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"his trajectory" is a perfectly acceptable phrase in written English.
You can use it to refer to the course someone is taking in life, their progress, or the direction of their future. For example, "After years of hard work, his trajectory has been pointing towards success."
Exact(59)
The painted contacts, which he has been doing for several decades, sum up his trajectory, employing painting, photography and a hint of movie-like editing.
Even as he was arriving at The New Yorker, his trajectory was taking him away from it and into the wider spaces of the novel.
His trajectory is instructive.
But his trajectory paralleled the age.
But consider his trajectory so far.
Could we have changed his trajectory?
Other Blair-watchers see his trajectory differently.
His trajectory underscores some of the ways that approach fails.
His people certainly saw his trajectory as a tragedy.
"His trajectory illustrated the transient nature of power".
Similar(1)
I wondered if his trajectory in New Orleans would be like Ewing's in New York — a diamond in the rough, who never got enough help.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com