The Solar System remained much the same as it is in our time until around 2170 AD. Around that time, a Gauna Mass Union Ship was sighted in the outskirts of the Solar System. An uneasy peace was maintained for 200 years, until, in 2371, the Mass Union Ship moved closer to Earth, and cast down 46 Gauna to the surface.
The Solar System of Sidonia is a much-changed place.
Earth has been split into two, all life destroyed. After the Gauna began their invasion, all life on Earth came under attack. Ocean life, humanity, and all other lifeforms were consumed by the Gauna. Humanity fought back, but found themselves unable to pierce the Gauna's True Body. After an unknown period of time, the Earth itself was cracked in two by the Gauna, splitting into two hemispheres. It is after this time that the Sidonia launched, and left the Solar System.
Whether the other planets of the Solar System remain, and whether any of humanity still lives in the Solar System, is unknown.