...There is, at least, enough light in the tent now to write by. She can do math on PAPER. 

Okay.

While she's busy breathing the 400L of oxygen in her suit tank, she needs to generate another (slightly less than) 400L to fill the now-nearly-empty storage. How long will that take.

...Depends how fast she runs it. Normally - in hospital conditions, say - the power usage is supposed to be closer to linear, but running it in cold conditions means it's also spending power on not freezing solid - it's a smart system, it can run fine with an ambient air temperature of -30° C - but when it's doing that, it's substantially more efficient per-L-generated to run it fairly close to maximum. And of course she'll also have to run the compressor, which doesn't vary much in power usage based on how "hard" it's running, it's pretty close to a 150 W draw regardless - and she can't cycle it on and off, she has nothing set up to reliably and fully capture uncompressed oxygen for later compression and then make sure none is wasted. And the compressor uses...almost as much power as the oxygen concentrator at its maximum, and significantly more than the concentrator at lower power. So she really should be doing this as fast as possible. 

At 4L/min it'll take - exactly 100 minutes to fill the canister all the way, or realistically a little bit less since it's going to be 10% full already. Call it 90 minutes. That's 300 Wh for the oxygen concentrator at max power and 225 Wh for the compressor. 525 Wh total. ...Round up for cold-related inefficiency, she has never actually tested running this particular setup with temperatures this cold.

Call it 600 Wh. That leaves her at 2500 Wh in her main battery, from 5000 Wh starting out. 

...She is fundamentally just not going to get solar power production keeping up with that rate of usage. Maybe she'll get as much as 1000 Wh over an entire long sunny day. 

(Key question: it's winter, she thinks, but is it before or after the winter solstice? If the days are getting shorter, she...has serious problems, even if they're not as serious as the problems she eventually expects to have in summer. If the days are already getting longer and the sun's arc is already getting higher, then the summer heat problem is that much more imminent, but her near-term power generation problem is more tractable.) 

Ugh. 

Okay, ignore historical data i.e. what she used yesterday and overnight. (The answer is "approaching 4000 Wh", between nearly-draining her power armor battery and using 40% of the even larger main storage battery. It's a bad answer.) 

She needs about 1000L of oxygen in 64 hours. (Less, tomorrow, if she can keep weaning herself down.) 250 minutes of running the concentrator-and-compressor, that rounds to four hours, which is 1400 Wh. That's not (very) negotiable. 

She knows that the maximum power draw on her suit is, like, 500 W, but that's normally for very brief periods – sprinting, jumping, using the various powered swimming modes at top speed. It's very, very optimized for power efficiency, honestly moreso than her medical equipment. It's packed full of electronics, but those don't use much power at all compared to what you need to concentrate oxygen out of the air and squish it into a canister at very high pressure, and she spent a lot of yesterday using the absolute bare minimum of its mechanical-assist functions. She ended the day with a little over 20% battery left, so she spent 1600 Wh over the day, which somehow only averages out to 60W, and then 200 Wh (averaging to 28W) over the last coming-on-seven-hours of not doing much except breathing and declining to die of hypothermia. 

(Wow, her power armor is incredible technology. Walking around in it takes like 1/6th the power draw of refilling her oxygen cylinders! Merrin has never been so grateful for the sheer ridiculous quantity of engineering optimization effort that went into that in particular. ...Would be nice if the same were true for her other equipment, but in fact it's optimized for very reasonable things, probably, like "lightweight" and "unlikely to have mechanical problems" and "not exploding if dropped with a lot of force".) 

If she hooks up her backup battery (400 Wh), she can do about 10 hours of activity matching yesterday's profile - though some of that was breaks, the actual carrying period must have been higher - and then she's out. She already needs more than her solar power generation can keep up with just to get enough air to breathe. 

...She has problems, doesn't she. 

Okay. 

There are two strategies she can take, here: 

1. Hunker down and recalculate and find some way to get her needs down to only a bit more than 1000 Wh. Hope she can eke away at it and get to something sustainable before she runs out of the stored power she arrived with.  

2. Leverage her remaining stored energy into one more frantic day of fixing her situation, or at least improving it enough that tomorrow will be survivable on just solar power. 

She really, really needs shelter that isn't stupid. Where the geography is cooperating with her needs. If she can find that, and set up a shelter that retains heat well enough that she can survive in just her sleeping bag through the nights, she can actually hunker down for a while until she can handle a normal activity level breathing 13.5% oxygen, and then make steady progress from there with more minimal use of her power armor. 

....She needs a still first. And to fill the saltwater reservoir before the tide impractically far out and she has to climb for ages to haul water up. It's still cold out, but she can afford some amount of suit heating today, and she probably can't afford to waste more of her limited daylight. 

