If the beauty of ballet lies in the harmony of its ratios and mathematics, then the ability to calculate the speed of the rotations in ballet lies in providing the numbers (the ‘maths’) of which to calculate the ratios.
So…
Solving the Riddle
I think the point of this riddle is to show a comparison between ballet and ‘planet orbital physics.’
How…
- the ballerina herself is rotating on her own axis,
- “tidally locked” with, or staring at her partner at all times,
- and yet rotating around her partner,
Just as…
- the moon itself is rotating on its own axis,
- “tidally locked” with, or staring at the earth at all times,
- and yet rotating around the earth.
Just as the beauty of ballet lies in its harmony, so too does the beauty of a star system (in reality) lie in its harmony, and as we know, harmony is based on mathematics. So too should the beauty of a star system in No Man’s Sky (in science-fiction) lie in its harmony, because as we know, NMS is based on mathematics, as well.
I think the inspiration for making this comparison comes from our discussion of “Developing the Sun” in No Man’s Sky in the “What More Can We Do With Space?” thread. I think the reason for making this comparison is because when Hello Games added ‘planet orbital physics’ to NMS, they decided to remove this feature sometime shortly before launch, because it proved too disorientating to the playtesters.
But since it existed in-game, that means it’s possible in-game, and if HG’s only reason for removing ‘planet orbital physics’ was some feelings of disorientation, then put it back with a toggle switch in settings, so the disoriented players can toggle it off, and every other player requesting this over the years can enjoy it fully.
Of course, if issues do arise in multiplayer, then just disable it in multiplayer, and make it a solo-experience.
Solve The Riddle of the Ballerina, and you solve The Riddle of ‘The Sun Revolving Around the Planets.’
Outstanding contribution, @Grohmanon. 
I sincerely hope you’re listening, @OldGods!