Quote from Mal on 08/20/08 at 23:26:19:

 
Why?
 
Yes, you can do this.
 
menu > Autopilot
Choose "Continuous Orientation" and select "towards" and choose your object in the left dropdown list, and choose the Sun in the right dropdown list.  Click the "Current Time" button.  Then press "Add"
This adds an autopilot command that tells it to always aim the asteroid towards the Sun beginning now.
 
While still in Autopilot
Choose "Thrust", select your asteroid, place 9.8 in the "meters/second/second" box, and make sure that "initiate" is choosen.  Press the "After Last" button.  Press "Add".
 
This adds an autopilot command that tells it to begin thrusting at 9.8 m/s/s in 1 second from now.
 
If you want it to thrust indefinately, then you're finished.  Simply press "OK".  If you want it to thrust for a specified amount of time, then enter the time and date you want the thrust to terminate.  Then choose "Thrust" from the dropdown list.  Select the asteroid, and choose "Cut off".  Press "Add".  Then close the Autopilot by pressing "OK".
 
I just tried it.  This is a pretty cool simulation.

Quote from frankuitaalst on 08/22/08 at 09:13:33:

Yes.  It's as if the asteroid has a rocket engine on it, and it aims straight at the Sun, accelerating at a constant 1g.  Where it's going to get the required energy to do this is a mystery.  Mal has some explaining to do.
 
It's initial orbital velocity is what keeps it from crashing into the sun.  And it can't leave the solar system either, since after it passes the sun, its as if it turns around to continue thrusting towards the sun.  It's actually more interesting if you start it at 1 AU instead of 40 AU.

Heh, that's awesome - it keeps missing - this is what it looks like after 20 months - the pink trails are the asteroid that keeps coming back to try to hit Earth .

Same thing, but the asteroid starts at 5 AU, not 40 AU. This is after 2 full years of simulation time - it's a very pretty pattern, but it's still missing the Earth
 
In all cases the rock's initial orbit around the sun is eccentricity 0.1, inclination 0 - would changing that make any difference at all?

Rock starting at 5 AU, with 6G acceleration toward planet. Still missing...! (after 1 year of simulation time)

Quote from frankuitaalst on 08/25/08 at 09:37:42:

 
Well the 6G rock was on a timestep of 1...  

You're right . I did some calculation and it takes about one year to reach c at 1g  
. Distance travelled is then more than 10^15 meters .  
However starting from 40 AU the speed may already be enormeous.