Short answer: This is The Voyage of the Luna 1 (1948) by David Cragie.
I asked a question about this book at the Reddit Tip Of My Tongue site about a month ago.
Someone with the user name ceefrock answered that it might be The Voyage of the Luna 1 (1948) by David Cragie, illustrated by Dorothy Cragie. It turns out that David Cragie and Dorothy Cragie were pseudonyms of Dorothy Glover (1901-1971). In the 1940s Dorothy Glover was the girlfriend of famous author Graham Greene, and some have speculated that Greene was the author of her books with "David Cragie" listed as the author.
I managed to have my local library order The Voyage of the Luna 1 by inter library loan and have read it. Since I don't know when I will be able to read it again I have included a lot of quotes from it here for my future reference.
There are a lot of important plot elements that I seem to have forgotten in the 58 years or more since I read it. But I did find the often minor plot elements I remember from reading it.
"I remember a children's book published by about 1961 in which a boy and girl who probably lived on a rocket base stowed away on an unmanned rocket to the moon."
The Voyage of the Luna 1 is copyrighted 1947 and the copy I borrowed in 2019 is the fourth printing, dated 1953.
The children, twins Martin and Jane Ridley, live in a small village in Kent, England, presumably about the era that the book was published. My more space age experiences probably caused me to falsely suppose they lived in a rocket base.
Actually a rich private individual, a Major Topham, finances the building of the rockets at a local aerodrome (airfield) within easy walking distance of their home, and his security is rather slack. The novel justifies the ability of the children to stowaway on the first unmanned rocket Luna 1 very well, much better it does the astronautics and the astronomy.
The fictional date:
In Part One, Chapter III, "The Beginning of an Idea", page 19:
"Yes; you'll know a lot when you comeback. No one has gone as high as Piccard so far, have they?" he asked.
"Oh, yes, they have," answered the professor, closing one eye and squinting down the fin. "He was beaten by several miles...."
Piccard's 1932 record of 16.2 kilometers (53,000 feet) was broken by several miles in the late 1930s.
In Chapter XIII "The Lost Trail", page 219:
He though of the road leading to the woods--woods, not lunar forest; tea, the six o'clock news on the radio--not hunger and endless twilight.
So Martin's family hasn't acquired a television yet like they would in the 1950s or 1960s.
In Part Two, Chapter XIV, "Despair, anger, and Desperation":, paged 232:
His eye caught the tiny Union Jack hanging limply from its mast far below him, marking the moon as a British possession. As there were no oceans, boundaries, or rivers to split up the land, so it would remain: no country in any world could claim a part of it, not territory to fight over, no claims to argue about.
In Part Two, Chapter XVII, "the Final Discovery", on page 246, Professor Erdleigh tells a British crowd:
"...We all know and love our Empire--the Empire for which we have fought many long and hard wars. To this Empire of ours has been added not another continent, or a country, er even part of a country, but another world--a world which may prove to be rich in minerals and properties so far unknown to us. When the specimens which these children collected have been analyzed, this Empire may be the richest in the world."
Actually the British government had begun granting independence to the possessions in the Empire when the book was written.
Erdleigh, like Martin, assumes that Martin's planting the flag made the entire Moon, instead of merely the tiny part Martin and Jane explored, a British possession. But in North American history, England, France, the Netherlands, Sweden, Denmark, Russia and other powers claimed and colonized various places reached by their explorers, ignoring the previous Spanish claim to all of North America, so I doubt that others would recognize British ownership of the entire Moon.
In Part One, Chapter II, "The Wood" page 11:
"one Day I'll have a real one, a huge one, and I'll be able to see everything, " Martin said dreamily. "I'd like to see the one in Mount Wilson Observatory."
"It's the most wonderful telescope you can imagine: the size takes your breath away. You'll see it one day, never fear, you'll see it."
The 100 inch (2.5 meter) Hooker Telescope at the Mount Wilson Observatory was the largest in the world from 1917 to 1949, when the 200 inch (5.1 meter) Hale Telescope at Mount Palomar Observatory was completed.
In Part Two, Chapter II "Accident and Discovery", PAGE 112, there is a drawing of a sheet of paper saying "Log of the voyage of "Luna 1. Martin Ridley. Oct. 3. ___". It looks like a 7 after the 3, but that is probably a 1 beginning a date of nineteen forty or fifty something.
