Over the summer a new show was aired on CBS called Salvation. The main plot of this show revolved around a giant asteroid heading towards earth. It was an interesting premise for a show and dove much deeper into the Physics of how to stop the asteroid than I would have thought. I decided to do some research and see what would have to be done in order to divert/stop an asteroid from colliding with earth. There are multiple ways to stop the collision, but there are two distinct methods from which it is thought an asteroid could be stopped. The first method of stopping an asteroid involves providing force on an asteroid to change its trajectory. The leading idea currently following this method is the idea of a gravity tractor. The idea is that a satellite could be sent out and put into orbit with the asteroid. Once orbiting the asteroid the satellite would create a very small gravitational force on the asteroid that over the course of years would divert it.
The physics for this model are summarized in the equation F = Gm1m2/r2, where F is equal to the force of gravity, G is the gravitational constant, the two masses represent the the asteroid and the satellite, and represents the distance between the two objects. Additionally if the two are gravitationally paired to one another in gravitational orbit, then the pair form a composite system. When the two become a system any force acted on one will act on the other through the means of gravity, unless that force allows one to leave the orbit of the other. With this being the case, once a satellite is put into orbit around an asteroid then theoretically by maintaining the orbit and using fuel to provide force to the satellite an asteroid we could control where an asteroid went.
The second method of diverting/stopping involves collisions. This can be done in a series of ways the most simple of which is flying a satellite into an asteroid. This collision is hard to perfectly calculate as it would be neither completely elastic nor inelastic. However as we know from the conservation of momentum v1 m1 +v2 m2 =v1f m1 +v2f m2 so even if the satellite were to be significantly smaller than the asteroid it would still affect the velocity of the asteroid by some amount. In the grandness of space if this were to occur far enough in advance of the collision with earth the asteroid would be diverted. A very slight change in speed or angle of an asteroid caused years in advanced, would cause the asteroid miss by a very large margin.
The first way of stopping an asteroid that comes to most people's minds is blowing it up. While most people think of nuclear devices, I will be looking at how an asteroid can be blown up using a laser. A powerful laser will will shoot at an asteroid and give it a lot of energy. This energy will superheat the asteroid which will cause it to explode. When the laser is fired it will provide enough energy to turn some of the molecules into a gas. Using the ideal gas law we can see that PV=nrT. So as the temperature of these gases is increased so too must their pressure of volume. If these gases are locked inside the asteroid they will provide increasing pressure until the asteroid is broken apart and there volume increases. This will cause an inelastic collision to occur, v1 (m1m2)=v1f m1 +v2f m2. Ideally this would would cause the asteroid to split into large chunks which then are moving in different directions that avoid earth. Let’s say theoretically that it splits into two equal halves, and that the asteroid is belining directly towards earth, and that the inelastic collision occurs such that the halves are both only given velocity perpendicular to the current motion of the asteroid. As this is perpendicular to current motion of the asteroid we can set v1 in our conservation of momentum to 0. And as m1=m2 we can determine that v1=-v2. This velocity would be the component of their velocity that is moving them out of the path of earth. If this were to occur far enough away from earth the two halves would pass on opposite sides of earth.