# MIT Portugal NanoLab Student Payload Competition

## the project - posat-2

The idea consists of two masses colliding with each other. The smaller one is at rest and the bigger mass comes colliding with a certain velocity from one direction. The number of collisions between the masses and the wall, within certain circumstances, gives us the digits of the number Pi. And which conditions are these? It must have no friction, and the masses when colliding, can’t lose any energy, for example, deforming themselves. The last condition is the relation between the masses. It can’t just be any mass. If we have one-to-one relationship, meaning that the bodies have the same mass, we will get 3 collisions. If the relation is 1 to 100, in other words, the bigger one is 100 times more massive, we will get 31 collisions. The same idea, for relation 1 to 10000, which we will get 314 collisions. So everytime we multiply the bigger mass by 100, the one that is not at rest in the beginning, we get a new digit of Pi.

#### Research

The goal of our experiment is to validate the method proposed in [1] to achieve the digits of Pi with the usage of two colliding masses; and given that we need to conduct the method in [1] on a very ideal and frictionless system, we propose to further deepen our understandings of Good Practices on experiments of such type.

Pi (3.14….) is a very interesting relation between the diameter of a circle and its perimeter, commonly found on other geometrical relations but unlikely – at first observation – on a subject like the one we are studying.

We hypothesise, from the the stated goals, that:

- The number of collisions tells us about some physical properties of the system we are studying.
- In microgravity we reduce the external forces acting upon the two bodies.
- By induced vacuum we further reduce forces due to friction.
- Thus allowing us to construct an ideal system.

- By [1], given a mass ratio of 100N, the number of collisions will be the first N+1 digits of Pi.

The need of a suborbital flight comes from the theoretical essence of the challenge. When the mathematical description of the event is constructed, it is under the assumption that the collisions are perfectly elastic. In this way, we need to reduce the interaction at the maximum between any external force, and we can accomplish that using a suborbital flight, during the small time window where we have microgravity. And since the greater mass will be launched into the center of mass of the lighter body, we need to insure that the trajectories remain straight, so that the masses won’t have deviations from the ideal course. Thus a suborbital flight is mandatory to conduct this experiment.

[1] G. Galperin. Playing Pool With π (The Number π from a Billiard Point of View). *Regular and Chaotic Dynamics 2003; 8(4): 375 – 394*

## the team

Members: Henrique Neves; Luís Gonçalves; Bárbara Matos; José Sousa; André Neves; Marlene Antunes; Giorgio Canezin; André Silva