Expert: Philip Stahl - 8/5/2006

Question
Dear Sir,

I am a 24 year old graduate in systems engineering, and am currently trying to plan a sci-fi story that I wish to write (non-professionally) which involves a very large lunar-based mass-driver used as a weapon to deliver artificial asteroid strikes upon Earth. I would like to roughly calculate the speed to which my lunar mass driver must accelerate the man-made asteroid in order for it to enter Earth's atmosphere at 50km/s. This will aid me in the design of the mass driver itself. I would be grateful for any help you can give me with this task.

My main concern regarding the calculation is the length of time the object will accelerate due to Earth's gravity as it nears Earth. To get a rough idea of the deceleration and impact effects I am using a web program designed for that purpose, found at http://www.lpl.arizona.edu/impacteffects/ The asteroid is composed of dense rock encased in metal/alloy so that it holds together during re-entry. The mass of the projectile is approximately 214,708,500 kg (for the purposes of the calculation, a sphere of 45m radius and 4500km/m3 density). I use a sphere because that is what is used in the impact effects calculator, although my story will involve an artificial "asteroid" shaped somewhat like a blunt bullet.

I'm only looking for a ball-park figure, not precise numbers, so please feel free to make and note any other assumptions you require.

Thank you for your help, and I look forward to your reply.

Regards, Dominic

Answer
Hello.

As far as I can tell the mass you are assigning is not consistent with the density arrived at (4500kg/m3). For a 90 m dia. sphere, your density would instead be ~ 570 kg/m^3 (e.g. the volume based on a 45 m radius sphere is almost 1000 times greater than the one you suppose). You may want to re-check these numbers.

In addition, the velocities of asteroids - especially nearing Earth - are typically no where near 50 km/s. (Comets do tend to exhibit such higher velocities).

Finally, even if you could accelerate the projectile to near 60 km/s from the lunar surface (near the minimum of what would be needed to achieve the end velocity you want - and I see no practical way of exceeding that) you are looking at hours for the thing to hit the Earth. This would provide would-be targets with ample time to direct ICBMs at the incoming projectile and knock it out.  

Anyway, good luck with your book concept!