Darkness and Dawn, published in 1914 and written by George Allan England. You can find a short summary here, but it concerns Beatrice Kendrick and Allan Stern, released from suspended animation after a disaster that carved a chasm 600-700 miles long where Middle West used to be (with said material perhaps forming the second moon). They find the biplane in Chapter 16.
Project Gutenberg also has a copy here. Here is some of the opening page:
Dimly, like the daybreak glimmer of a sky long wrapped in fogs, a sign of consciousness began to dawn in the face of the tranced girl.
Once more the breath of life began to stir in that full bosom, to which again a vital warmth had on this day of days crept slowly back.
And as she lay there, prone upon the dusty floor, her beautiful face buried and shielded in the hollow of her arm, a sigh welled from her lips.
Life--life was flowing back again! The miracle of miracles was growing to reality.
Faintly now she breathed; vaguely her heart began to throb once more. She stirred. She moaned, still for the moment powerless to cast off wholly the enshrouding incubus of that tremendous, dreamless sleep.
Then her hands closed. The finely tapered fingers tangled themselves in the masses of thick, luxuriant hair which lay outspread all over and about her. The eyelids trembled.
And, a moment later, Beatrice Kendrick was sitting up, dazed and utterly uncomprehending, peering about her at the strangest vision which since the world began had ever been the lot of any human creature to behold--the vision of a place transformed beyond all power of the intellect to understand.
For of the room which she remembered, which had been her last sight when (so long, so very long, ago) her eyes had closed with that sudden and unconquerable drowsiness, of that room, I say, remained only walls, ceiling, floor of rust-red steel and crumbling cement.
For what it's worth, the search I did was science fiction novel second moon chasm suspended animation.