"I remember that when the newspapers revealed that they stowed away on a moon rocket various stereotypical characters read of it, including an Indian maharajah and a wealthy Mexican ranch owner.
As I remember, the maharajah marked the newspaper story with his bejeweled mechanical pencil, and the Mexican hacienda owner leaped up when he read the story and fired his silver pearl-handled pistols into the air. But I don't remember such "minor" details as the names or fate of the protagonists!"
Actually, I miss remembered a little. In Part Two, Chapter VI "The World's News" reports of the Morse code messages sent by the boy from the Luna 1 are printed. On page 150 of the fourth printing, dated 1953:
The private secretary to the Maharaja of Jedphore was shorting the morning newspapers for His Royal Highness when his eyes caught a headline on the front page of the Bombay Times.
By our London Correspondent.
During the last few days further news has been anxiously awaited concerning some extraordinary messages reported to have been picked up by an amateur wireless expert. The messages, coming from a region somewhere near the sun, were at first thought to be hoax, but it is learnt on good authority that this is incorrect, and a statement is to be made shortly. In an interview with Mr. Dutton, who first received messages, it was learnt that he was working on a receiving set which he had made a short time ago, and he flatly denied and suspicion of a hoax: he is convinced that these messages are arriving from some agent in the vicinity of the sun.
The private secretary carefully marked this paragraph with his gold, ruby-studded pencil.
Jedphore was probably suggested by the kingdoms of Jaipur and Jodhpur in British India.
On page 152:
Don Pedro lay in a hammock under the trees, in his beautiful garden, gently fanned by the faint breeze from the Gulf of Mexico. Between sips from the long glass filled with golden liquid and tinkling ice he languidly glanced at the piles of newspapers that his servant had just brought him. Thee was very little to interest him until he saw one tiny paragraph.
ENGLISHMAN REACHES THE SUN
From time to time there have been claims made that scientists from all parts of the world have been in contact with the sun, but a few days ago an Englishman living in one of the London suburbs received messages from travelers either on the the sun or near that planet. There can be little doubt that these messages have come from a party of interplanetary explorers.
Don Pedro leapt to his feet and drew two tiny silver and pearl pistols from his sash.
"I salute the beautiful Sun Maidens," he cried, and gallantly fired into the air.
Eight other persons read the news in that chapter, but those are the only two I remembered.
"On the trip to the moon the boy looked at the sun through a telescope and when he looked away he was temporarily blind and couldn't see anything. I remember as a child thinking that looking at the sun through a telescope would likely to be instantly extremely painful to the eyes and that nobody could have forced himself to stare at the sun as long as the book said."
I remembered a little incorrectly.
In Part Two, Chapter V, "Marooned in Space", page 143:
"She might," answered Martin, crossing to the open shutter and putting his his sun-glasses. "Here, Jane," he called, "bring the telescope."
So Martin is wearing sunglasses when he views the tremendously impressive sight of the Sun through the telescope.
On page 144:
Martin turned away from the window at last and took off his sun-glasses.
"Here, put these on and look at it through the telescope. It's the most wonderful thing I've ever seen in my life--nothing we've seen so far is as wonderful as that." He rubbed his eyes, careful to keep his back turned towards the window. "Isn't it a marvelous sight?" he asked, after a few seconds.
So the children were more careful than I remembered to not look at the Sun with the naked eye or the telescope without sunglasses protection, which still seems rather inadequate.
On page 146, after viewing the Sun for some time and putting away the telescope:
He fastened the shutter down, cutting out the merciless glare of the sun, and jumped to the ground, nearly blinded by the brilliant light; for he had forgotten to put on his sun-glasses. He stumbled across the gloomy floor, blundering into any object that lay in his path. He fell headlong on his face.
"The Moon seemed to have enough air for them to travel outside the rocket."
I don't know exactly when astronomers realized the Moon doesn't have a significant atmosphere. In 1824 Gruithuisen published his observations of an alleged "city" on the Moon, so the Moon should not yet have been known to be airless.
But the Moon was known to be airless decades before The Voyage of the Luna 1 was published, putting it definitely in some alternate or parallel universe.
The atmosphere of the Moon is mentioned as early as Part One, Chapter VII, "The First Sight of the Luna 1", on page 70, when professor Erdleigh says:
"No," he answered; "that is to open the parachute wings to break our fall when we arrive near the moon."