It's not complicated to make a smallish and not-perfectly-efficient setup, and she mentally planned it out enough during the endless night that executing on it takes minutes. She has a collapsible water tub that can hold 100 liters; she sets it up on a smoothish patch of rock. She also has a lightweight cooking pot that holds 3L. It goes in the middle. She has a bunch of tough waterproof plastic sheets, though "a bunch" is not nearly as much as she wishes she had, given the incredibly versatile usefulness of plastic and the fact that it's practically free to manufacture in dath ilan and impossible here. She has adhesive sealant strips that are "reusable" though only, like, a dozen times before they've picked up too much dust to re-stick well.

The annoying part is hauling water up the stupid valley side. It's a slope, not a cliff, and walking up isn't too bad, but walking down with too little cautious risks a tumble dropping her directly into the fast-moving current. It's probably only 15m of elevation but each trip is still taking a while.

(She does take the opportunity, on her first trip down, to rinse out the removed suit drinking bladder with seawater. She'll want to clean it more properly than that before drinking out of it again, but at least the gunk from the meal replacement shake won't get any more glued on or start to mildew in there.) 

She fills the tub to maybe 10cm deep. ...At which point it occurs to her that she should really stash it in her tent, which is warming up much faster than the ambient air as its insulated walls absorb heat, it's still well below freezing but the water probably won't freeze into a block of ice before the sun is hot enough to do any effective evaporation. She hauls it, with careful effort, and manages not to spill any, and then she places her pot inside in the middle - weighted with one of her stainless-steel metal tools at the bottom so it doesn't try to float, she doesn't know the local composition of the rocks or if she wants to risk any of it leaching into her drinking water. 

She uses a small rock from the ground to weight the middle of the sheet so it's pulled down in an inverted cone with its point over the pot. In theory, condensation will tend to trickle down and drip from the cone's point into her collection pot, though she'll lose some that will just drip right back into the seawater at the bottom. 

And then it's time to equip herself for a little sortie, and EXPLORE. 

Merrin packs another liter of water in her front pouch. ...She should probably actually be drinking more than she is, she's consumed 5 liters in...two and a half days, by dath ilani reckoning...which is less than the 2.5L/day minimum for an adult woman her size, and a lot of that was with high activity levels though she at least wasn't sweating much in the armor. The frozen pee in the bucket is a very deep yellow color, but she doesn't have a headache or feel lightheaded, her body seems to be coping with mild dehydration. She'll see how much drinkable freshwater she can get today with her stupid un-optimized still. 

She sets up the oxygen concentrator and compressor to start filling the now-mostly-empty O2 tank. She should be back in an hour; if she's not, the concentrator should detect a blockage once the compressor detects sufficiently high pressure and switches itself off, and it should switch itself off in turn. 

She makes sure the auxiliary suit battery is seated properly. (With it properly snapped into place, the seal should be waterproof, though she always feels like she can notice the change to her streamlined silhouette. The primary oxygen tank and battery are bulky as well as heavy, but the armor is custom-fit to her and the bulky necessary storage is smoothly incorporated into the suit's back.)

...She checks on the solar panel output. 

The sun is still at a low angle in the sky. Even with the panel tilted optimally, she's getting, like, 7W. 

OH RIGHT ONE MORE THING she's gonna spend fifteen minutes improving her sundial measurement apparatus, and improvising a sextant – she doesn't carry one with her supplies, anymore, since she knows how to make one out of general-purpose making-stuff supplies which she could in a different scenario with different needs make into something else.

She measures, and writes down as accurately as she can - it's not gonna be super accurate - the altitude angle of the sun in the sky, and then her even-less-accurate best guess of the azimuth angle given that she did not actually mark the spot where the sun first appeared since she was at that point hiding in her tent. She adds the exact time in minutes-since-dawn, realizes that she's stupidly wasting mental math capacity on generating that from the suit clock time-since-switched-on, and figures out how to manually change that to the actual estimated time since dawn (78 minutes, somehow she's already spent over an hour of her 28 hours of daylight...) 

There. She should be making regular trips back to this base camp today, she'll keep taking measurements, and then she'll have a baseline to compare tonight and judge if the day is getting longer or shorter. 

And NOW she will actually go explore her exoplanet surroundings! 

It's a plain of sedimentary rock – probably mostly limestone, it looks like, and definitely a kind that's partially soluble in slightly-acidic water and thus easily weathered and eroded by rainfall drainage.

No real mountains in view, just sort of rippled undulating hills. 

The lichen-like biofilms are tenacious, clinging to the rocks despite the current lack of any moisture whatsoever. The area clearly gets rain, to cause all the fascinating erosions patterns, but it's very unclear when it last rained. Maybe the lichens get some water from the humidity in the air, during the periods when the enormous intertidal zone is wet and exposed to the peak heat of the sun. 

The lichen - it's probably not technically a lichen by the dath ilani biology definition, which is a whole complex and specific symbiosis and who knows if this planet even has three distinct evolutionary branches for "plants", "animals", and "fungi", but whatever - anyway, it's got to be, like, 50% UV-protective molecules by dry weight, to not get all of its DNA-or-equivalent completely shredded by all those long endless days with zero shelter from the sun. 

