Orbital plane constraint applicable for in-situ measurement of sub-millimeter-size debris

Space debris smaller than 1 mm in size still have enough energy to cause a fatal damage on a spacecraft, but such tiny debris cannot be followed or tracked from the ground. Therefore, IDEA the project for In-situ Debris Environmental Awareness, which aims to detect sub-millimeter-size debris using a group of micro satellites, has been initiated at Kyushu University. First, this paper reviews the previous study on the nature of orbits on which debris may be detected through in-situ measurements proposed in the IDEA project. Second, this paper derives a simple equation that constrains the orbital plane on which debris is detected through in-situ measurements. Third, this paper also investigates the nature and sensitivity of this simple constraint equation to clear how frequently impacts have to be confirmed to reduce the measurement error. Finally, this paper introduces a torus model to describe the collision flux observed from the previous study approximately. This collision flux approximation agrees rather well with the observed collision flux. It is concluded, therefore, that the simple constraint equation and collision flux approximation introduced in this paper can replace the analytical method adopted by the previous study to conduct a further investigation more effectively.