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"on a trajectory" is correct and usable in written English.
You can use it to describe a path or movement that is in progress and has a specific direction, as in, "The project is on a trajectory towards completion."
Exact(60)
Now he seems to be on a trajectory to make gay rights one of his Administration's most lasting accomplishments.
It is on a trajectory to get worse.
"We have set ourselves on a trajectory," Mr. Fillon said.
Harm is defined as a normative judgment on a trajectory.
Furthermore, Windows 8 and Windows Phone look as though they're on a trajectory of convergence.
The show is three decades old but hard to place on a trajectory of the times.
He added: "We are on a trajectory to reach record levels of car manufacturing by 2020".
Scalable startups are on a trajectory for a billion dollar market cap.
We're nowhere close to being on a trajectory for achieving that.
NovaStar was on a trajectory that would take the shares above $70.
"Clearly today Egypt is not on a trajectory to democracy, pluralism, tolerance.
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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