Worth Watching: Randall’s Trauma on ‘This Is Us,’ MLK Jr. Day on ‘mixed-ish,’ ‘Project Blue Book’ Tackles Roswell

This Is Us - Season 4
Ron Batzdorff/NBC

A selective critical checklist of notable Tuesday TV:

This Is Us (9/8c, NBC): There’s a reason Sterling K. Brown has Emmy, Golden Globe and SAG Awards, and multiple nominations, for his role of Randall Pearson, the deeply sensitive adopted son and (not the greatest storyline) newly minted Philadelphia councilman. This episode could easily secure him future nominations, when Randall’s anxieties for his family are triggered by a home-invading burglar. Flashbacks reveal a history of night terrors even before his beloved father Jack (Milo Ventimiglia) died. And now that he’s carrying the secret that his mother, Rebecca (Mandy Moore), is experiencing “‘mild cognitive impairment,” Randall’s need for control is severely shaken. It’s another great showcase for a great actor.

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mixed-ish (9/8c, ABC): The black-ish spinoff takes us back to 1986, when Martin Luther King Jr. Day was first nationally recognized. It’s a big day for the Johnson family, with Paul (Mark-Paul Gosselaar) eager to speak about his personal connection to the late civil-rights leader at the school assembly. Fearing embarrassment from their peers, the kids decide to ditch. On the work front, Alicia (Tika Sumpter) wants to hold father-in-law Harrison (Gary Cole) to his promise to take pro bono civil-rights cases on the holiday instead of golfing. Good luck with that.

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Project Blue Book (10/9c, History): The speculative period piece, revisiting once-classified investigations into UFOs, opens its second season with a doozy: the iconic Roswell incident. In the first episode of a two-part story, astrophysicist Dr. J. Allen Hynek (Game of ThronesAidan Gillen) and Captain Michael Quinn (Michael Malarkey) follow General Harding (Neal McDonough) to the New Mexico site, reopening the file on the infamous 1947 crash after an anonymous townsperson threatens to expose evidence of extraterrestrials.

Inside Tuesday TV: PBS’ absorbing Finding Your Roots (8/7c, check local listings at pbs.org) investigates the Jewish heritage of actor Jeff Goldblum, revered Fresh Air radio host Terry Gross and GLOW star Marc Maron… With International Holocaust Remembrance Day next Monday, PBS marks the 75th anniversary of the liberation of Auschwitz with a special edition of Secrets of the Dead (9/8c, check local listings at pbs.org), “Bombing Auschwitz,” which explores the debate on whether the Allies should have bombed the camp, risking Jewish lives to avoid future atrocities… PBS’s Frontline (10/9c, check local listings at pbs.org) follows with “The Last Survivors,” featuring interviews with some of the last survivors of the Holocaust… Fox’s The Resident (8/7c) finds a way to bring Conrad (Matt Czuchry) back to Chastain, when he encounters a popular soccer star with mysterious symptoms… National Geographic Channel’s Running Wild with Bear Grylls (10/9c) ends its season with Zachary Quinto (Star Trek) racing through a Panamanian jungle with the adventurer to reach an extraction point before a storm reaches land… The outrageous Southern-fried comedian Fortune Feimster (The Mindy Project) scores her first Netflix comedy special, Fortune Feimster: Sweet & Salty, with reflections on her childhood as a Girl Scout and how a certain movie helped her realize she was a lesbian.