collision. The information selected as input data for the asteroid characteristics is derived from several sources1 and is representative of the larger known asteroids in space. The physical characteristics used for evaluating Mars is found in the literature2. Based on the data, the mass, momentum, and energy of the asteroids and Mars are determined. The program first calculates of the system prior to the collision and next calculates the energy of the system immediately after the collision. It is assumed that there are no external forces acting on the system at the time of the collision. Further, the collision, due to enormous energies involved between the colliding masses, is in effect a non-elastic collision, that is, all of the energy of the asteroid is deposited on Mars.
The variables used in the computer program are:
The damage resulting from the impact of the asteroid and Mars can be compared against the Torino Scale3 shown in Table 1. This scale evaluates the possibility of a collision occurring and the potential damage. The results of the calculations performed show that the damage is consistent with a scale of 8. It is assumed for purposes of calculation that the collision
occurs and that all of the energy of the asteroid is transferred to Mars.
The formulas used in the program are4:
It is assumed that the asteroid is spherical in shape, a head on collision, no frictional losses and no external force is acting upon it.
4.0 Results
The results for the program are:
Many of our variables stayed the same but two variables changed in increments. These two variables changed the results for other variables. The results could change if different increments were selected.
5.0 Conclusion
Our program calculates the energy that is given off by an asteroid that collides with Mars in terms of Hiroshima bombs. At first our program calculated the kinetic energy of both objects and added the totals together. One of the objects had a larger kinetic energy than the other and when they were added they didn’t change the larger number. We then took out the kinetic energy of Mars and changed it to the gravitational energy of Mars. Using the kinetic energy and potential energy of the asteroid we calculated the total amount of energy that is released by the two objects. In order for the Mars to be split in half the asteroid had to exceed 3,711,620,000 joules of energy. In order for the asteroid to release enough joules of energy it had to have a radius of 659, a mass between 180 and 248 kilograms, and a velocity between 5 and 65 kilometers per second.