Efficient approach of painting asteroids for planetary defense using network data envelopment analysis

Abstract

The potential dangers of asteroids hitting the Earth are one of the challenges for mankind to preserve the human species. Various missions have been proposed to defend asteroids. Changing the Albedo magnitude by painting asteroids is a suitable and low-cost idea for the asteroid defense plan. Moving away from the Earth requires fuel consumption and the limitations of carrying the necessary materials for painting. Due to these limitations, we are not able to paint the entire asteroid, or for other reasons, we have to paint parts of the asteroid. Therefore, we should find a relative compromise between the variables to get most efficiency from painting parts of the asteroid. In this paper, we present a network structure of Data Envelopment Analysis (DEA) and consider the relationships of all variables including physical and orbital characteristics, spacecraft limitations, effective solar mass, albedo change rate, and elapsed time of the mission. We look for parts of the asteroid’s surface where we can get the most displacement by spending the least amount of raw material. One of the advantages of the proposed method is the capability of sensitivity analysis to any of the variables affecting the magnitude of the final displacement. The theorems related to the stability were proven analytically, and we show how to reduce the elapsed time by maintaining efficiency in asteroid painting. The performance of the proposed model was analyzed using real and hypothetical data from asteroid Apophis 99942.