EarthSky.org's What will the sun do next? says:

On December 6, 2018, the Center of Excellence in Space Sciences India (CESSI) reported that two of its scientists have made a prediction for the upcoming sunspot cycle. Solar physicist Dibyendu Nandi and his Ph.D .student Prantika Bhowmik devised a new prediction technique, which simulates conditions both in the sun’s interior, where sunspots are created, and on the solar surface, where sunspots are destroyed.

Earlier predictions (like this one) have suggested the coming sunspot cycle 25 will be weaker than the current cycle 24. But, based on their model, Nandi and Bhowmik believe cycle 25 might be similar to or even stronger than 24. They expect the next cycle to start rising about a year from now and to peak in 2024. Their work was published December 6, 2018, in the peer-reviewed journal Nature Communications.

There are plans to build a Lunar Orbital Platform or Gateway around the Moon for astronauts to visit, and use to travel to the Moon's surface.

The goal of this within five years has been mentioned, though it might take a little longer. Either way this will be happening during a period of increases solar activity, possibly even near solar maximum!

  1. How will the radiation issue be addressed on the Lunar Orbital Platform around a solar maximum

  2. How long could astronauts stay on the Lunar Orbital Platform then, without significant risk to their health?

Bhowmik and Nandi prediction for sunspot cycle 25 compared with the current sunspot cycle 24. The work suggests the coming sunspot cycle will be similar to or slightly stronger than the activity levels that are just ending. Image via CESSI.

EarthSky.org What will the Sun do next?

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    $\begingroup$ The moon spends 6 months in Earth's magneto-tail, other than that there will be very little shielding if they do not put something to shield it on the craft itself. $\endgroup$ – Magic Octopus Urn Apr 10 '19 at 17:45
  • $\begingroup$ You've asked a really good question! I've added some background material, I hope you don't mind. $\endgroup$ – uhoh Apr 11 '19 at 1:09

How this is managed is a bit complex. The short answer is there may well be some clever ticks but weight constraints mean an effective radiation shield is not really a feasible option and apollo-style steel/aluminum capsules are near guaranteed, with the addressing being left to management things like returning crews near their limit of exposure.

As for the total time, it's a stats thing, not an absolute time. This is because earth-facing CMEs are not frequent enough to be smooth over the time periods considered. However, in terms of orders of magnitude:

The number of CMEs varies with the solar cycle, going from about one per day at solar minimum, up to two or three per day at solar maximum. So significant, but not a game changer, even if these where the only source of radiation. However radiation doses are pretty borderline for long moon missions so that factor of 3 might be pretty important.

NASA estimates for the Apollo missions were that: a 9-day mission to the Moon which led to 11.4 mSv was about the worst to date. They also consider 2.50 Sv a cutoff for the max lifetime exposure for a male 35 year-old of which only 0.5 Sv is permitted annually. So in theory the time span is of-the-order-of stay being limited by the lifetime limit not the annual limit. There the astronaut turns out to be more of a deal for them than solar weather: a 25yo female is only permitted to be exposed to 1 Sv, but a 55yo male 4 Sv.

If you read this far: https://www.nasa.gov/pdf/284273main_Radiation_HS_Mod1.pdf is a good bit of light reading...

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