I heard this song via Yuming's（ユーミン）big 4-CD collection of her best works, "Seasons Colours" from 2007. However, "Giacobini Suisei no Hi" (The Story of Giacobini's Comet) was originally part of her 8th album, "Kanashii hodo O-Tenki"（悲しいほどお天気...The Gallery in my Heart）from 1979.
By this point in the late 70s, it was Yumi Matsutoya（松任谷由実） and not Yumi Arai（荒井由実）, but listening to this introspective song, I couldn't help but feel that there still was that New Music of the Arai days in this story of comet sightings and lost romance. The singer-songwriter based the song on her own experiences of seeing the Giacobinids meteor shower (officially known as the October Draconids) back in October 1972. Listening to her sing about dragging the chair to a window in her darkened room while also relating about the one that got away can get one into that melancholy mood.
"Kanashii hodo O-Tenki" peaked at No. 6 on the album charts.
Here is a short excerpt with appropriate video.