Promising to boil into a dye and treat a bandage-derived textile to make herself a UV-proof robe? 

...That's a later priority. Merrin keeps walking. 

There's an area where wind and rain has eroded the stone in taller spire-like patterns! Not really tall enough to provide shelter, though, and it sure is a hint that this particular spot is perhaps subject to high-force driving winds during storms. 

And a bunch of them look like they're ready to fall apart the next time they're subjected to those forces. It's eerily beautiful, and Merrin takes a moment to savor the view because if she DOESN'T let herself indulge a little bit in the few parts of the situation that are fun and cool then she will GET REALLY DEPRESSED and MAKE POOR SURVIVAL DECISIONS. But it's not a good place for a camp. 

On her walk back, she finds a sinkhole! 

They're a pretty common feature of land like this. The water-erosion happens underground, too, the whole area is probably riddled with underground rivers - at least in the rainy season, if rain is strongly seasonal - and you get caves with awesome stalactites and stuff, and then sometimes they get too big and the ground above can no longer hold up and it collapses into a pit. 

This one doesn't appear to still connect to any cave systems. Judging by the water-marks on the inside, it does flood at the bottom, if not with every tide then at least at some point seasonally. 

Nothing usable yet. But there are promising signs! A sinkhole would do, she just needs to find one that's on slightly higher ground and has clearly been dry for at least the last few decades.

Merrin walks the rest of the way back to camp. She's been pausing to take notes, checking the angle of the sun to get an approximate sense of direction to draw a map. 

...It occurs to her once she gets back that she's very silly. She had been assuming that her suit location records would be completely useless because the GPS obviously isn't getting any kind of reading. 

But her suit does, also, have a backup magnetic compass, and inertial reference tracking software. She's literally done training scenarios where she had to turn off all the external-satellite-uplink functions because ""the entire planetary satellite network had gone down"". The magnetic compass is less reliable, it'll be thrown off if there happens to be a whole bunch of iron ore nearby, and also it is not necessarily even very close to the rotational axis of the planet, but she hasn't been covering enough distance for it to be likely that the reading is all over the place. 

Accessing the inertial "map" of all her activity since she turned the suit on for this "training scenario" is going to be incredibly frustrating on her tiny wrist panel screen. It miiiiight, in fact, be worth turning on her actual electronics for this, briefly, so she can copy stuff onto paper. Probably not now, she'll keep doing an approximate map, but later on she can fix all the angles and distances on it to be close to exact. 

...It is easy to pull up the compass reading. The sun is angled on the south per the magnetic compass readings. She already knew she would have been in the "northern" "hemisphere" if this were dath ilan, from the angle at which the sun's arc is inclined, but now she also knows that this planet rotates the same way, and that the magnetic pole isn't wildly off from the rotational pole; it won't match exactly, but with her shitty measurement setup she can't pin down the difference yet. 

Neat. Now she can navigate in cloudy weather, if for some reason she has to do that. 

It's now 2h57min after dawn. Her oxygen cylinder is full and the equipment has nicely switched itself off.

The outside temperature is already up to -29.9° C. The temperature inside the tent is warming even faster; it's just -6° C. The water in her tub has not at all started evaporating, unsurprisingly, but it's also not frozen. 

Her solar panels are now generating 13 W. The 500 Wh auxiliary battery they're hooked up to still has tons of space, of course. 

She has plenty of O2 and battery left on the suit. Walking around unladen on mostly-flattish ground didn't require too much power assist, even with the higher gravity, but it did give her enough of a workout that the suit detected her starting to sweat and turned down the heating, which BOTH stretches the battery life AND minimizes water loss from sweat. Super convenient, that.  

Time for further exploration and adding to her map!

(After quickly putting down another data point for the time and sun angles, for later analysis.) 

Another trip back and forth, with a water break in the middle. (It's actually really annoying not having the suit bladder in usable shape, she has to unseal the helmet to drink.) 

Meal break back at camp. 

Another trip. 

More notes. 

Back to camp. 

It's now been 6h since dawn. (Less than halfway to solar noon; the sun is still not actually that high, though the bright, unobstructed, too-bluish light makes it feel like it's closer to midday than it is.)

The outside temperature is up to -18° C; a glance at her suit analytics would show that today seems to be trending a little bit warmer than yesterday. The temperature in her tent is above zero. 

The tide is now down to around how she remembers it yesterday. 

Her solar panels are getting 24 W. She's banked a total of 80 Wh so far today. 

And it keeps feeling like she's getting close to halfway through her daylight and she ISN'T, she has 22 HOURS LEFT, she is in fact only TWENTY PERCENT of the way through today. 

...She should attempt to retrieve her box of backup supplies, rather than leaving it to endure ANOTHER tidal bore. Maybe it's still down at the bottom of the river channel? 

She might as well not cut it too close to low tide and the turning point, to avoid more STRESS. She can just wait, like, another couple of hours until the tidal waterline is solidly below her landing point. 

Time for another walk, then!