Celestial Method

Nonoka Komiya moves with her family to her old hometown of Lake Kiriya City, which now has a large flying saucer floating above it. While her father is out the next day, Nonoka encounters a strange girl named Noel, who claims they met each other a long time ago. As Nonoka tries to remember who Noel is, she gets mad at her when she assumes she had cracked a photo of her late mother whilst unpacking her things, telling her not to appear before her again. Upon later learning that the crack was actually an accident on her father's part, Nonoka searches for Noel in order to apologize, during which she remembers knowing Noel from her childhood, realizing she had been waiting at the observatory for her return. As the two reunite at the observatory, Noel states her desire to fulfill her promise to grant Nonoka's wishes.

On her first day at school, Nonoka befriends with a girl named Koharu Shiihara, but becomes alienated by another girl in headphones, Shione Togawa, both of whom she had previously encountered whilst searching for Noel the other day. Another girl, Yuzuki Mizusaka, vents her irritation that noone else in town seems to be concerned about the saucer that appeared seven years ago, roping Nonoka into helping her protest against it. After getting into an argument with her brother, Souta, Yuzuki prepares to go fight against the saucer herself, but is stopped by Nonoka, who decides to help her with her cause provided she not do anything dangerous. Later that night, Nonoka asks Noel for help in getting the saucer to leave the city as well.

While on an orienteering trip with the others, Nonoka feels confused as to why Shione is so hostile towards her. The girls soon encounter Noel along the way and have her join their group. Later, when it seems that Shione has strayed from the group, Nonoka goes off in search for her, unaware that Shione had actually gotten ahead of them, winding up lost herself. After ending up at an abandoned kindergarten and eventually being found by Noel, Nonoka remembers that not only was she friends with everyone seven years ago, but she was the one who suggested they call forth the saucer, with Noel revealing she is the saucer itself.

Nonoka remembers having tried to call with her friends seven years ago. Yuzuki, having regretted what she'd done, takes it out on Nonoka. Nonoka insists she didn't remember, but Shione remains dismissive. Noel arrives the next day at Nonoka's house, for some reason apologizing.

Things are still awkward between Yuzuki and Nonoka. Nonoka, believing something might change if they could fulfil their promise from seven years back to watch fireworks together, begins working towards that with Koharu's help.

Nonoka and Noel participate in a raffle at the shopping district. Noel wants the first prize -- tickets for a stay at a hot spring -- but Shione wins that prize instead.

Nonoka, Yuzuki and Koharu go on a trip to the outskirts of town. Meanwhile, Noel and Souta are busy trying to heal the store's symbol, Kirigon.

Wanting to grant Shione's wish without waiting for the next meteor shower, Nonoka and the others decide to make a planetarium for the school's Hokubi Festival, inviting Shione to participate. The next day, Shione decides to visit Noel, who she had also met seven years ago, having previously received a message from her that Nonoka would return to watch the meteor shower with her, though the time she waited led her to become distrustful of her. Shione expresses to Noel how she is afraid of putting her trust in Nonoka again, but Noel gives her some encouragement. Later that night, Shione arrives at the finished planetarium, where Nonoka firmly states her desire of watching a meteor shower with her, with the two making up with each other. However, the next day, after Shione recalls Noel calling herself the saucer, she tells Nonoka that they can't be together.

As Nonoka decides to put her trust in Shione and wait for her, Shione learns that Noel will disappear when she has granted everyone's wishes. While everyone else helps to finish the planetarium, Shione makes plans to move out of town, recalling how she and the others each made wishes while summoning the saucer. On the day of the festival, Nonoka escorts Noel around the school, becoming anxious over whether Shione will show up or not. Learning Shione is absent, Nonoka goes off to confront her over why she's trying to stay away from her, but is unable to get through to her. Noel then goes off in search of Nonoka, only to collapse in front of her.

Realising Noel's condition is from straying too far from the saucer, Nonoka calls her father to take them back home to where she can see the saucer. After getting Noel back safely, Nonoka tells the others the truth that Noel is the saucer they summoned seven years ago, which is why she can't leave town. Nonoka later then learns from Noel that she will disappear when she fulfils her assigned wish, in this case, Shione's wish to smile together with Nonoka. The next day, Nonoka learns that Shione is transferring and goes to talk to her once more, learning that she intended to move so that Noel wouldn't have to disappear. As Nonoka becomes conflicted over choosing between Noel and Shione, Shione explains the situation concerning Noel to the others, who argue over who should leave so that Noel can stay. Truly wishing for everyone to smile together, Noel tells Nonoka they will have to part ways.

With everyone still avoiding each other, Nonoka makes a decision to invite everyone to the observatory to watch the meteor shower, despite the cloudy weather. As Nonoka speaks with Shione, stating her desire to make everyone happy and asking her to speak to Noel, Souta, Yuzuki, and Koharu do their own reflecting, believing Noel granted their wishes to become friends with everyone. Later that night, Shione speaks with Noel, who says she is happiest when everyone else is happy. Afterwards, everyone, Shione included, gathers at the observatory, where they take some pictures together before Noel receives a signal telling her to go home. After a tearful farewell, everyone watches the meteor shower together, where Noel finds herself unable to hold back her tears as well before both she and the saucer vanish.

Nonoka suddenly finds herself returning to the day she arrived in Lake Kiriya, this time with the saucer nowhere to be seen above the city, like it was never there to begin with. Furthermore, she discovers none of her friends have any memories of Noel or the saucer, and Shione is nowhere to be found, later learning she moved away during elementary school. As Nonoka starts to doubt herself over whether Noel even existed in the first place, Shione appears before her, revealing that she has also retained her memories of Noel.

After Shione encourages Nonoka to not give up on Noel, the two of them concoct a plan to bring everyone to the observatory. The others, despite still not remembering Noel, feel there is something important they are forgetting and agree to try and summon the saucer once more. Together, they wish to see Noel again, after which a large field of sunflowers suddenly appears near the observatory, but no Noel. The next day, Nonoka learns from her father that someone was in her house, while the others start to regain their memories of Noel, and together they head towards the sunflower field, where Noel is waiting for them.