"begin its descent" is correct and usable in written English.
You can use it to describe a gradual, downward movement, such as the gradual decline of a stock market index. For example, "The Dow Jones Index began its descent in the second quarter of the year."
The grapevine is now a hundred feet long, stretching from the yard to the back of the house, up four stories, and across the roof; another few years and it should begin its descent toward the front stoop.
Yet he also helped begin its descent by playing upon chauvinist Muslim fears for political gain.
At 11 59 the ball will begin its descent, accompanied by pyrotechnics at midnight.
At Souvenirs on 5th, a gift shop on West 34th Street, Carlos Flores had time to rearrange merchandise just 12 hours before the crystal ball was to begin its descent toward the throng in Times Square.
The platform, which SpaceX calls "the autonomous spaceport drone ship", is the intended landing site for the rocket, which is as tall as a 14-story building and will begin its descent moving at nearly a mile a second.
When the novelist Robert Musil, on the first page of "The Man Without Qualities," placidly launched his Viennese epic on "a fine August day in the year 1913," he was indulging in the deepest irony: a year later, with the beginning of the First World War, the Austro-Hungarian Empire would begin its descent into ruin.
In another incident, a drone had a near-miss with an Airbus A320 as it began its descent into Heathrow.
Once SR 89A reaches passes over the mountains, it begins its descent into the Verde Valley.
On most coasters without a pre-drop, the weight of the train tends to pull on the lift chain as it begins its descent because the latter half of the train is still being lifted by the chain.
On the solstice and for several days surrounding it, the sun stands sentinel at dawn, hovering, as it were, before beginning its descent into dark.
The soap opera genre, it turned out, had begun its descent into irrelevancy, and the situation wasn't going to improve.
