Illustration of OSIRIS-REx above asteroid Bennu with an inset of the spacecraft's contact-pad samplers.


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 eighth set, students use the mathematical constant pi to determine how many spacecraft contact pads need to touch the surface of asteroid Bennu to meet mission sample collection requirements.



In this black and white animated image, a circular device stretched out from a robotic arm descends quickly toward a rocky surface, touches it, and then ascends as debris flies all around.

Captured on Oct. 20, 2020, during the OSIRIS-REx mission’s Touch-And-Go (TAG) sample collection event, this series of images shows the SamCam imager’s field of view as the NASA spacecraft approached and touched asteroid Bennu’s surface. Image credit: NASA/Goddard/University of Arizona | › Full image and caption

NASA’s OSIRIS-REx mission has flown to an asteroid and collected a sample of surface material to bring back to Earth. (It will arrive back at Earth in 2023.) The mission is designed to help scientists understand how planets form and add to what we know about near-Earth asteroids, like the one visited by OSIRIS-REx, asteroid Bennu. Launched in 2016, OSIRIS-REx began orbiting Bennu in 2018 and successfully performed its maneuver to retrieve a sample on October 20, 2020. In the Sample Science problem, students use pi to determine how much of the spacecraft's sample-collection device needed to make contact with the surface of Bennu to meet mission requirements for success.


NASA’s OSIRIS-REx mission was designed to travel to an asteroid called Bennu and bring a small sample back to Earth for further study. To achieve its mission, the spacecraft needed to make contact with 26 cm2 of asteroid Bennu’s surface and collect millimeter-size particles using its "contact-pad samplers." These are 1.5-centimeter diameter circular pads of Velcro-like stainless steel. There are 24 pads on the mechanism designed to collect the samples.

How many pads needed to make contact with Bennu's surface to meet the mission requirement?

If all 24 pads contacted Bennu, how much asteroid surface area would the contact pads sample?

› Learn more about the OSIRIS-REx mission

Illustration of OSIRIS-REx above asteroid Bennu with an inset of the spacecraft's contact-pad samplers.

Image credit: NASA/JPL-Caltech | › Download PDF


Illustrated answer key for the Sample Science problem

Image credit: NASA/JPL-Caltech | + Expand image

Download text-only answer key (doc)


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