Quake Quandary: A 'Pi in the Sky' Math Challenge
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 identify the timing and location of a seismic event on Mars, called a "marsquake."
During a seismic event on Mars, or a “marsquake,” a type of seismic wave called surface waves travel outward from the epicenter, across the planet in all directions. Scientists expect these surface waves to arrive at NASA’s InSight lander, designed to study the quakes, at three different times: R1, when the first wave arrives, having traveled the shortest distance from the epicenter to the lander; R2, when the second wave arrives, having traveled the other way around Mars; and R3, when the first wave again impacts the lander, having traveled all the way around Mars. Let’s imagine InSight records marsquake waves at the following Earth times:
R1 = 08:38:09.4 UTC
R2 = 10:04:48.2 UTC
R3 = 10:25:43.0 UTC
*Note times are in UTC, which is written in hh:mm:ss format.
Use the formulas below to determine the velocity (U) in rad/s of the surface wave, the distance in radians on the sphere from InSight to the epicenter (Δ), and the time the marsquake occurred (t0).
ExtensionsPi 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 5
- Pi in the Sky Challenge (slideshow for students)