Introduction: Simulating Galaxy Collisions With Arduino
Astronomy has always fascinated me. In the 1980s, around the age of 16, I regularly bought the magazine Astronomy. One of the issues covered the simulation of galaxy collisions. I was immediately intrigued by the article and tried out the provided code right away. I wondered how such a short code could simulate the complex motions of stars. At that time, I didn't yet understand the physical background. Later, with the knowledge of Newton's equation of motion F = m*a and the simple, iterative Euler-solution of differential equations, the fog cleared, and I began to understand simulation. Interactions between galaxies can be observed very well with a telescope. A famous example is M51, the Whirlpool Galaxy. Here, two nearby galaxies interact. I wrote the original computer program in BASIC. The current implementation was done with an Arduino in C++.
Supplies
For this science project you need just an Arduino Due and a 320x480 pixel display you can plug on the Arduino Due. For the input you need 5 resistors, 5 push buttons and 1 potentiometer, that's all.
With the 5 push buttons you change the zoom, the time-step and one button is for continue in the menu. With the potentiometer you can input the number of stars and their mass.
Step 1: The Mathematical Background
The individual stars and black holes interact via their gravitational force. Newton's law of gravity describes the force F between the two masses m and M at a distance r. According to Newton's equation of motion F = m*a, this force F leads to an acceleration a of the masses. However, the acceleration a is equal to the change in speed per second.
The change in speed delta_v is therefore: delta_v = v_after - v_before = a * delta_t with the time step delta_t. If we know the current acceleration a and the previous speed v_before, we can easily determine the speed after the time step v_after. The relationship v = delta_s / delta_t = (s_after - s_before) / delta_t applies to the speed v.
If we know the position before the time step s_before and the current speed v, the position after the time step s_after can be calculated. To increase the accuracy of the calculation, the velocity v is taken as the average of the velocity before and after the time step, i.e., v = 1/2 * (v_before + v_after).
Thus, using this Euler method, we have calculated the positions after the time step. Using these new positions, we again determine the force F using the law of gravity, and then subsequently determine a_after, v_after, and s_after.
If you have, say, 100 stars in the simulation, each star exerts a force F on the others. So, you have to calculate (100 2) = 100! / (98! * 2!) = 100 * 99 / 2 = 4950 interactions. That's quite a lot... The force from star 36 on star 58 is the same as the force from star 58 on star 36. Therefore, the binomial coefficient (100 2) is sufficient.
Step 2: Black Hole Vs. Galaxy
With the first Arduino-sketch you can simulate the gravitational interaction between an intruder-black hole and a galaxy.
Step 3: Galaxy Vs. Galaxy
With the second sketch you are able to simulate the interaction between two galaxies like M51...
Step 4: Videos
With this "simple" arduino sketch you're now able to simulate galactic collisions and compare it with real results in the night sky. Nearly 40 years after I got in contact with this type of simulation you can be fascinated like I was back in time. If you are interested in further physics projects, here is my Youtube-channel and homepage:
In this sense Eureka and stay curious
