Black Hole War
Earth has been at war with the Andromedons for the past millennia. Earth finally managed to gain the upper hand, which forced the Andromedons to use their ultimate secret weapon. The Andromedons have turned the matter in the Sun into a super-dense material, such that the Sun is now a black hole with Schwarzschild radius equal to the Sun's original solar radius.
Luckily, a thousand year long space war lead to a lot of advancements in mankind's weaponry, and they've developed 100% energy efficient 1 exatonne antimatter bombs. With the help of a giant 100% energy efficient solar sail attached to the Earth, humankind can use these bombs to altar the trajectory of the Earth.
How many of these bombs need to be detonated to eject the Earth from the solar system to safety?