TL;DR at the bottom.

I grabbed a screenshot of the now famous Crescent moonish O in Frontiers trailer and measured it to be approximately 100px in Diameter (if not, I scaled it). Therefore the radius is 50px.

I then measured the distance from the furthest edge of the black crescents right side to the outer edge rim of the larger circle and deduced that the inner circle would be 75px in diameter.

My first thought was to figure out how much of the area the crescent takes up of the smaller circle, which is ~ 1590px of the larger ~ 4415px whole smaller circle. Math goes something like this:

(Big Circle Radius² – Non Crescent Radius²) * 3.14 = ~1590px for the crescent.

I then nearly disregarded the math… because well… 36% is quite a bit of crescent for this little circle, while mathematically correct… but then it dawned on me that the crescent could actually be of the bigger outer circle.

This outer circle comes in at a total px count of 7850px and the crescent portion is ~1590px giving us 20.25% Crescent

The Moon Phase calendar here: Moon Phase for August 13, 2021 – Moonrise, Moonset, Moon Age, Moon Distance (mooninfo.org) shows that on Thursday we will have 19% illumination and Friday we will have 29% illumination. I'm not sure where in the sky the moon is at during these calculations of illumination of the crescent…

Further digging the rabbit hole we could go into assuming that since these Moon Phase calculations are done in UTC, and Guildford is UTC +1. The 20.25% Crescent calculated above would put us at 21:00 UTC or 22:00 BST for a 8pm BST Time.

If we tack on a bit of history:

Beyond was announced on the 2nd of August 2019 to be released on the Wed. 14th of August 2019 (though the Beyond Launch Trailer was added to YouTube on August 8th, 2019 and my memory is foggy on when it actually launched), Wed October 28, 2020 we saw Next Generation launch trailer, Wed. September 23, 2020 for Origins trailer so you get the picture. All of these patches rolled out by end of day on those respective days.

Thanks to the following post for piquing my interest in calculating this out:

https://www.reddit.com/r/NoMansSkyTheGame/comments/p1hpft/the_o_of_beyond_vs_the_o_of_frontiers/

tl;dr: I calculated the Crescent portion of the moon in the Frontiers teaser trailer, while I'm probably wrong, but knowing how Sean likes to play games with math and the like – the update could drop between Wednesday and Friday this week, but it also might not drop for several months because this is all speculation.