（翻译）2016美国数学建模MCM B题（离散型）翻译:Space Junk太空垃圾

PROBLEM B: Space Junk

The amount of small debris in orbit around earth has been a growing concern. It is estimated that more than 500,000 pieces of space debris, also called orbital debris, are currently being tracked as potential hazards to space craft. The issue itself became more widely discussed in the news media when the Russian satellite Kosmos-2251 and the USA satellite Iridium-33 collided on 10 February, 2009.

A number of methods to remove the debris have been proposed. These methods include small, space-based water jets and high energy lasers used to target specific pieces of debris and large satellites designed to sweep up the debris, among others. The debris ranges in size and mass from paint flakes to abandoned satellites. The debris’ high velocity orbits make capture difficult.

Develop a time-dependent model to determine the best alternative or combination of alternatives that a private firm could adopt as a commercial opportunity to address the space debris problem. Your model should include quantitative and/or qualitative estimates of costs, risks, benefits, as well as other important factors. Your model should be able to assess independent alternatives as well as combinations of alternatives and be able to explore a variety of important “What if?” scenarios.

Using your model, determine whether an economically attractive opportunity exists or no such opportunity is possible. If a viable commercial opportunity exists as an alternative solution, provide a comparison of the different options for removing debris, and include a specific recommendation as to how the debris should be removed. If no such opportunity is possible, then provide innovative alternatives for avoiding collisions.

In addition to the required one-page summary for your MCM submission, your report must include a two-page Executive Summary that describes the options considered and major modeling results, and provides a recommendation for a particular action, combination of actions, or no action, as appropriate from your work. The Executive Summary should be written for high level policy makers and news media analysts who do not have a technical background.

B: 小碎片在轨道上绕地球金额已日益受到关注。据估计，超过50万件的空间碎片，也被称为轨道碎片，目前都被跟踪的潜在危害航天器。这个问题本身变得更广泛的讨论，在新闻媒体时，俄罗斯卫星的Kosmos-2251和美国铱卫星-33相撞2009年2月10日。

有许多方法以除去碎片已被提出。这些方法包括小的，基于空间的水射流和用于针对特定的碎片高能激光器和设计，以清扫杂物，其中包括大型卫星。从漆片的废弃卫星的大小和质量的碎片范围。碎片“高速轨道进行采集困难。

开发时间依赖模型来确定的替代品，私人公司可以采取作为一个商业机会，以解决空间碎片问题的最佳替代品或组合。您的模型应该包括成本，风险，效益的定量和/或定性的估计，以及其他重要的因素。您的模型应该能够评估独立的替代品的替代品，以及组合和能够探索各种重要的“如果？”的情景。

使用模型，确定了经济上有吸引力的机会是否存在，或没有这样的机会是可能的。如果一个可行的商业机会的存在作为一种替代解决方案，提供了不同的选择去除杂物进行比较，并包括具体建议，以碎片应该如何去除。如果没有这样的机会是可能的，然后提供用于避免碰撞的创新性的替代品。

除了必需的单页摘要您的MCM提交，你的报告必须包括一份两页的内容摘要，介绍了考虑的选择和主要模拟结果，并提供了一​​个特定的行动建议，这些动作的组合，或无动作酌情从你的工作。执行摘要应为高层决策者和新闻媒体分析谁没有技术背景来写。