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The Dawn Mission -- Ion Rockets and Spiral Orbits
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The Dawn Mission -- Ion Rockets and Spiral Orbits

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Short Description: Students determine the shape of the trajectory taken by a spacecraft using a constant-thrust ion motor using differential and integral calculus for arc lengths.

Topic: Far Ranging Robots, Space Math

Grade Level: 9-12

Body: Asteroids, Dwarf Planets

Mission: Dawn (Dwarf Planets)

Science Education Standards:

Benchmarks

By the end of the 12th grade, students should know that

  • Technological problems and advances often create a demand for new scientific knowledge, and new technologies make it possible for scientists to extend their research in new ways or to undertake entirely new lines of research. The very availability of new technology itself often sparks scientific advances. 3A/H1*
  • Mathematics, creativity, logic, and originality are all needed to improve technology. 3A/H2
  • Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems. Scientific knowledge provides a means of estimating what the behavior of things will be even before they are made. Moreover, science often suggests new kinds of behavior that had not even been imagined before, and so leads to new technologies. 3A/H4** (SFAA)
  • Complex systems have layers of controls. Some controls operate particular parts of the system and some control other controls. Even fully automatic systems require human control at some point. 3B/H3
  • The more parts and connections a system has, the more ways it can go wrong. Complex systems usually have components to detect, back up, bypass, or compensate for minor failures. 3B/H5
  • To reduce the chance of system failure, performance testing is often conducted using small-scale models, computer simulations, analogous systems, or just the parts of the system thought to be least reliable. 3B/H6

National Science Education Standards

Science and Technology -- Content Standard E

Grades 9-12
UNDERSTANDINGS ABOUT SCIENCE AND TECHNOLOGY

  • Science often advances with the introduction of new technologies. Solving technological problems often results in new scientific knowledge. New technologies often extend the current levels of scientific understanding and introduce new areas of research.
  • Creativity, imagination and a good knowledge base are all required in the work of science and engineering.
  • Science and technology are pursued for different purposes. Scientific inquiry is driven by the desire to understand the natural world, and technological design is driven by the need to meet human needs and solve human problems. Technology, by its nature, has a more direct effect on society than science because its purpose is to solve human problems, help humans adapt, and fulfill human aspirations. Technological solutions may create new problems. Science, by its nature, answers questions that may or may not directly influence humans. Sometimes scientific advances challenge people's beliefs and practical explanations concerning various aspects of the world.

Source: SpaceMath@NASA


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Last Updated: 1 Jul 2014