Final answer:
The most compelling detail illustrating Katherine Johnson's expert skills is her ability to calculate the trajectory for the first moon landing and her reverse-engineering approach to launch timings. Additionally, her authorship of numerous research articles and glowing endorsements from academic mentors and peers corroborate her expertise and reliability.
Step-by-step explanation:
One detail that best supports the idea that people count on Katherine Johnson for her expert skills and accuracy is her ability to calculate the trajectory for the first moon landing. Katherine Johnson's expertise was crucial when she confidently addressed the problem of timing space launches by reverse-engineering the desired landing outcome. She famously said, "You tell me when you want it and where you want it to land, and I'll do it backwards and tell you when to take off." This not only displays her sheer computation prowess but also her innovative approach to problem-solving. Additionally, Johnson's significant contribution of writing or co-writing 26 research articles during her 33 years with NASA further strengthens the belief in her expert skills and accuracy. Her dedication to understanding her work, as evidenced by her curiosity and comprehensive approach, made her a dependable and remarkable mathematician at NASA.
Yet another aspect that showcases her expertise is how she was regarded by her peers and mentors. Statements like "She was one of our best students throughout her course and graduated with an unusually broad and thorough training" demonstrate the respect and high esteem in which she was held by those who were familiar with her intellectual capabilities. Johnson's remarkable background and her lauded academic journey underscore her reputation as a trusted and accurate mathematician.