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Most people think of Microsoft Excel as a tool for relatively simple tasks like calculating taxes or generating charts. Brian Sutter used an Excel spreadsheet to help design one of the most complex series of orbital trajectories a spacecraft has ever traveled.

Brian is Lockheed Martin’s mission design lead for NASA’s?Lucy?spacecraft, a first-of-its-kind journey to Jupiter’s Trojan asteroids. Lucy successfully launched on Oct. 16, 2021, and now the spacecraft and its full fleet of scientific instruments will fly past one Main Belt asteroid and eight Trojan asteroids looking for clues to the outer solar system’s origins.

The Trojan asteroids are leading and trailing Jupiter in its orbit in gravity wells, making them harder to get to. That’s why Lucy’s orbital trajectory is so complex and includes three Earth gravity slingshots that provide the spacecraft with the “push” it needs to travel so far and on such a precise path.

Brian is being modest when he says Lucy’s four-billion-mile cumulative journey consists of “a very complex series of independent trajectories that I have patched together to create one full-length mission that lasts 12 years.”

NASA originally wanted to rendezvous with two asteroids, but Brian thought there might be a way to explore more of the rocky space objects at a lower cost with a series of flybys. Lucy Principal Investigator Hal Levison of the???was on board and supplied a list of scientifically intriguing Jupiter Trojans that Lucy could visit. “Maybe we can get to three or four, or five or six – let’s try to inspire people,” Brian says.

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Brian took the list and created a baseline trajectory that took Lucy from the Trojan asteroid Eurybates and on to another called Orus. Brian thought, “Maybe there’s other stuff in between that we’re going to be flying by.”

With 750,000 asteroids in the solar system – perhaps only less than 5,000 of them Trojan asteroids – Brian had to find a way to pinpoint ones that Lucy could visit. That’s where the spreadsheet came in.

“I put an orbit propagator (equation) in one of the cells, then I just copy the cell and the ability to say the spacecraft is at this position and velocity in space at this particular time,” Brian explains. “I also have the list of asteroids and their positions and velocities.”

He then used Excel’s macro tool to cycle through all 750,000 asteroids to check for close encounters with interesting Jupiter Trojans. Brian let the tool run until he had a manageable set of “keepers” for Hal. “That’s how I found Leucus and Polymele.” Brian refined possible trajectories further and added two more that Hal particularly wanted to examine: the Patroclus-Menoetius binary. The pair was nowhere close to Lucy on Brian’s original designs, but “I decided to do my homework and figured out how to make Hal happy.”

The initial process took about six months, with Brian refining the trajectories with a commercial software?package?called the Satellite Toolkit (STK). “It gives you the ability to do everything from landing on the Moon to flying a small Earth orbiter, but the Lucy mission took it to the very edges of its capabilities,” Brian says.

The orbital path still needed more tweaking, but Brian had to submit the mission proposal to NASA. In 2017, NASA selected Lucy for its Discovery class of missions. The announcement caught the attention of Jacob Englander, a technologist at NASA’s Goddard 兔子先生 Flight Center who had developed a novel tool called the?Evolutionary Mission Trajectory Generator (EMTG)?.

The fully automated tool makes it easier and much faster to design trajectories for hard-to-reach deep space destinations. Jacob had reverse-engineered the orbital design for Lucy and wanted to know if it resembled Brian’s.

“I said, ‘Holy cow, this is in some ways better than what I had spent the last six months coming up with,” he recalls. “From that moment on, Jacob and I became like peas and carrots, as Forrest Gump would say.” In a few days, the EMTG tool completed optimizing Lucy’s trajectories, at last perfecting it for flight.

Now that Lucy has launched, Brian marvels at the “happy mystery” of how the mission design came together with the right tools, people and timeframe. “We tried looking at doing the mission in another year, but it turns out that this year is the only time we can fly this mission. The bodies literally come into alignment for this 2021 opportunity, and minus a small backup launch window in 2022, that never happens again.”

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With all the gravity assists and flybys, Lucy’s orbital path resembles a pretzel.

First the spacecraft will do a one-year loop around the Sun and then do a close Earth flyby for its first gravity assist. “That might seem like a waste of time, but from an orbital mechanics standpoint it makes sense,” Brian says.

That gravity assist will “slingshot” Lucy past Mars, where it will do a deep space maneuver to change its trajectory so that when the spacecraft returns to Earth orbit for a second time, it will be traveling much faster – from its initial 27,000 mph relative to Earth to 34,000 mph. The second gravity assist, scheduled in 2024, will take that greater velocity and redirect Lucy to the Trojans.

Normally, it takes nine months for a spacecraft to reach Mars. With the gravity assist, “we’re just screaming past the Earth,” Brian explains.? “In four months, we would not only have blown past Mars orbit, but we’re already smack-dab in the middle of (Jupiter’s) main belt asteroids.”

These gravity assists also mean that Lucy needs to bring less propellant on board, significantly saving on weight and cost. Without the gravity assists, the spacecraft would have had to carry five times more fuel to get where it’s supposed to go.?

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