A radar beam extends down from a spacecraft flying over Earth's horizon, forming a swath of measurements.


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 11th set, students use pi to figure out how much data the NISAR spacecraft collects every day.



An illustration shows the NISAR spacecraft orbiting above Earth.

The NISAR satellite, shown in this artist’s concept, will use advanced radar imaging to provide an unprecedented view of changes to Earth’s land- and ice-covered surfaces. Image credit: NASA/JPL-Caltech. | > Full image and caption

Orbit Observation

The NISAR mission is an Earth orbiting satellite designed to study our planet's changing ecosystems. It will collect data about Earth's land- and ice-covered surfaces approximately every 6 days, allowing scientists to study changes at the centimeter scale – an unprecedented level of detail. To achieve this feat, NISAR will collect massive amounts of data. In Orbit Observation, students use pi to calculate how much data the NISAR spacecraft captures during each orbit of Earth.


Orbit Observation

NISAR is an Earth-orbiting satellite mission designed to measure centimeter-scale movements and other changes of Earth's land- and ice-covered surfaces twice every 12 days – a scale of coverage and sampling never before achieved.

Using a technique called Synthetic Aperture Radar, NISAR will produce more than 85 terabytes of data products every day (1 TB = 1,000 gigabytes) that will allow scientists to better monitor and mitigate natural disasters and understand the effects of climate change.

NISAR has an imaging swath of 240 kilometers, but the ground track spacing is 231 km to allow overlap between swaths. Given that the Earth’s radius is 6,371 km, how many orbits are executed in one day? How much data is produced per orbit on average?

› Learn more about the NISAR mission

A radar beam extends downward from a spacecraft that is passing over Earth's horizon and coming toward the observer. The beam touches Earth's surface perpendicular to the path of the spacecraft, forming a swath. An inset shows Earth with multiple swaths that wrap around the planet like a ribbon.

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


Illustrated answer key for the Orbit Observation problem.

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

Download text-only answer key (Google Docs)



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