## SHHS alum, space mathematician, has asteroid named after him

February 14, 2017

Fred Krogh doesn’t think it’s that big a deal, but the 1956 graduate of Sweet Home High School has an asteroid named for him.

“This thing kind of happened to me (as) a big surprise,” said Krogh, 79, while taking a break from coding at his personal computer at home in Tujunga, Calif. “It was certainly a surprise to have this named for me.”

Krogh was a longtime employee of the Jet Propulsion Laboratory, based in the Pasadena, Calif., area, the leading center for robotic exploration of the solar system. He learned that his name was assigned to the asteroid on Dec. 16.

According to the JPL, Krogh developed an accurate, flexible and fast numerical integration algorithm used to track and navigate NASA interplanetary spacecraft since the 1970s, and his work is at the core of JPL planetary, asteroid and comet orbit solutions and ephemerides, which are the positions of naturally occurring astronomical objects and artificial satellites at any given time or times.

The asteroid, called 5927 Krogh, was first observed on April 9, 1938. The main-belt asteroid (located in the asteroid belt between the orbits of Mars and Jupiter) is approximately 15.8 kilometers in diameter.

“Basically, what I’ve provided is a method for solving differential equations,” Krogh said of his contribution to space science.

Differential equations are about rate of change of a system, Krogh said. “The concept is really a fairly simple concept.”

At its simplest, he explained, a differential equation can be used to calculate the position of a vehicle as it accelerates over time.

“If bacteria are not limited by anything, and they can reproduce in an hour, then they double every hour,” Krogh said. “That is an example of a simple differential equation. (Isaac) Newton’s law of gravitation says that the attraction between bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.

“If you are using this to follow a spacecraft or another body, then the effect from all the planets and other big bodies will affect the path of a spacecraft, according to this law. This is a system of many differential equations that can be solved by computing the change in the solution one small step after another.”

The person Krogh believes nominated him uses differential equations to track solar system bodies that may at some point threaten to hit earth, he said.

“At the time I did the work, it ran about twice as fast as other existing methods,” Krogh said. “That is no longer the case, but it has held its own for many years.”

Krogh has some familiarity with the application of his work, he said. He understands the basics, but he is not an expert. His expertise is in the math and coding. He spent his time with JPL developing a math software library for use by JPL.

“I was a toolmaker,” Krogh said. “It’s like I made a hammer, and they used it to pound some nails.”

As an eighth-grader, Krogh moved with his family to Sweet Home from Kelso, Wash., where his father worked for Weyerhaeuser., His dad had taken a job with Willamette Industries Foster Mill.

Krogh’s older sister, Carol Lindstedt of Portland, said Krogh always had an imagination. Lindstedt herself taught at Oregon Health Sciences University for 41 years.

“Fred was always unique from the time he was born,” she said. “He was kind of a nerd. He was brilliant. He’s still doing research. His work is his love.”

Lindstedt said that as a youth Krogh used to memorize and recite stories and poems, such as “The Rime of the Ancient Mariner” by Samuel Taylor and “The Raven” by Edgar Allen Poe.

“Sweet Home was a nice place,” Krogh recalled. “When I went to high school, I had an interest in science.”

He wanted to be a chemist, he said, crediting his interest to a “good chemistry teacher” at Sweet Home High School, Michael Fiasca. Fiasca, who earned a Ph.D. in science education after teaching in Sweet Home, would drive Krogh to then-Oregon State College for a science project and to work with graduate students.

After graduating from high school, Krogh enrolled at Oregon State, majoring in chemistry. He remained in chemistry until the end of the first term of his junior year. That’s when the ALWAC computer was installed at the college – in 1958.

“I have always felt that I wanted to do stuff that was used directly,” Krogh said. In chemistry, he had planned to work on batteries.

The arrival of the computer at Oregon State, among the first college and universities to get one of the new machines, provided a new opportunity in another area he loved: mathematics. With the computer, he realized that he could be a mathematician and do something beyond teaching.

That computer, which had vacuum tubes and took up a portion of a modestly sized room, had 512 bytes – not kilobytes, he noted – half a kilobyte of memory. It had 32 kilobytes of mass storage. Modern smart phones measure memory and storage in gigabytes – A gigabyte is about 1 billion bytes of information or roughly 1 million times the size of a kilobyte, 1,000 bytes.

“It was amazing to me what you could do with these little computers,” he said, and he began learning to use computer code to solve math problems.

Krogh graduated in 1960 with a bachelor’s degree in math.

“I had no plans to get a Ph.D. at that time, but an offer of an NDEA (National Defense Education Act) fellowship that paid all expenses to get a Ph.D. at OSU was too good to pass up,” Krogh said. He earned his Ph.D. in math in 1964.

“I had no plans for a research career, actually,” Krogh said, but his first job sent him into a two-job career that didn’t really hasn’t ended, even after retirement.

He went to work at TRW, Inc., located in Redondo Beach, Calif., after graduation. The company is best known today for credit reporting, but in those days it was primarily an aerospace company that contracted with the government. Redondo Beach is a center of the aerospace industry.

Along the way, Krogh married Anne-Marie Krogh, his wife of 25 years. He has two children and two grandchildren.

When he started at TRW, the company wanted help for engineers who were having difficulty with math using computers, and TRW gave Krogh the assignment. Among the work were differential and “stiff” equations. Stiff equations require extremely small steps, perhaps so many that a researcher may retire before getting a solution, using typical methods.

Not all problems were ones Krogh could solve, he said.

“I was asked to work on finding solutions for shock spectra. This problem starts with a differential equation and a known solution and asks for the function driving the differential equations. This is a problem that is extremely ill-posed. This means that it has lots of solutions that fit the data and no obvious way to choose between widely differing solutions.

“At the time I had to work on this, it was clear to me and to my boss that neither of us had any idea what to do. So I tried to come up with something, but nothing worthwhile and I knew it. Now there are ideas using regularization that might guide one, although even with that I think you would need more that I was given to have a reasonable chance of coming up with something that made sense.”

He discovered he really liked mathematical research, and he stayed at TRW for four years. Krogh got interested in JPL because of the research opportunities there.

“My boss said he was going to try to find something that would keep me there,” Krogh said. “He found no research funding and I left the secure job there for the less secure job at JPL. That group at TRW was disbanded about three years after I left.”

He found a good fit at JPL, joining a team of six, and worked there for another 30 years before retiring in 1998.

“We were funded to do research in computational math,” Krogh said. “The kind of work done in our group was of more general use than NASA was later interested in funding. Our work was heavily used at JPL, and so we became part of the ‘burden’ budget.”

His team reached seven or eight people at one point, Krogh said. As funding dwindled, the group shrank to three then to two and finally to one person – Krogh.

When NASA reduced funding to half-time, he decided to retire and keep doing the thing he loved, developing software to solve math problems more quickly. Right now, he is working on integer programming, programming where all variables are restricted to integers (whole numbers).

“I’m still doing it,” Krogh said. “But nobody’s paying me for it (except for one company sometimes). I’m happy doing my work. I felt good about the work I did at JPL. Most of the time I was there, I did exactly what I pleased, and people used my work. I felt good about the contributions I was making at JPL.”

The interesting thing about the work is that it’s about finding new ideas “that are better than the way we did them before,” he said. “One nice thing about math is it never ends. There’s always new stuff. I feel like I could work for 1,000 years and I’d never be done.”