Finally, the Doctor is a woman. Sunday night, Jodie Whittaker became the Thirteenth Doctor, replacing Peter Capaldi as the star of the long-running British science-fiction adventure series “Doctor Who” (seen here on BBC America).

It’s a big step in the life of the series, which also installs Chris Chibnall, formerly the head writer of the “Who”-spun “Torchwood,” as its new showrunner. And yet it is very much like all such steps before it: One actor passes the role to another; the Doctor — a Time Lord from the planet Gallifrey — takes on a new form and personality, which is not entirely distinct from his, now her, preceding selves. Thus has it been since an ailing William Hartnell, who played the First Doctor, transformed into Patrick Troughton, Doctor Two, back in 1966 — an invention mothered by necessity.

“We’re all capable of the most incredible change,” the Doctor will say, of herself and everybody, making a point not incidentally germane to the series itself. “We can evolve while still staying true to who we are. We can honor who we’ve been and choose who we want to be next.”

After 55 years, 36 seasons, one TV movie and 12 officially numbered Doctors, to have gone with yet another white male — in a series where everything is possible — would have seemed almost pointless. As in the actual world, we have had many, many, many variations on that old theme; a new tune is called for. Whittaker being named to the part came not just as a great news — she’s a wonderful actress, to start, and one fit for the job — but as a kind of relief.

Chibnall created the small-town mystery series “Broadchurch,” in which Whittaker costarred (alongside Tenth Doctor David Tennant), and there’s a convincing ordinariness underpinning the fantastic events here; he takes his time introducing the alien elements. We are in Sheffield, an industrial city in South Yorkshire — you might think of it as the Pittsburgh of England — near where Whittaker, who uses her own accent here, grew up and where Chibnall went to university.

The human characters, some of whom will continue in the Doctor’s company — the Doctor likes company — are seemingly regular folks whose most extraordinarily shared ability is to accept the apparently impossible without losing their minds. Ryan Sinclair (Tosin Cole) works in a warehouse and entertains thoughts of becoming a mechanic. We meet him trying to ride a bike — he has a “coordination disorder” — with the help of his grandmother, Grace (Sharon D. Clarke), a nurse, and her second husband, Graham O’Brien (Bradley Walsh), a retired bus driver.

Ryan will discover a … thing — reviewers have been asked to be discreet about details — which will lead to him meeting Yasmin Khan (Mandip Gill), an old primary school classmate, now a probationary police officer longing for “something that will test me, me, something a bit different.” And they will all find themselves together in … a place, confronted by a … danger. Suddenly, the Doctor enters from above, like a classical goddess in a Renaissance play. “Should buy us a few seconds” are the first words she speaks, as Ron Grainer’s theme pulses softly behind her. It’s a thrilling moment.

At 36, Whittaker is a little younger than Christopher Eccleston was when he played the first 21st century Doctor, in 2005, and a little older than Tennant was when, later that same year, he followed Eccleston into the role. In this respect, she resembles the Doctors of the Russell T Davies era — it was Davies who brought the show back from limbo to newly international success — more than of the Steven Moffat, who were much younger (Matt Smith), or much older (Capaldi).

She has both authority and energy; she is playful yet mature, a little mad but not manic, funny and agile and perhaps will turn out a shade less judgmental than some of her predecessors.

“The Woman Who Fell to Earth” does feel like a fresh start; Moffat’s later years were heavy in tone and hobbled by long arcs and psychology. If only for a transitional moment, but maybe longer, the new season has put that baggage down.