Comment Kim Stanley Robinson, "Red Mars" (Score 1) 361
Martian colonists get angsty, and decide to get liberated. The Earth-based companies that own the colonies decide (naturally) to launch a transport full of a few thousand space marines to retake control. That trip takes a few months, minimum, even on the fastest, least fuel-efficient course that the transport is capable of making. So the colonists know that the marines will be dropping in, well in advance of their showing up in orbit.
Now, instead of using the ship's main engines to decelerate completely on arrival, most of the Earth-Mars ships aero-brake in the thin Martian atmosphere, which conserves fuel (which can instead be used at the beginning of the trip, to accelerate out from Earth, so that the whole trip takes less time). The ship slows down partially with its engines, and then flies into the beginnings of a very close hyperbolic "slingshot" pass that grazes the upper reaches the atmosphere. The added friction slows the ship down, curling the orbit inward and turning the actual course into a parabola. In theory, if done correctly, the ship would end up in a stable "parked" orbit, with zero fuel expenditures after the slowdown and course-correction it performed at the beginning of the approach.
But, unfortunately for the intrepid space marines, a crafty scientist amongst the colonists builds a small, cheap solid-fuel rocket with a basic guidance system and a nasty payload: An explosive packed with scrap-metal shrapnel. As the marines' ship approaches and its pilots initiate their aero-braking manoeuvre, the lone colonist launches his flak rocket into the ship's approach path, where it explodes and scatters a cloud of metallic debris.
The ship's radar detects the sudden appearance of the cloud of space junk, and the navigation computer performs an emergency space-ward course adjustment to avoid a collision with the potentially dangerous debris. But the new course is too high in the atmosphere to burn off enough of its momentum, and its course stays hyperbolic--the transport ship "skips" off the Martian atmosphere and continues back out into space at high speed, on a random new course. Sorry, no invasion, this year.
The troop ship has enough fuel left to change course toward Jupiter, and it takes a conventional hyperbolic return course around the gas giant to get back heading toward the inner Solar system. Eventually, it DOES manage to get into a Martian orbit (much more carefully, this time), but the additional Jupiter round-trip buys the colonists the extra time they need to prepare to handle the invaders on the ground.
Amazing stuff, fantastic book (and trilogy, too).