The Invading Asteroid by Manly Wade Wellman (1932)
Okay, so it's a pretty big stretch to call this a book -- it's only 23 pages, after all. But Wellman bibliographies list this as a book so who am I to argue. Beginning in 1929, Amazing Stories editor Hugo Gernsback began issuing a series of chapbooks containing from one to two science fiction stories; The Invading Asteroid was the fifteenth of the eighteen chapbooks issued.
The time is 2675 and Earth is experiencing a lull in its war with Mars, which is currently on the opposite side of the sun -- the distance making attacks almost impossible. Three young cadets in the Terrestrial League's space force, anxious to experience flight without a supervising officer, use this quiet time to "borrow" an unarmed fighting ship to go for a joy ride. Twenty hours away from Earth, they are attacked by an armed Martian scout ship. The "almost impossible" has become very possible. Using their sneaky Earthly wiles, the trio capture the ship and its pilot, a young Martian named Yaxa. It turns out that Yaxa came from an "asteroid" that is heading towards Earth.
The asteroid, of course, is a hollow construct carrying two thousand armed Martian ships and six hundred thousand Martian warriors, sneaking up to take Earth unawares. Thanks to our plucky threesome Earth, however, is aware and our heroes suddenly become instrumental in thwarting the attack.
Since this was first published in 1932, and science fiction for the most part was pretty crude, there's not much nuance or logical plotting in the story -- just slam-bang pulp action. And that's all right with me. It's not top-notch Wellman, but it's an interesting part of his literary past.
Pulpville Press reissued a number of these chapbooks, two to a volume, a few years ago. The volume containing The Invading Asteroid also contains The Girl from Mars by Jack Williamson and Miles J. Breuer, which was the first in the Gernsback chapbook series. (The Williamson-Breuer story has a strange illustration by Frank R. Paul in which a girl in the background appears to have a goose growing out of her neck. Go figure.)