The force on a satellite in the earth’s upper atmosphere depends on the mean free path of the molecules (a length), the density , the diameter of the body , and the molecular speed such that . Using the method of repeating variables, determine a non-dimensional functional relationship for the force. Hint: Use 3 repeating variables instead of 2 in order to simplify the problem by reducing the number of required pi terms needed.

The force on a satellite in the earth’s upper atmosphere depends on the mean free path of the molecules (a length), the density , the diameter of the body , and the molecular speed such that . Using the method of repeating variables, determine a non-dimensional functional relationship for the force. Hint: Use 3 repeating variables instead of 2 in order to simplify the problem by reducing the number of required pi terms needed.