Time Until Impact
During avatar creation it is possible to adjust the scheduled asteroid impact time. It can be adjusted between 6½ and 7½ days from when the avatar first spawns on their first world. It is recommended to select late time so you have time to react in the few critical hours prior to impact.
Cities with an observatory report the presence of an asteroid in its solar system, which is necessary to detect asteroids at extreme range. Asteroids known to be on a collision course with a world will cause an event log alert in the city report.
The asteroid won't physically spawns in the solar system until the the last 8 hours before the scheduled time. The asteroid will at first spawn around 50 AU away and travel at ~1000m/s towards the homeworld. The travel speed with automatically increase and decrease to ensure the asteroid will impact with the homeworld it is locked onto at the exact scheduled time.
The asteroid is marked as enemy, and can thus be targeted from a fire control station. It will also appear on the Unit list for attack and follow orders.
Depending upon the size difference between the asteroid and the world world being impacted, devastation could range from destruction of all cities on the world, to complete annihilation of the world body.
Asteroids of any size is are absorbed by gas giants harmlessly.
Extinction Level Event
When a smaller asteroid impacts a world it will create a huge crater, and all cities and buildings on the world are destroyed.
The moons of a world are unharmed, unless subsequently hit by another asteroid. They will spin on an additional axis and tumble in the asteroid belt.
The system survey and star map XML export of the solar system with the destroyed world will still show the system as it was originally created. To obtain the proper resource information for any remnants of the world, you'll need to perform a manual scan with the sensor station. According to Haxus, this is because "The system scan is generated based on a seed value. It doesn't know the planet was destroyed."
The goal is to develop the needed technology to get into space and either destroy the asteroid or evacuate the homeworld.
Energy weapons are highly recommended, as projectile weapons aren't easily used by the crew.
Note: It is not recommended to rely on military weapon systems to defend against an asteroids, as they will not be able to damage the asteroid enough by the time it gets into range. At most it can downgrade it from a world destroyer asteroid to multiple extinction level asteroids right before impact.
Breaking Apart and Smaller Asteroids
The asteroid will break apart into smaller asteroid pieces as it is damaged. These smaller asteroids will not be locked onto the homeworld, but will have some of the same trajectory as the original asteroid. in most cases smaller asteroids will simply be pulled in by the gravity of larger celestial objects, such as a sun or gas giant.
The easiest way to defend against an asteroid is with a spacecraft and energy weapon bay technology.
A spacecraft stationed in orbit with an energy weapon bay, system ranged sensors and a commanding officer will be able to take care of an incoming asteroid on its own. The officer will automatically order the crew to attack the asteroid once it is in sensor range.
Note: An easy way to gather the resources needed by energy weapon bay and lens is to make small colonies on inferno and frigid planets of your starting system. This way you only have to put down an airport terminal to instantly get any resource from your main city. It makes it easier to colonize and build a decent mining colony. Don't be shy about corrosive atmospheres. Use pressure tents to be safe from the corrosive effects.
Haxus visited the homeworld of Tamunshin to help with an asteroid, however they were unable to destroy it before the impact. Haxus recorded a video of the impact which can be seen here: http://hazeron.com/Playlists/Scenes%20of%20Hazeron/AsteroidImpact.mp4
Also, this was discussed in this thread on the forums: http://hazeron.com/mybb/showthread.php?tid=2062