tire track; wheel track
A physical line or mark left by a tire or wheel; in everyday speech タイヤの跡 is often plainer, while 軌跡 sounds a little more descriptive or technical.
Clear tire tracks remained on the snowy road.
traces; path taken; record of a course
Used figuratively for the path, development, or trace left by a person, organization, work, or event over time. Common in phrases such as 軌跡をたどる and 軌跡を振り返る.
A book tracing the course of his research was published.
This exhibition presents the artist's forty-year journey.
locus
Mathematical term for the set or path of points satisfying a given condition.
Find the locus of point P that satisfies the condition.
A program tracing the path of his life was broadcast.
It was an interview looking back on 40 years of history.
This curve is the locus of points equidistant from the origin.
足跡 literally means footprint but is often used figuratively for someone's achievements, much like 軌跡 is used for the path of a person's career or history.
歩み emphasizes the steady progress or development of something, while 軌跡 emphasizes the trace or path that progress has left behind.
軌道 refers to a course or orbit something follows, while 軌跡 refers to the trace or path actually left behind as it moved.
奇跡 is a homophone meaning 'miracle,' completely unrelated in meaning and kanji to 軌跡.
軌跡 refers to a trace or locus left behind by movement (often used abstractly or mathematically), whereas 軌道 refers to a planned or fixed path such as an orbit or track.
軌跡 shares the kanji 跡 with 痕跡 but means the path or trajectory something has followed, not a leftover mark.
軌跡 (a near-homophone) means the path or trajectory something has traced, not a sign of a past event like 形跡.
Standard kanji spelling. Be careful not to confuse it with the homophone 奇跡, meaning “miracle.”
Sino-Japanese compound. 軌 is associated with a wheel track or course, and 跡 with a trace or mark; together they express a track, trace, or path.