I voted for 1. Robin III, 2. Spoiler, and 3. Oracle

@MichaelKjörling the answer is rather long, you have slim error in the visible angles calculation(you use good approximation for the case, but you didn't stated it is approximation and didn't validated it use) (you should used arctan), for the planet it adds error in digits at precision you have used.

second error is in - invalid division of 0.664/7.124≈... you used different circles to calculate them but then you use it as values for the same circle. Instead, you should calculate the sector of the orbit around the planet(as a distance or as an angle) and use that angle to determine the amount of time the planet spends in shadow.

and the difference is significant, about 5 times less or so

third not mentioned moment is the planet creates shadow cone, same way as on the picture ask-aladdin.com/images/eclipse_dia_big2.jpg

the cone begins to end at 12 million km from the planet (opposite side od the sun) and compared to second moment (where we can consider and approximate the sun as a point source), in this case it adds another may be 10% of error if we do not consider sun as point source

if it is not enough for you to catch those errors I can add a paragraph and few pictures to the answer which you can remove later and edit the answer accordingly, but I hope the current information is enough for you to catch those imperfections. Over all nice formatted answer.

@MolbOrg Wrong chat room, I think. I'll have to look those over, but can't at the moment. Have saved your comments for later reference. Feel free to add them as comments to the answer as well; then people can take them into account when reading the answer until I've had a chance to fix it.

completely unrelated to the chat topic, but a question I've pondered on for a while: there is sometimes a number under some names in chat - currently I see the number 3832 under MolbOrg's name - but I can't figure out what it means. The number does not seem to be related to neither character count, reputation nor ID....

does anyone know what the numbers come from?

@Mrkvička it seems to amount to the total sum of rep over all SE sites.

@Mrkvička @PatJ is correct; it is the network-wide amount of reputation of the user that the chat account is associated with.

I think it shows only when more than four lines of chat text show next to the user's avatar.

aaah, that explains it - I didn't think of summing the rep from all places. Thanks!

You're welcome. Remember to vote. ;-)

seems to be a nice turn-out too - I get it to ca 260 people voting so far

and then perhaps even more, I dunnow if one can get the badge more than once

ah, I need to learn to read - it does say "can be rewarded multiple times" - then it is ca 260 pervs so far

It can be awarded multiple times because it is awarded once per election.

I noticed - I just can't read before I write ;)

or, to quote Arne Anka: "to think before one talks is to wipe ones butt before one takes a dump"

@MichaelKjörling it to long of comments, and probably needs pictures to explain. General idea is pretty close to what have to be written, so for most people, there is no problem as long as idea is healthy. Correct answer would involve choosing the star size, size of GG planet and may so happen that there is no solution for OP's request, would be pretty interesting result-argument for big universe where may exists everything we can imagine ))

so I hope you will figure out

@MolbOrg I appreciate the feedback. Hopefully I'll be able to sit down tonight and actually look over the answer with what you wrote in mind (but no promises); you made some good points.