The plot involves a scientific paper on asteroids. In the original Conan Doyle stories, Holmes's arch-enemy Moriarty is the author of a scientific paper on the dynamics of an asteroid.
Julius Kent teases Sherlock for having believed, at age 8, that the sun moves around the earth. The original Holmes, on being told that the earth goes around the sun, said he would do his best to forget that bit of information, to make room for something useful to him.
This the 100th episode of the series.
Celebrity astronomer Julius "Cosmos" Kent with "jazz hands" is an obvious nod to Neil deGrasse Tyson.
Although the characters of Sherlock and Julius Kent are supposed to be around the same age and knew each other when Sherlock was 8. Owain Yeoman (Julius) is actually 6 years younger than Johnny Lee Miller (Sherlock).