The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the set, students use the mathematical constant pi to find out how many images NASA's Dawn spacecraft needed to take to map the entire dwarf planet Ceres.
Part of NASA’s Discovery Program, Dawn is a mission to the two oldest and most massive bodies in the asteroids belt – Vesta and Ceres, These diverse worlds offer scientific snapshots of the birth of our solar system 4.6 billion years ago. Asteroid Vesta is rocky, while dwarf planet Ceres appears to be icy. Together they bridge the rocky worlds of the inner solar system and the ice bodies far beyond Saturn. By using the same instruments to study diverse destinations, Dawn is uncovering new insight into the early solar system. Powered by an efficient ion engine, Dawn was the first mission to orbit a main belt asteroid. And it was the first to visit a dwarf planet and orbit two targets on a single mission.
Dawn delves into the unknown and achieves what's never been attempted before. A mission in NASA's Discovery Program, Dawn orbited and explored the giant protoplanet Vesta in 2011-2012, and now it is in orbit and exploring a second new world, dwarf planet Ceres.
Dawn's goal is to characterize the conditions and processes of its earliest history by investigating in detail two of the largest protoplanets remaining intact since their formation. Ceres and Vesta reside in the main asteroid belt, the extensive region between Mars and Jupiter, along with many other smaller bodies. Each followed a very different evolutionary path, constrained by the diversity of processes that operated during the first few million years of solar system evolution. When Dawn visited Ceres and Vesta, the spacecraft stepped us back in solar system time.
- The Dawn spacecraft is orbiting Ceres – a nearly spherical dwarf planet with an average radius of 475 kilometers – in a perfectly circular polar orbit. While in orbit, Dawn will snap images of Ceres’ surface to piece together a global map. From its lowest altitude orbit of 370 kilometers, Dawn’s camera can see a patch of Ceres about 26 kilometers on a side. Assuming no overlap in the images, how many photographs did Dawn have to take to fully map the surface of Ceres?
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