Lesson .
.Finale Fanfare: A 'Pi in the Sky' Math Challenge
Overview
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 and Kepler's third law to find out when a Saturn orbiter will make its mission-ending plunge into the ringed planet.
Materials
- Pi in the Sky 4: Finale Fanfare worksheet – download PDF
- Pi in the Sky 4 answer key (third problem) – download PDF
Procedures
In 2017, after more than 12 years at Saturn, the Cassini mission came to an end with a plunge into Saturn. The finale was designed to keep Cassini from impacting and possibly contaminating any of Saturn’s scientifically intriguing moons. First, mission operators planned a daring series of orbits that took Cassini closer to Saturn than ever before. Cassini used the gravity of Saturn’s moon Titan to alter its trajectory and fly into the gap between Saturn and its rings. It all began with a flyby of Titan on April 22, putting Cassini on a new orbital path whose first apoapsis was on April 23. Then, it completed 22 elliptical orbits with an average periapsis altitude of 63,022 km and an average apoapsis altitude of 1,274,828 km. A final flyby of Titan placed Cassini on a half-orbit trajectory for Saturn impact.
Use Kepler’s third law below to find approximately how many days each orbit took. Approximately what day did Cassini dive into Saturn’s atmosphere?
- µcb (gravitational parameter of Saturn) = 3.7931187 x 1016 m3/s2
- aSC = semi-major axis of Cassini's orbit
- TSC = orbital period of Cassini
In 2017, after more than 12 years at Saturn, the Cassini mission came to an end with a plunge into Saturn. The finale was designed to keep Cassini from impacting and possibly contaminating any of Saturn’s scientifically intriguing moons. First, mission operators planned a daring series of orbits that took Cassini closer to Saturn than ever before. Cassini used the gravity of Saturn’s moon Titan to alter its trajectory and fly into the gap between Saturn and its rings. It all began with a flyby of Titan on April 22, putting Cassini on a new orbital path whose first apoapsis was on April 23. Then, it completed 22 elliptical orbits with an average periapsis altitude of 63,022 km and an average apoapsis altitude of 1,274,828 km. A final flyby of Titan placed Cassini on a half-orbit trajectory for Saturn impact.
Use Kepler’s third law below to find approximately how many days each orbit took. Approximately what day did Cassini dive into Saturn’s atmosphere?
- µcb (gravitational parameter of Saturn) = 3.7931187 x 1016 m3/s2
- aSC = semi-major axis of Cassini's orbit
- TSC = orbital period of Cassini
Assessment
Extensions
Pi Day Challenges
- Pi in the Sky
- Pi in the Sky 2
- Pi in the Sky 3
- Pi in the Sky 4
- Pi in the Sky Challenge (slideshow for students)
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Lesson Last Updated: Oct. 11, 2024