The first woman to win the Gold Medal of the Royal Astronomical Society was Caroline Herschel (who is already at Level 4) in 1828. The only woman to win the full award since then was Vera Rubin in 1996.

Rubin found the first observational evidence for unseen dark matter in the universe. It has since been ruled out that dark matter could be explained by macroscopic objects (e.g. neutron stars, white dwarfs, ejected planets) that are just too faint to be detected. The only options that leaves are: (1) dark matter is made of a new elementary particle --- the prevalent idea, or (2) the laws of gravity need to be refined at galactic scales. Either way, Rubin's discovery indicated there is some new fundamental physics that has yet to be discovered. It is widely accepted by astronomers that Rubin should have won the Nobel Prize for the discovery of dark matter, but was snubbed (see the New York Times or Popular Science for instance).

As Gabriel Fahrenheit is not on the list, I presume Anders Celsius is not here just because he has a temperature scale named after him. Out of the three temperature scale people, Lord Kelvin is probably the only one who deserves to be at this level. Celsius does not have any significant contributions in astronomy compared to what the other astronomers listed at this level have done.

Most of the astronomers at Level 4 either made major contributions to understanding the Earth's place in the universe (Galileo, Copernicus, Kepler, Brahe, and to some extent Halley, both Herschels, and Sagan) or to understanding fundamental physics (Hubble and Lemaitre). Celsius doesn't really fall into either of those categories. On the other hand, Rubin clearly falls into the second one.

Billie Jean King isn't just the most vital women's tennis player, she is the most vital woman's athlete in any sport. When she was last removed from Level 4, the discussion was centered around what she did as a player. While she may only be the 6th-best player in the Open Era (with Court 4th), it's important not to overlook her other accomplishments.

King founded the WTA Tour, and also played a key role in establishing the first women-only professional tournament. Moreover, King's victory over Bobby Riggs in the Battle of the Sexes in 1973 made it legitimate for women's tennis to become professional, and for women to earn a respectable amount of prize money compared to men. Today, tennis is the only sport where women's athletes can earn anywhere near the same amount of prize money as men's athletes, and King is the main person responsible for that.

Court's main accomplishment is that she holds the record for most Grand Slam singles titles. Yet, this record did not hold that much significance until recently. The idea of counting Grand Slam titles in general is somewhat misleading given that it wasn't until this century that it became the norm for players to compete regularly at all four Grand Slam tournaments, a fact that tennis historians are aware of. Even players who came after Court (e.g. Navratilova, Graf, Connors) did not regularly enter all four major tournaments each year like all players do today. The fact that Graf has just two less Grand Slam singles titles than Court, and Serena one less than Court, along with the fact that half of Court's titles came before the Open Era also diminish this accomplishment and have led experts to rank players like Serena, Graf, and Navratilova ahead of Court despite them having fewer Grand Slam singles titles.

"Frequently mentioned as a candidate for the Nobel Prize,"... "her work helped usher in a Copernican-scale change in cosmic consciousness, namely the realization that what astronomers always saw and thought was the universe is just the visible tip of a lumbering iceberg of mystery." [1]

In 1996, Rubin became the first woman to win the Gold Medal of the Royal Astronomical Society since Caroline Herschel (in 1828), who is also at this level. Rubin is also the first female astronomer to have a major observatory named after her. [2]