Minimum Energy
The best way to explain this is with a diagram:
(coming soon)
And a lot of math and probability to determine whether this experiment is even feasible (this is a very garbled sheet, there should be a better version soon):
General setup information:
For this experiment, the two telescopes are set up at varying distances from
each other- with the variable being the distance R from the center of the two
telescopes. For our feasibility calculations we used R values from 1 through 3
meters.
To determine minimum energy, this radius R is assumed to be the axis of the
cosmic ray shower. This axis is where the cosmic ray is incident upon the
atmosphere before scattering into a shower of muons and other exotic
particles. The energies of the muons from these showers that are detected are
recorded onto a data table. From this data, the minimum energy of the total
shower can be calculated.
With that large data table full of math, our goal is to find out whether we
can collect enough data of similar sized cosmic ray showers to make a
statement about what kind of cosmic ray events we have witnessed. Can we do
this? We still must work the bugs out of our Excel sheet, and make sure that
the errors are not in our equations. With results, we can discover whether it
is possible for us to get quality data for our experiment.
To put the math in perspective, here are the equations behind the data table:
N(muons) for > 1`GeV = .95*10^5 *(N/10^6)^.75
N= total number of shower particles
Density (muons) =(1.25 N(mu))/(2pi*.906402*1.25)*(1/320)^1.25*r^-.75*(1+r/320)^-2.5
Frequency of vertical muons:
F( v mu) =5.58*10^-8*(10^6/N)^(1.52+.055log(N/10^6)) [m^2 sec strad]^-1