As part of the phyphox talk at the International Conference on Physics Education 2022 and in honor of IUPAP’s 100th anniversary, we determined Earth’s radius/circumference with phyphox.

The following map shows the contributions from the conference and the possible distances of at least 1000km that were available for the calculation.

After filtering 50% outliers (iteratively removing the result that most deviates from the current mean) we got an Earth radius of 6015 km. (Actual average radius is 6.371 km.)

## Physics background

In order to determine Earth’s radius, the participants will submit the altitude and azimuth at which they see the sun at their locations. The altitude is determined from the inclination of the phone as measured with its accelerometer. The azimuth is measured by the magnetometer, acting as a compass.

These measurements are to be taken at the same time, so that the position of the sun in combination with the distance between the locations of the participants can be used to calculate Earth’s radius – similar to the method used by Eratosthenes in about 240 BC.

However, there are two critical details in the original experiment by Eratosthenes that are extremely simplified in our version: The distance between locations and the time. Originally Eratosthenes needed two places at a known distance to measure the length of a shadow at the same time. Since time measurement was nowhere nearly precise enough, he relied on two locations being on the same longitude and measuring at noon.

In order to allow participants to contribute from any place during the conference, we instead coordinate the measurement with any modern clock and communication tools available. Furthermore, we simply derive the distances from GPS coordinates.

So, considering that the knowledge of Earth’s radius is quite certainly a prerequisite to operate a global navigation satellite system, this aspect should be viewed as a demonstration of the principle and of the network interface of phyphox.