I feel that any scientific experiments that are involved in order to verify the shape of the planet should use the metric system.
By adopting the metric system for these experiments, we will broaden the reach that these experiments have with the rest of the planet.
There is no point in using both systems when the metric system is the dominant system in use. If the objective is to demonstrate to the largest possible number of people as to what the shape of the planet is, then it would only make sense to use the system of measurement that most people are familiar with.
Scientific tests need to be able to be reproduced and measurable. By using only the metric system, they will be allowed to be reproduced and measurable for the largest number of people on the planet.