We all ask this question at some point.
Here's a simple way to work it out (well, works for me)

Pick someone - anyone - who has a similar playstyle to you.
Find out their productions.

Divide your planets number by theirs
Divide your top production structure by theirs (eg 10/12)
Multiply the two answers together.
Multiply their productions by the answer, and you have what they'd have at your rank.
If they're a production boosting race or profession, divide the relevant answer by 1.2 if they're vygoid, 1.1 for excavator/miner.

If you don't know their planet number, you can guess by dividing their rank by 4, +1 to the answer.

Example (fictional):
Me - 50 planets, +10 structures.
Friend - 125 planets, +12 structures.
They have say 6K mining, 12K artis and 9K research

50/125 = 0.4
10/12 = 0.83
0.83*0.4 = 0.332

6000*0.332 = 1992 MP/hour
12000*0.332 = 3984 AP/hour
9000 * 0.332 = 2998 RP/hour

I know this doesn't take into account mission planets/scientists, but it's a guide.

so much for trying to follow along...

You should have enough RP that your modules are expensive enough that you can barely cover you upkeep, but enough mining to do so. Then you should get all AP

sooooooo... in your example.... the guy with 125 planets has mining and artifact production levels that caps after the 10th hr and a research level that caps after the 8th hr....
and your proposed rough guide estimates for yourself for 50 planets would be mining and artifact capping after the 12th hr and research capping after the 10th....

that goes back to my simpler solution.... divide your current max by the production per hour, and your next planet should be whichever is the highest number.... and try to go no lower than an 8 hr cap so you don't waste dark smuggler caches

it should be the cap divided by the number of hours that pass before you can be back on.
if you can only be on 1 time a day, production cap divided by 24 = production per hour.
or 2 times a day, cap divided by 12 = production per hour.
or 3 times a day, cap divided by 8 = production per hour.

or you can just max out everything to your research level.
multiply by how many hours will pass before your on and buy storage units to meet your needs
so you waste no production.

for those poor saps who have to work and cannot get to facebook at work- then this is irrelevant- just get the resources you need for the game

For Artifacts, I would say 25-30x Your rank is AVERAGE

yes... casual folks should do whatever the fluff they want to....
my suggestions are for the dedicated gamer that can actually play when they want to...


if you have a life, mark off what times you're able to get to the computer... then look at the longest period of time you would be away from the computer for..... and aim for that to be your production capping time...

we can tell who these dedicated gamers are, glued to the tube 24/7, and yes it is an addiction
when you have to take your lap top to the bathroom with you.