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I remember a book from about 25-30 years ago. The main character was a young girl in possibly her early teens. She was in a fall-out bunker of some kind alone, but had learned a lot about survival and science from her father.

When she leaves the bunker, she initially thinks she is alone, but discovers others are still alive on Earth. During her journey to meet up with someone, she ends up in space - where I remember specifically the discussion of orbital mechanics, and needing to "slow down" to "catch up" (something I later had fun with in Kerbal Space Program).

Can someone identify this book for me? I'd love to re-read it.

I’d be pretty sure that’s Emergence by David Palmer, first published (in one volume) in 1984. There’s a sequel, Tracking, written decades later.

The following day a worldwide attack, featuring a bionuclear plague,
wipes out virtually all of humanity (i.e., Homo sapiens). With pet
bird Terry, a Hyacinthine macaw, her "lifelong retarded, adopted twin
brother," who tends to "parrot" Candy's words even before she speaks,
she survives the attack in the shelter beneath their house. Emerging
three months later, she learns of her genetic heritage and sets off to
search for others of her kind.

First the hunt turns up "Adam", a cheeky, irrepressibly punning,
multitalented 13-year-old boy, who immediately sets out to win Candy's
heart; next, Rollo Jones, a middle-aged physician with a broad history
of survival-in-the-wilds experience ranging from a stint in the Peace
Corps to mountain climbing; and finally, Kim Melon, an early-20s mom
whose background is in computer engineering with Lisa, her
six-year-old daughter. Rollo reveals himself as a sociopath, whom
Candy is forced to kill defending Terry and herself. Adam, Kim, and
Lisa join Candy's quest for the AA community. As part of the search,
Adam reveals that he is an ultralight aircraft pilot. Later he teaches
Candy to fly.

Thereafter, an ultralight engine failure separates Candy from the
others. After getting it running again, she spots a contrail, which
leads her to Vandenberg Space Shuttle Launch Complex, where Teacher
and the AAs are laboring to preflight a shuttle, renamed the Nathan
Hale. They have identified those who wiped out mankind, the Bratstvo,
translated as the "Brotherhood", a cabal of H. sapiens, working from
inside the Russian military to destroy all H. post hominems. As
insurance, they have placed a doomsday device in geosynchronous orbit,
a Strontium-90 bomb whose fallout will render Earth uninhabitable for
200 years.