And he shows the kids how the parachute wings open and close. During the voyage Martin worries about how to know when he should open the parachute wings, even though the plan was for the Luna 1 to make the voyage with nobody aboard and thus presumably there should be some automatic mechanism to deploy the parachute wings at the proper time.
If the lunar atmosphere is dense enough for airplane like wings to work, it should be at least as dense as Earth's atmosphere at about 100,000 feet or about 19 miles high.
In Part two, *Chapter IX "The New World", pages 173-176, Martin & Jane's dog is outside without bottled oxygen like they use and starts to show distress after a few minutes.
After they get Scruff some oxygen back in the ship, on page 177:
"Now, unless we can fix one of the spare oxygen masks to his collar, poor old Scruffy mast be shut up here all the time, " Martin told Jane despondently. "We can't take him out for more than a few minutes."
So the dog was fine breathing the lunar atmosphere for a few minutes and then began to suffer from oxygen deprivation.
That may mean that the pressure of oxygen in the lunar atmosphere might be similar to that in the mountaineering "death zone" above about 8,000 meters or about 26,246 feet. Some people managed to reach the tops of mountains higher than 8,000 meters, including Mount Everest at about 8,848 meters or 29,029 feet, without using bottled oxygen and so have managed to exert themselves in the "death zone" for hours at a time, and survive. But that is very dangerous, being at such heights harms the body with oxygen deprivation even when using bottled oxygen. So the lunar atmosphere should be denser than in Earth's "death zone" and thus equal to that of Earth at a somewhat lower but still high altitude.
Martin & Jane first discover crawling lunar insects in Part Two, Chapter IX "The New World" on page 178:
Jane sat down to take off her shoes, which were full of clinkers, when she noticed a movement in the powdery ground by her side. In a few seconds swarms of objects that at first appeared to be tiny bits of stick wriggled their way out of the ground. Jane's shoes lay forgotten while they examined these strange moving things. They were about one inch to four inches long, and of no particular shape. Some had as many as six or seven tiny twisted "legs" that moved stiffly; others only one that they used as a king of oar with which to steer themselves along the ground: the mass of greyish-brown, twig-like creatures slowly worked their way through the ash to the surface.
Martin took some of them in his hand and examined them. They seemed to have no eyes, noses or mouths, and one felt they would be brittle to the touch and break off in pieces like dry sticks. In fact, that probably accounted for the legless state of so many of these strange creatures.
I have no idea what minimum atmospheric pressure would be needed by those strange "moon ants".
They discover other animals that live in the lunar ash in Chapter XIII "The Lost Trail" page 217:
A movement under Jane's foot made her start back. Out of the grey ash something wriggled and turned. At first it simply made a series of tiny hillocks and appeared and disappeared slowly: then a sharp point pierced its way through the surface of the mountain path, freeing itself from the ash with the slow, graceful movements of a snake. This upheaval of the surface was preceded by thousands of moon ants fleeing in all directions, tumbling blindly over each other. Jane called Martin from his telescope to watch this new happening.
The sharp-pointed object had now grown into a snake-like creature about as thick as Jane's arm, and built up out of rough, rocky segments. It was of a uniform grey, and looked like lumps of pumice stone strung together, with cord. It wormed its way to the surface, crushing the fleeing ants like a tank crushing stones into a road, as it proceeded slowly on it sway down the mountain side. As Martin and Jane watched it, other hillocks appeared, following swarms of unfortunate moon ants.
In Chapter X "The Lunar Valley", page 186, Martin and Jane try to eat outside on the Moon:
Jane took out two pieces of cake from her store and handed one to Martin. He bit it; it was like trying to bite a lump of granite. They looked at each other in astonishment. Martin unscrewed a bottle of ginger beer. Instantly the air was drawn from the liquid, and it vaporized, leaving the bottle dry. It was obviously useless to attempt to eat or drink outside their cabin.
In Chapter XIII "The Lost Trail", page 216:
A tiny, jagged piece which looked like black iron grazed Martin's ungloved hand. It healed instantly as the moisture from the blood vaporised, leaving a dark smear.
I wonder if liquids could evaporate so fast in an atmospheric pressure dense enough for the kids to survive in, even with bottled oxygen.
[added 01-24-2020]This scene is during a meteor shower where tiny meteorites strike the ground around them.
