Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Here are just some of the ways pi helps us explore space.
Artist's rendering of MSL's parachute deploying on Mars

1. Parachuting on Mars

While no Mars landing is exactly the same, they do share one thing in common: parachutes. Slowing down a rover or lander as it drops through the thin Martian atmosphere is imperative if engineers hope to slow the spacecraft enough to give the descent rockets time for a soft landing. NASA’s engineers take all sorts of things into consideration when designing a parachute: the mass and velocity of the spacecraft, the elevation of the landing site and the density of the atmosphere, just to name a few. Pi helps engineers determine how big the parachute needs to be in order to generate the drag needed to slow down.
The Cassini spacecraft's orbits about Saturn from 2004-2017

2. Getting new perspectives on Saturn

NASA’s Cassini spacecraft spent 13 years orbiting Saturn, discovering seas and jets of water ice on its moons, and observing its majestic rings. Twice during the mission, engineers used a technique called a pi transfer to alter the spacecraft’s orbit. With a precisely steered flyby of Saturn’s largest moon, Titan, Cassini’s orbit was flipped 180 degrees to the opposite side of the planet. (In radians, 180 degrees is equal to pi, hence the name pi transfer.) With the lighting conditions also flipped 180 degrees, from Cassini's perspective, the spacecraft was able to see Saturn and Titan in a whole new light. 

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Animation of the Juno spacecraft mapping Jupiter

3. Mapping unexplored (and familiar) worlds

Just like Earth’s ancient explorers, when spacecraft visit other planets and worlds, they make a map. Even spacecraft that orbit familiar places, like Earth, make maps of processes scientists want to understand, such as how water flows around the globe. Spacecraft make maps by taking images as they orbit. Their cameras often have rectangular fields of view that capture images in “bands” on the surface of a planet. Scientists use pi in the formula for surface area to figure out how many images it will take to map the entire planet or body.

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4. Landing on Mars

Engineers use pi to help estimate the amount of uncertainty in the position where a Mars lander or rover will touch down. Many aspects of landing on Mars are uncertain: winds, air density, the initial speed and position of the spacecraft when approaching Mars from Earth. Even the exact position of Mars itself is not perfectly known. Before a Mars landing, most of these uncertainties can be modeled using mathematical distributions that include pi in the calculations. When simulated together, the result is potentially miles of position uncertainty surrounding the targeted landing spot. Engineers take this uncertainty into consideration and are careful about where they aim! For example, they can aim close, but not too close to a mountain – like they did with the Curiosity Mars rover, which landed near Mount Sharp.

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Animation of planets transiting their star

5. Exploring new worlds

Scientists use pi to search for exoplanets, which are planets that orbit stars other than our own Sun. Powerful ground- and space-based telescopes track how much light is emitted by distant stars. When a planet passes in front of its star, the telescope sees a dip in the amount of light emitted. Knowing the percentage of this decrease and the formula for the area of a circle, scientists can deduce the planet’s size.

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6. Discovering potentially habitable worlds

When scientists discover new exoplanets, one of the things they want to know is whether these worlds could support life as we know it. These “potentially habitable” worlds orbit within what’s known as the habitable zone of their parent stars – a location that’s a safe distance from the star, not too close, where water would turn to gas, and not too far, where it would become ice. Scientists use pi to locate the inner and outer edges of the habitable zone around a given star. And they use pi, along with Kepler’s third law, to calculate how long it takes the exoplanet to make one full orbit of its star, which reveals the planet’s location and whether it’s in the habitable zone.

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Artist's concept of the InSight Mars lander on the Red Planet

7. Locating quakes on Mars

Scientists use pi to study earthquakes and, soon, marsquakes! NASA’s InSight Mars lander is equipped with an instrument for measuring seismic activity on the Red Planet, which will tell us more about what’s going on inside the planet. During a marsquake, surface waves – a type of seismic wave – travel outward from the epicenter in all directions on Mars. By timing the arrival of these surface waves at the InSight lander and using pi, scientists can determine what time the marsquake occurred.

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A DSN Antenna in Goldstone, California

8. Talking to spacecraft

Sending messages to distant spacecraft and receiving them requires a network of massive antennas stationed around the globe so that, as the world turns, we never lose contact. Together, these antennas make up NASA’s Deep Space Network, or DSN. The engineers who communicate with spacecraft through the DSN use pi in the math equations needed to send messages and process those that are sent back. It’s a pretty important task considering the messages are used to do things like land rovers on Mars and get images from a spacecraft flying closely by Pluto for the first time.

