Heaven's Reach

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Heaven's Reach is the third novel in the Uplift Storm series by David Brin. Like the first two, it follows the adventures of the Terran scout ship, Streaker. This novel, though, features more alternate storylines than its predecessors, tracking not only the humans, but the Jijoan exiles as they re-enter mainstream Galactic society, the chimpanzee hyperspace scout Harry Harms, the Jophur as they chase the humans, and the humans hiding on the Jophur ship Polkjhy.
The book takes the Streakers off the planet Jijo and back in space. Still trying to reach Earth, they come into contact with various orders of life: Hydrogen Breathers, the Retired, Machines, and the Transcendent. Soon an impending event of universe-shattering importance is revealed — and the Streakers are recruited by the Transcendents to play a part in it, before limping back to Earth with one trick left to play.