When they reach the Earth's upper atmosphere, meteoroids have velocities between 11 and 72 km/sec. The average meteoroid will burn up at an altitude of between about 80 to 120 km. A large fireball may make it down to 50 or even as low as 20 km. It is interesting to note that the meteoroid does not lose much velocity until most of its mass has been ablated away. Some bright meteors or fireballs may explode at the end of their travel. This occurs because the atmospheric decleration pressure exceeds the internal strength of the material and it implodes. This can cause a spectacular sight.
So the kids should be in an atmospheric pressure lower than that of Earth at 80 to 120 kilometers high - and that atmospheric pressure should be low enough to be swiftly fatal to them even with bottled oxygen.[end of 01-24-2020 addition]
In Chapter X "The Lunar Valley", page 190:
It's true the temperature was below freezing point, but they were wearing all the clothes that they had brought with them,and had been moving briskly,; but here the ice-cold seemed to cut through their clothes, although there was no wind.
So how low would the air pressure have to be for liquids to evaporate instantly at temperatures below freezing?
In Chapter X "The Lunar Valley", page 188:
The explorers were too intent on watching the last of these stick-like insects wriggling to safety to notice the vast cloud bearing down on them from the heights of the slope. They thought at first that it was a a dust-cloud, but remembered that, as there was no breeze, it obviously could not be dust. Something touched Martin's forehead above his mask, scratching him sharply across his temple, then something else brushed across the eye-hole. Jane gave a little scream and shook her hair: tangled in her curls there seemed to be something that moved. Scruff barked, and tried to snap at at an unseen object. Martin held out his hand and snatched at the air. He opened his hand and saw a long, twig-like shape with wings--they were in the centre of a swarm of flying moon ants fleeing from the mountain landslide to the safety of valley.
In Chapter XI, the Forest of Watching Eyes", page 197, the children find that a dark & shadowy "forest" of stone-like objects shaped like "trees" is inhabited by many creatures. While retreating toward open ground the kids get a first good look at one in the light from the flashlight.
An icy touch on his forehead made him duck his head and flash his light upwards. In the rays he caught sight of the strangest object he had ever imagined. Its gnarled body was like apiece of tree-root about eight inches long, and running down the creature was a kind of fin that waved as it flew through the darkness giving it the appearance of a fish swimming. As it flew out of the torch rays the eyes lighted again. Martin was able to see in the flash of its rapid charge that its eyes were enormous--out of all proportion to its size.
In Chapter XIII "The Lost Trail", page 220 a dead moon bat is found:
It was about fourteen inches long from nose to tail, and seemed to be of a hard rock-like substance; in appearance not unlike a small crocodile, but without the long jaws and muzzle. Its nose was thick and short, like a pig's snout. Close to the head were a pair of bat wings, now close and limp; and large eye-sockets out of all proportion to its size. The eyes were now covered with heavy lids in death; but a thin, white streak showed where they were only partially closed. Those were the lamps that had added to the terror of the forest. Its rocky body ended in a sharp spike of a tail. Evidently this spike was used for attack, for the point felt as sharp as a needle. And, like all other creatures and vegetable matter on the moon, it was of a grey color, dry and stony.
How thick would the lunar atmosphere have to be for insect and bird sized creatures to fly in?
Insects can fly and kite at very high altitude. In 2008, a colony of bumble bees was discovered on Mount Everest at more than 5,600 metres (18,400 ft) above sea level, the highest known altitude for an insect. In subsequent tests some of the bees were still able to fly in a flight chamber which recreated the thinner air of 9,000 metres (30,000 ft).
Birds, mostly large birds, can fly in air as thin as up to 37,000 feet. Alpine choughs, the size of crows and possibly the size of "moon bats", can fly as high as 8,000 meters, or 26,500 feet.
And there is supposedly no wind on the Moon, despite the fact that there are detectable winds on Triton, where the atmospheric pressure is low enough to be fatal within seconds without a space suit.
in Part Two, Chapter IX "The New World" on page 180 Jane asks if they will be able to find their way back to the ship:
"Yes," answered Martin, "we'll just follow our tracks back; the marks are very distinct and there's no wind to disturb them."
