There are words and ideas you study in the classroom, but you think you will never encounter them again after you graduate. Words and ideas that you are entirely sure you never will encounter for the rest of your life.

Often you’re absolutely right.

Until, one morning, decades after you first heard terms like “elliptical” and “hyperbolic” in high school math class, there stands before you an accomplished professional, talking about his work, his career, and the crucial role those mathematical geometric concepts and their attendant equations play. Because he uses them to calculate the paths of spaceships headed to and from the planet Mars.

Yes, it’s rocket science.

But as Aaron Brown made clear to the assembled high school boys of the Torah Academy of Bergen County last week, rocket science and the design of manned missions to Mars is no longer science fiction. It’s real.

And it’s also a career you can pursue — assuming you’re willing to embark on a lifetime of actually using geometry and trigonometry and calculus — while being an observant Jew.

Mr. Brown came to TABC in Teaneck as the keynote speaker for the high school’s annual Book Day, when the usual school schedule is cast aside for special speakers, discussions, and activities focusing on one book that had been assigned reading for the entire school. A committee of students works over the summer to pick that coming year’s book. This year’s choice was “The Martian” by Andy Weir.

It’s the story, in the tradition of Robinson Crusoe, of an astronaut left for dead on Mars by colleagues who think him lost; they assume he died in the sandstorm that aborts their mission. In fact, he is only unconscious. He awakens to the sound of the oxygen alarm going off in his space suit, pulls out the piece of metal that pierced his suit and leg, and heads back to the now empty base. Having fixed his spacesuit and saved his own life, he next discovers that his food will run out before the next scheduled mission from earth, and that the radio antenna used to communicate with earth was lost in the sand storm.

Determined not to become the first man to die on Mars, he sets about improvising what he needs to survive.

“There’s a wide variety of scientifically oriented ideas as well as psychological ideas in the book,” Dr. Carol Master said. Dr. Master chairs TABC’s English department and  together with librarian Leah Moskovits runs Book Day — which this year featured more than two dozen different sessions on topics ranging from physics to Jewish paradigms of self-reliance, as well as presentations from the Coast Guard and an Escape Room.

“It’s a full day, one that’s very exciting for the students,” she said. “We bring in people who normally would not be here.”

Orbital diagram for mission to Mars.

Normally, Mr. Brown is in Houston. He works at NASA’s Lyndon B. Johnson Space Center, part of the Orion project, which is building a spacecraft to send humans into deep space — first around the moon, then onto the moon, and then, sometime in the 2030s or 2040s, to Mars.

Specifically, he works on Orion’s onboard navigation system.

“If we don’t know where we are and what speed we’re traveling, we can’t figure out how to get where we’re going,” he said. “Even if I know precisely where the moon or Mars is, I can’t guide the spacecraft to get there.”

To figure out where it is, the Orion will rely on GPS when it’s close to Earth. Further out, it tracks its position using celestial navigation — figuring out where it is in relation to the stars.

So how does a spacecraft plot its course to Mars?

“There’s a classic problem in orbital mechanics called an Earth-Mars transfer. It’s the kind of stuff I studied in college and grad school,” Mr. Brown, 41, said.

This is when he showed the students an illustration of the planets, their orbits, and the path the spaceship would take. Describing the moment when the spaceship maneuvers from its orbit around the sun, which took it from Earth to Mars, to its new orbit around Mars, he said: “At this moment you can think of your orbit as being both a hyperbola and an ellipse. Hyperbolic in respect to earth, elliptical in respect to the sun.”

And there you have it. High school math terms, used in real life.

Speaking to the high school, Mr. Brown drew a broader lesson from this bit of orbital mechanics, which is known as patched conic analysis.

“Holding these two contradictory pictures of the orbit in my mind is exactly what’s required to get more to the emes” — he used the Hebrew word for truth — “of the fuel that I need to switch orbits. This is analogous pretty much to any page of Talmud that you open. There’s a contradiction between two verses, or between a mishna and another text. In the Gemara we find a contradiction and the Gemara works its way out of it. Here in patched conic analysis we work our way through it.

“That skill of holding two contradictory viewpoints in our mind at the time to get to the emes is the same in both Gemara and patched conic analysis. The takeaway message is to practice this skill anywhere you find a contradiction in life, whether in Talmud or science or relationships or politics. This method of holding these two contradictory points in our mind is often the only way to get to the emes.

“The Martian,” chosen for TABC Book Day

“NASA is very supportive of religious practice,” Mr. Brown said. “I never experienced any anti-Semitism or restriction of religious practice.

“I often get questions at work from colleagues about Judaism. One of my good friends there, a mentor of mine, is a very devout Mormon. Not surprisingly, non-Jews don’t really know a lot of what Judaism is about. I feel we have an obligation to know what we’re talking about when non-Jews asks us questions about what Judaism is or what it believes.”

Mr. Brown, who is from Peoria, Illinois, and later moved to Buffalo Grove, a suburb of Chicago, did not grow up observant. That might have made it easier to embark on his path to rocket science, which began with attending space camp as a child.

“I started on the path to observance from the questions I got when I was working in NASA,” he said. “It’s my non-Jewish work environment that helped me shape and enhance my Jewish identity. On a practical, day-in day-out level, I bring all my food with me every day. I go find an unoccupied office and have a siddur app on my iPhone to daven.

“Thankfully, Shabbos isn’t a problem in the division I’m working in.”

It did come up in a previous NASA posting: From 2000 to 2006, he was a flight controller in the mission control center for the International Space Station.

Operating a space station, unlike designing a rocket, is a 24-7 task.

“It’s very possible that when you’re working in mission control that you’re scheduled for a Saturday,” he said. “I had to have someone cover my shift when it happened.”

Mr. Brown was a trajectory operations officer at mission control. “My job was to monitor the orbit of the space station and make sure it was where it was supposed to be. I worked with my Russian counterpart to execute burns to adjust its orbit.

“A trajectory operations officer watches out for orbital debris, or space junk. If a piece of debris is orbiting and predicted to collide with the space station, you have to do a debris avoidance maneuver to get out of the way. It changes the orbit of the space station so the two pass by safely and there’s no chance of a collision.”

As for other possible collisions between religious observance and the workplace, “there is almost always a way to make things work,” Mr. Brown said. “The key is to be prepared. I try to anticipate whatever religious needs I have, where there might be conflict points. I talk with my rabbi about what I need to do and I work it out with my boss. It’s always important to be respectful of your employer.”