The phrase "a trajectory that would" is correct and usable in written English.
It can be used when discussing a path or course of action that is expected or intended to lead to a certain outcome.
Example: "The research indicates a trajectory that would lead to significant advancements in renewable energy technology."
Alternatives: "a path that would" or "a course that would".
NovaStar was on a trajectory that would take the shares above $70.
Linvill helped launch Stanford on a trajectory that would ensure Stanford's continuing leadership in electronics engineering for decades to come.
A tawny, humpbacked grizzly had ambled down the left bank and was casually swimming across the river on a trajectory that would, within seconds, intersect our own.
For Rotolo, it was a trajectory that would take her from the sweetness of first love to the trauma of abortion.
It's a trajectory that would make fame-hungry hustlers weep, yet Jones has remained largely under the radar outside the fashion industry.
Pyongyang has not, however, proved it has the capability to marry a miniaturised nuclear warhead with a long-range missile and send it at a trajectory that would hit US cities.
Born to Ruby and Aubrey Pryde, on a depression-era farm near Sunnyside, Washington, Harry planned a life trajectory that would take him from asparagus fields in the Yakima Valley, to Seattle, to Washington D.C., and to most of the world.
Opposition leader Morgan Tsvangirai told the BBC he hoped that Zimbabwe was on a "new trajectory" that would include free and fair elections.
As such, reducing risk to hurricanes in the post-disaster reconstruction efforts locked Montserrat in to high exposure to volcanic risk and a development trajectory that would prove difficult to alter in the face of an abrupt change in the volcanic hazard.
In the knockout stages of the Champions League, Manchester United, Lyon and Deportivo fell before the final against Monaco, another side on an upward trajectory that would soon lose Jérôme Rothen, Ludovic Giuly and loanees Hugo Ibarra, Édouard Cissé, and Fernando Morientes.
With these signatures and their golden records on board, the twin spacecraft were launched in late summer of 1977 from Cape Canaveral and placed on a "grand tour" trajectory that would carry them on fleeting, but historic fly-bys of Jupiter and its moons, and then on to Saturn and its rings.
