The beauty of ballet lies in its harmony, and as we know, harmony is based on mathematics.

So here is, very simple puzzle.
The ballerina makes ordinary dance circles around her partner.
When performing this maneuver, she wants to simultaneously perform a full 360-degree rotation around its own axis.
What’s more, she wants her partner to be able to watch her beautiful face all the time during these maneuvers.

Can you calculate the speed at which the ballerina must rotate around her own axis
and at what speed she must make circles around her partner
so that the entire process would be called a synchronous rotation (tidally locked),
thanks to which she will be able to look at partner with her charming eyes all the time and hold his hand also ?

No. Her speed (and his) are irrelevant. It’s the ratio that matters - and that’s 1:1. She makes one full rotation about her own axis for every rotation she makes around him. How fast they do it doesn’t matter.

However, if you’re talking about planetary bodies, the speed does matter. That’s because the rotational speed has to exactly match the combined gravitational attraction of both bodies. Too slow, and one will fall into the other - too fast, and the smaller one will fly off into space.

My daughter took ballet for years. When spinning, the dancer’s head does not spin around with their body. If it did, they would become too dizzy to remain upright. They actually face forward then snap their head around quickly as their body finishes the rotation. So technically, she could face him the whole time except for the second at the end of each of her rotations.

I have never attempted ballet, but I did study some anatomy.

If, in real life, you were to turn a dancer’s head through 360 degrees, the most likely consequence is that their head will come off. Really messes up your stage show.

So you say that it is enough to maintain the appropriate speed ratio of both maneuvers performed simultaneously to accomplish this synchronous rotation ‘operation’ (360-degree rotation around its own axis & circle around partner) while holding his hand the entire time, correct ?

I’m saying that the actual speed the dancers move at is irrelevant to the synchronisation of the movement. Not only that, but from the parameters you originally gave, it’s not possible to calculate their speed of movement.

The speed the dancers move at relative to each other is important. In order to maintain continuous eye contact, she must rotate about her own axis exactly once for ever rotation she makes around him. But that could be any speed. She could circle him at 1 m/s, 2 m/s, or 3m/s. Provided the 1:1 ratio was maintained, the outcome would be the same.

Since we would get the same outcome, regardless of the speed of rotation, it follows that it’s not possible to determine that speed from the information originally given.

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!

Part 2
The most basic role of riddles is to induce its participants to Think. And maybe give a bit of entertainment too.
At least that’s how i see it.

But be careful, if You pay attention enough, your worldview can change drastically. Don’t say i didn’t warn You. You do this at your own risk

Believe what You see, not what You’re told

Small hints.
However, to use them, You need to use your imagination a bit, a little bit of mental effort and pay enough attention (crucial).

Synchronized rotation requires two maneuvers.
So let’s go through each of them separately first.

In your room place a chair in the middle. Just as a reminder of your partner. Then perform a full 360-degree rotation around your own axis - or use imagination to do it in your head.
Because it is not a ‘synchronized circulation’ and You are practically standing in one place, You will not be able to constantly see your partner’s face or hold his hand.

Next, make a simple circle around our chair (on your toes like a ballerina, of course ). Remembering to look at it all the time and also have your hand extended to it (symbolizing holding your partner’s hand). Of course, again You can do this using a tool called imagination

So it’s time to combine both. Perform both maneuvers at the same time. You can also do it in two variants.

a. In the first, make few 360 revolutions around your axis during one circle around chair.
b. Second, this time try to do a synchronous turn. Perhaps Polyphemus’ advice will be helpful - the key is not speed but the 1:1 speed ratio between them.
Perphaps.

X. After successfully (or not…) performing synchronized rotation:
Draw your own conclusions
and if You dare, share it