He can do the first half of a very small Gate and see if his search-spell gives him the familiar feeling of recognition and finding a destination, since he's mostly aiming this via memories of the specific ship rather than dead reckoning. (The blind direction-and-distance kind of Gate doesn't give you nearly as clear a sense, it's more guesswork, but this should.) If he finds nothing, or has to give up to avoid draining himself to exhaustion before the search completes, then he's probably 'out of range'. 

That won't tell him for sure he's found the right ship, though, it's not impossible his Gate-spell could land on some different ship currently closer in z-space with a similar-ish interior, he can't confirm without finishing a Gate and poking something through. Which will alert the Yeerks very loudly, so his first full Gate had better be a regular-size one that he can use to board the ship and take it over. 

It'd be very awkward if he accidentally boarded a different ship but probably not a lethal mistake, no one really prepares for their ship being boarded since in normal space combat it's pretty much impossible.

Well, he'll give it a try. He's honestly still confused how 'range' works on this kind of Gate, especially for the extremely weird thing they're doing now, attempting to route through the Void between two different pockets of material-plane space floating through it. 

He gets a tiny Gate threshold up and starts spooling out his search-spell on the approximate bearing they're following while they chase the Pool ship. 

it doesn't feel like there's anything there.

He gives it a while, but doesn't drain himself to utter exhaustion.

"I suspect it is too far," he tells Cayaldwin. "Or not in z-space at all, but 'too far' seems more likely. I could in theory resolve that the same way I did the Velgarth kind of Gate, by doing some more complicated routing through additional planes to shortcut through the 'distance' in hyperspace, but I was only able to do that to Earth because I had hyperspace coordinates for it and could spend a week on it. And because it was not moving. I - think I will not be able to reach the ship until we are in range for the ordinary kind of Gate." 

<That makes sense. We're faster than it; I assume they hoped we would not bother with pursuit, or else just panicked when the coup failed and figured anything was better than staying.> Which is reasonable enough from their perspective, really.

:That seems likely: 

Leareth rests and peers at Cayaldwin's planar mapping program and updates personal notes on the last week (it seems suddenly more urgent that he have records, in case he does die and need to get up to speed again...) He thinks about the war and the coup and what they're going to do in the various possible scenarios - where the message was real and the coup opportunistic, where the message was fake but it is still Yeerks, where the message was fake and it's actually Andalite reinforcements... 

He waits twelve hours (gets some sleep in there) and tries the Gate again. 

Still too far. 

On Earth he records some more messages condemning the evil Yeerks for their willingness to kill innocent humans in their effort to undermine the peace, and answering common human questions about Andalites (how did they evolve? what is their home planet like?). For the delicate questions like 'do you have a cure for cancer' and 'can you save my specific dying child' he explains that Andalites do lots of their medicine with morph, but the good Yeerks and the Velgarth humans both might be able to advance the medical state-of-the-art.

The dying children are going to die, and he could cure them, and -

- he has a lot of feelings about this but the one that sits most comfortably is 'angry with Seerow.' He's so angry with Seerow.

There are still like fifty Velgarth Healers around and they're pretty happy to volunteer themselves to go to hospitals all over the country and try to combine their skills with existing human medicine to save some dying children, it seems good for PR and Leareth would approve of that and besides they're really bored. (With mage-bodyguards ready to Gate them out. A disadvantage of this plan is greater exposure but an advantage is that they're spread out, and surely it's intractable for anyone to try to take out all of Leareth's people by attacking forty different human hospitals in enough force that a combat-trained mage has no time to escape.)

Vanyel is convinced to do some public showing-off with his various Gifts. He hates it. 

Mostly he's distracted by being very worried about Leareth. He assuages this by spending as much time as he can close enough to Matirin that he could personally shield him from an orbital strike.

...He wonders if Matirin knows how important he is to Leareth. Maybe that kind of thing is less obvious to aliens. Possibly he should - bring it up, or something, except that seems really awkward. 

Melody talks to Earth therapists about the freed Controllers she's treated (in the abstract, no specifics of course) and if they can help set up a system for it, she'll see the worst-off people herself. 

Yfandes is in Van's head and kind of fed up with the thing where he spends ages being indecisive about social situations and then usually settles on 'do nothing about it because it's awkward.' 

Her Chosen, unsurprisingly, continues to do nothing about it. Well, maybe she'll have to take matters into her own hands. 

:Hey, Matirin: she says at some point, when he's pacing again in their new shielded base. :You busy?: 

<No, do you need anything?>

:I...wanted to talk to you about something. Or ask you. I don't know, exactly. Just, Van and I both noticed that Leareth seems quite attached to you. Which is unusual for him, I - don't think he has very many close friends. Or people he trusts that much. I wasn't sure if you had noticed because, well, you're an alien: 

<I am an alien> he agrees. <I value our alliance with Leareth and his people highly. I...do not know that it will make sense for us to be deployed on the same planets for the rest of the war.>

Yfandes is really unsure how to respond to that. :No, that makes sense. I assume Leareth is going to endorse doing whatever makes strategic sense, there, that seems like what he'd do. Just, I - think it's maybe good for him, feeling close to literally anyone. Also it seems awkward if he enjoys your company a lot and you - don't enjoy his as much: She can't read Matirin very well. He's an alien. 

<I think I enjoy his company a normal amount.> Matirin sounds slightly confused, though. 

Okay no wonder Van put off doing this, this is so awkward. :That's...good. I guess: She sounds slightly confused too. 

<If I were a human is there something I could - usefully do ->

:...I don't know. If he was anyone except Leareth, I would - be betting he's romantically interested in you. However, he's Leareth and also you're an alien so I have no idea. I think having friends is good for most people, though, human or not. Even if they're Leareth and have spent two thousand years singlehandedly trying to save the world: 

<What sorts of things do humans do if they are trying to be friends instead of being allies?>

:Ummm. Sometimes have conversations that aren't about war logistics? ...Conversations about feelings, that's a common one, but not everyone. Keep each other company when one of them is sad. I don't know, go out for coffee together? Gossip about mutual friends?: The latter one might be most strongly a Companion thing. 

<We talk about feelings sometimes but I do not know that I would do it recreationally. It seems like a good thing to have context on, though.>

:Mmm: 'Recreationally' is such an odd framing there. :Anyway, I haven't talked to him directly or anything, just - I've literally never seen him hug anyone except you. So that seemed notable: