For clean and safe space environment – three dimensional standard routing problem

We have launched the first artificial satellite in 1957. Since then, a new environmental problem has been brought about by ourselves. That is the space pollution. Everything we have lifted up can become space debris when we lose control of it. The space debris is accumulated around the outer atmosphere more than forty years and is propagating by collision and explosion of itself. As the debris has high kinetic energy, the space pollution affects the safety of our future space activities. For the sake of reducing the debris and preserving clear and safe space environment, we have been developing spacecraft of various types, such as for observation, for sweeping the debris up, or for shooting them down. Even if we may take any one of these responses to the debris, a concrete operating plan of spacecraft has not declared till now. In this paper, we propose one of the efficient operating plans of the spacecraft. If a spacecraft flies along the route constructed by our proposing procedure, it will be able to respond more efficiently to individual drifting debris. When we construct the 3-dimensional standard route of the spacecraft, we extend the routing methods in 2-dimensions that was applied to make standard routes of an aircraft in surveillance operation at sea. In these methods, the standard routes (piecewise linear) are constructed under the policy of maximizing the expected value of the detected ships locally within an operation. That objective value is calculated as integration, along a given route, of product value of the detecting probability from the plane and the density of the ships in the area. In this 3-dimensional extended case, we also use non-linear optimization technique (quasi-Newton method) to make the spacecraft routes. By numerical experiments, we can construct 3-dimensional standard routes that close to drifting debris.