Imagine a WIMP
orbiting the sun. As it orbits the sun, it looses energy and falls into
the sun. It then meets and annihilates with an anti-WIMP. This annihilation
gives off gamma rays. Gamma rays can't penetrate earth's atmosphere
but these gamma rays can cause a chain reaction with other particles which
can pentrate earth's atmosphere thus causing a cosmic shower. The Milagro
detector can detect this cosmic showers.
Our team proposed
to write a program stimulating the orbits of a WIMPS and anti-WIMP. We
photocopied many articles from the "Scientific American" magazines from
January 1996 to October 1998 related to our project. We probably
even cleaned a whole search engine (Yahoo!) in trying to find all the information
- especially pictures for visualization because we're visual learners -
on WIMPS and atomic particles. We had a wonderful advisor who answered
our questions in great detail through email.
We (my partner
and I) thought that to attack the programming, we should concentrate on
the annihilations of the WIMPS and Anti - WIMPS. Our advisor advised that
we used the "Monte Carlo approach" in trying to find an angle at which
these two particles were to collide. We were also advised to perhaps use
polar coordinates, which has x, y, and z axis's - three dimensional. That
proved difficult, we couldn't find the math formula for the Monte Carlo
approach anywhere on the internet. Instead, we could only find reports
which mentioned the use of the Monte Carlo approach in their research.
So we decided
to try and concentrate on the orbitsof the WIMPS and anti-WIMPS. We found
a formula, which is Kepler's third law. In this (T1/T2)2 = (p1/p2)3 where
T = time and p = period. This means that for objects orbiting the sun,
the orbit sweeps out equal areas in time.
As you can see,
as the planet (the little black dot on the left side of the picture) orbits
the sun, it travels slower ( that is, it covers less area) when it is farther
away from the sun and slower when it is closer to the sun. The force of
the sun's pull increases and the planet de-accelerates when it is closer
to the sun and vice versa.
How to go about
writing Kepler's law in computer code was another problem. We have already
told you the geometric version of Kepler's third law, but there is also
a calculus version. This version was difficult to understand at first,
but now one of our team members has a better understanding because she
has Calculus.
Then there was
another problem, how are we going approach the computer program in putting
together so many concepts? Our program would have to calculate and keep
track of where the WIMP was, whether it was inside or outside the sun.
If it was inside the sun, then the math formula for force was different
the math formula of the WIMP outside the sun. All of this proved very complicated.
We do have a
program which we received from a computer programming text book. It was
a program on integration. We also have some other unfinished programs.
One was on finding the derivative and the other on Kepler's third law.