It appears that the one of the MoteAI coming in from interstellar space is changing its orbit so that it will pass over the Earth, but it is still traveling faster then 618 kilometers per second, which means that the MoteAI would still be able to fly out of the solar system with no additional trust.  The MoteAI velocity is often referred to as the "escape velocity" of the solar system.  Humans have created similar spacecraft, Pioneer 10/11 and Voyager 1/2, and a new spacecraft New Horizon that was launched in 2007.  On the Pioneer 10/11 a plague describing the peaceful mission was included, and on Voyager 1/2 the along with a plague a type of recording was included along with the sensors to be able to read the recording, go to the link and listen to the communications.  The problem with the recording is that any intelligence (either mechanical or biological) has to intercept the spacecraft and set-up the instruments to listen to the recordings. 

The human race now has a decision to make: Can any of our spacecraft intercept the MoteAI as it transverses the solar system?  The answer is no, the New Horizon craft that is currently near Jupiter is not able to make course corrections to intercept the MoteAI.  How do the scientists know this?  The process, the scientific process, not the political process, is made using a concept called: Orbital Mechanics.  Our MoteAI would have a comet like trajectory, and an unmanned spacecraft like the New Horizon has just enough fuel to make the minor course corrections needed to intersect Pluto, which is New Horizons mission.  As to somehow rocketing humans into the cometary orbit, humans just do not have the technology to do so, even if the humans crew was willing to do a one way trip.

For fun, how would you write simple program to calculate a simple orbit?  You can do so using your TI-83/89 calculator, you could use the Microsoft Calculator included in the Student Math package, and it is a great calculator!  Or you could use the Visual Studio Express, VB or C#.  We will cover the programming tomorrow, but for today, take a look at the algorithms below:

Start with the basic principle behind all circular orbits. Set the centripetal force equal to the gravitational force.

 
Fg = Fc
 
Replace the speed with the circumference divided by the period.

Gm1m2    =   mv2  =  m    ( r )2 =  2mr

 r2                     r          r           T                T2

Solve for radius to arrive at a general formula

 
r = ∛(  GmT2  )
2
 

In the next entry, we will write a program in C# that will tell us the circular radius of an orbit.  I will show you why it is good to use a software package to do this type of calculation rather then a calculator.