# The Effect of Angle of Elevation on Muon Flux

**Sudheshna Gullanki (Troy High School) and Tanner Allen (Paul K Cousino High School)**

**Teacher Mentor: Mike Niedballa (Michigan Collegiate High SChool)**

**Research Mentor: Gil Piz (Wayne State University)**

**The purpose of our research is to study and experiment the correlation between the angle of the cosmic ray detectors and the count of incoming muons. We believe that the more perpendicular the stacked detectors are to the earth, the more muons will be detected, inversely the more horizontal the stacked detectors are to the earth the less muons will be detected.**

**We tried to keep the data as accurate as possible. We collected data more approximately eight hours for each angle of elevation. We never never changed the position of the placement of the detectors. We also used many different kinds of graphs to prove our experiment correct. We made a flux study to compare results between the detectors. A box plot was made to show a standardized way of displaying our results of minimum, first quartile, median, third quartile, and maximum. Then we conducted an ANOVA test to statistically analyze the difference between data. Lastly we also mathematically verified our experiment’s validity using a unique theoretical equation for predicting muon flux at a given angle of elevation written from scratch.**

**Our hypothesis was accepted. We hypothesized that angles of elevation closer to vertical would have higher rates of directional muon flux, and they did. However, why does this work? Muons are typically formed by cosmic ray collisions with particles in the atmosphere about 10-15km from the Earth's surface. Since they are traveling so quickly (.98c), Einstein's principles of relativity allow them to reach the surface of the Earth in relatively large numbers; almost 4.9% of muons at that altitude and that speed reach the surface of the Earth before decaying. However, when the angle of elevation shifts away from vertical, the distance muons must travel to reach the surface from any given altitude increases exponentially. For example, if all muons in a given trial decayed at 15 km, vertically aligned muons would only travel through 15 km of atmosphere and reach the Earth only a couple units of mean lifetime later, whereas muons traveling from the horizon have to cross almost 450 km of atmosphere before reaching the detectors, spending about 130 mean lifetimes.**