Celestial Method (2014)

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.