In Chapter XI, the Forest of Watching Eyes", page 201, The kids follow their trail back toward the ship:
The trail was most certainly there--the trail left by their footprints when they came down the slope on their way to the valley--but here and there an unaccountable gap in the trail puzzled him. There was no wind to disturb the dry, powdery ash, but all the same the trail had been disturbed, and thee was a slightly different appearance about the slope.
In Chapter XIII "The Lost Trail", page 216:
It was very difficult to gauge one's sense of direction in this strange world where there was no wind or color, sound or smell, and where everything look so much the same.
Sounds are not as loud on the Moon as on Earth.
Part two, Chapter IX, "A New World", pages 174-175:
As it was, the had to be content with cheering, but their cheering, accompanied by Scruff's exited yelps, sounded like whispers in this land of silence, where....
Part two, Chapter X, "The Lunar Valley", page 181:
She climbed on one of the hillocks of the sloping path and tried to shout loudly; but her voice was like a whisper.
"Why didn't you shout?" Jane asked. "how did you expect me to find you?"
Shout?" he answered indignantly. "I should jolly well think I did shout; but the odd thing--or one of the odd things--about the moon is that our voices don't carry far. It doesn't matter how loudly you shout, it sounds like a whisper. I heard you faintly once, but it seemed as if you were miles away..."
I am not certain there is any atmospheric pressure and composition which could satisfy all those requirements.
So on November 18 the thought occurred to me that possibly when Martin goes to sleep between chapters two and three, or when he goes to sleep again between chapters four and five, or possibly later, he might dream about stowing away on the rocket Luna 1, and might possibly still be dreaming in the last paragraph of the book:
The copper, misty moonlight came through the open bedroom window on the sleeping boy. On a chair beside his bed was a human skull and a tiny red glass button.
In any case, I must remember that when I find the story I wrote has vital but impossible or contradictory elements in it, to put in hints that part or all of it might be a dream, to keep readers from complaining too much.
"The surface seemed to be full of ashes..."
In Part One, Chapter II, "The Wood" page 11, Professor Erdleigh describes the Moon based on telescopic observations:
"I doubt if people live there; no, I think that's impossible. I I think it' quite possible that there is insect life. You see, we know the moon is made up of volcanic ash..."
And in Chapter III, "The Beginning of an Idea", page 30, he says:
"I'm very doubtful. Insects, I think, are the only possibility. Extreme heat and cold, lack of water, just ash, and no light. It's like a mirror reflecting the sun and our earth; obviously no vegetation."
When the kids venture out on the Moon in Part two, Chapter IX, "A New World", page 173:
The first sight of the lunar landscape filled the boy and girl with wonder. The grandeur and beauty of this grey, cold, silent land surpassed anything they had ever dreamt of. Immense mountain ranges threw shadows into caverns fathoms deep: the earth-light made plains hundreds of miles wide appear rivers of shimmering silver. Lava thrown from the extinct volcanoes fell into weird shapes, like pre-historic animals fossilized in the icy cold....It was a world of sharp contrast, black and white, heat and cold; and all substances appeared to be of the same grey, dry pumice stone in various degrees of texture.
The explorers stood gazing at this spectacle in bewilderment, their feet sinking into the soft, ashy dust, and forgetting the ice-cold conditions of their newly discovered world or the trials awaiting them.
On page 175:
Their feet sank into the grey, powdery dust as they climbed slowly over the uneven ground.
Jane sat down to take off her shoes, which were full of clinkers, when she noticed a movement in the powdery ground by her side.
...for the surface was mainly composed of the same powdery ash as they had found everywhere, and only a rock here and there to cling to;...
...The lava ash had formed delicate, lace-like patterns,...
And many other examples. I believe that British astronomers favored a volcanic origin for lunar craters in the 1940s.
"...and they found what seemed to be a human skull in the ashes."
In Part Two, Chapter XVI, "A Blinding Flash", on page 243, while running for his life, Martin picks up a lump of lava rock. And in Chapter XVII, "the Final Discovery", on pages 251 to 252, Professor Erdleigh finds something in the lava:
The family looked inquiringly at each other as the Professor prodded the ash with a delicate forefinger, then picked up a rounded object and held in the palm of his hand. It was a human skull.
"Your ants, your bats, and your snakes were interesting," the professor said, still in a suppressed, high-pitched voice, "but this proves without the slightest doubt that there was once human life on the moon. How many thousands of years old this fossilized skull of a human being is we don't know: we may find out sometime."