2016美国数学建模MCM B题 翻译:Space Junk太空垃圾
MCM: The Mathematical Contest in Modeling
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题：太空垃圾
已经提出许多方法以除去碎屑。这些方法包括小的，基于空间的水射流，并用于针对碎片的特定部分高能激光器和大型卫星，旨在清扫杂物，等等。碎片的大小和质量范围从漆片的废弃卫星。碎片“高速轨道捕获做出困难。
开发时间依赖模型来确定一个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替代品的最佳替代品或组合。您的模型应该包括成本，风险，收益定量和/或定性的估计，以及其他的重要因素。您的模型应该能够评估独立的替代方案以及替代品的组合，并能够探索各种重要的“如果什么？”的情景。
使用你的模型，确定经济上有吸引力的机会是否存在没有这样的机会是可能的。如果可行的商业机会的存在作为替代的解决方案，提供了用于去除碎屑的不同选项的比较，并包括特定建议作为对碎片应如何除去。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方案。
除了为您的MCM提交所要求的一页纸的总结，你的报告必须包括一份两页的摘要描述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，从你的工作为宜。执行摘要应为高层决策者和新闻媒体分析师并不具有技术背景谁写的。
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