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Animation of the Curiosity rover driving on Mars

9. Driving Mars rovers

There are no joysticks or steering wheels on Mars rovers. Instead, rovers receive commands from operators on Earth that tell them when and how to drive, take pictures, turn their wheels and use their robotic arms. Some of these functions are measured in degrees and others in radians (slices of a circle), so pi is regularly used to convert between the two.
Animation of Juno's orbit insertion and orbits about Jupiter

10. Getting spacecraft into orbit

Engineers use pi to put spacecraft into orbit around other planets. To do this, they have to slow down the spacecraft just enough and at exactly the right time for it to get pulled into orbit by the planet’s gravity. Engineers determine how much that gravity will tug on the spacecraft, how fast the spacecraft is going and the details of the new orbit. Using those numbers, along with pi, they can compute exactly how much they need to put on the brakes – which for a spacecraft, means firing its forward-facing thrusters at just the right moment.

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Animation of asteroid 'Oumuamua

11. Tracking the movements of asteroids

One of the jobs of comet and asteroid hunters, like those at NASA’s Center for Near-Earth Objects, is to determine how quickly an object is rotating. From their observations of the object, scientists can estimate how long it takes the object to make one complete rotation on its axis. Then, unit conversion is used to find the object’s angular velocity, which is often measured in radians per second. (You can think of radians as slices of a circle, or better yet, slices of pi.)

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Curiosity rover wheel marks

12. Keeping rover wheels turning

Rover wheels have distinct designs on them that leave patterns on the ground as they turn. These patterns serve as visual markers that help operators while driving the Mars rovers remotely from Earth. Pi is used to calculate how far the rover should travel with each wheel rotation. By measuring the distance from one wheel mark to another, rover drivers can determine if the wheels are slipping or if they’ve driven the expected distance.

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Jupiter's icy moon Europa

13. Investigating alien ice

Scientists studying extreme environments, such as those on comets and the moons of Jupiter and Saturn, want to learn how processes unfold on their surfaces. In the case of icy environments, one way to do that is by using lasers in the laboratory to explode ice samples and then studying the chemical reaction that takes place. Scientists use pi to calculate the beam width of the laser and understand how much energy is hitting their ice sample.

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Technicians install a special radiation vault onto the propulsion module of NASA's Juno spacecraft at the Lockheed Martin facility in Denver, Colorado.

14. Fueling up spacecraft

Just like cars, spacecraft require fuel to get where they’re going and to maneuver throughout their journey. But in space, there’s no refueling along the way. Determining how much fuel a spacecraft will need and how much it has used is a delicate task. Engineers use pi to compute how much fuel is available in spacecraft tanks, which are commonly spherical, and how quickly that fuel travels through their cylindrical fuel lines. Even donut-shaped (toroidal) tanks, which can hold a lot of propellant but take up much less space, require the use of pi.

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Pluto in false color as imaged by NASA's New Horizons spacecraft

15. Measuring the size of Pluto's heart

While studying the surfaces of other worlds and even Earth, scientists use pi to determine the size of features on the surface. To size up circular shapes, such as craters, the math is simple, while unusual shapes, like Pluto’s “heart,” require trigonometry or calculus.

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Craters on Mars as imaged by NASA's Mars Reconnaissance Orbiter

16. Revealing crater clues

Craters can tell scientists a lot about the surfaces of planets, moons and other bodies. Just by determining how circular a given crater is – using pi and the crater’s perimeter and area – planetary geologists can reveal clues about how the crater was formed and the surface that was impacted.

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Artist's concept of the metal asteroid Psyche

17. Revealing what planets and asteroids are made of

How do scientists find out what other planets and asteroids are made of if they can’t visit them in person? Using pi, of course. Planetary scientists use pi to determine the volume of rocky planets or asteroids. Volume, together with the object’s mass, tells them its density. And because planetary materials like rock, ice and metal have known densities, scientists can make informed guesses about what the planet or asteroid might be made of based on the object’s density.

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Illustration of the interior of Jupiter

18. Peering below Jupiter's clouds

One of the ways that scientists study what’s happening inside the thick swirling clouds on gas giant planets, like Jupiter and Saturn, is by sending spacecraft that can analyze the chemical makeup of these worlds. Scientists then use pi in combination with the spacecraft sensor data to estimate the volume of materials in the planet’s atmosphere. For example, in 1995, the Galileo spacecraft dropped a probe into Jupiter and detected unusually low levels of helium in the upper atmosphere. After studying the data, scientists hypothesized that helium could be raining out of the upper level of Jupiter’s atmosphere and pi held the key to how much. Today, the Juno spacecraft, which arrived at Jupiter in 2016, is helping scientists get an even better picture of what’s going on inside the planet.

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