It looks like 99942 Apophis is a 330 m (1300 ft) wide rock. Such a rock if it is primarily composed of stony-silicates in a loose 'rubble-pile' configuration (density of about 1500-2000 kg/m^3) will mass in the neighborhood of about 33 million metric tons.

If impact velocity were about 10 km/s, the impact energy would be approximately:

K=1/2*m*v^2 or about

0.5*33*10^9kg * (10^4 m/s)^2=1.65*10^18 J.

This is about the same amount of energy liberated as the simultaneous detonation of about 18,000 Fat Man (Nagasaki 20KT) sized atomic bombs: nearly 400 Megatons.

This is more than plenty to completely obliterate any city on the planet unfortunate enough to be beneath the impact ellipse of such an object.

A water strike by such an object, provided it was far enough out in the ocean, may have little effect on the coasts. However, a close impact of say anything less than 100km will still be pretty devestating to the coastal areas adjacent an impact. A nearby strike would be horrendous!

Deflecting such an object is difficult, although the relative scale of difficulty is a function of the delta-v required to move such an object. And the required delta-v to cause a 'miss' goes up rather drastically with decreasing time until impact. Thus, if we can find and characterize the orbits of such objects decades in advance of their estimated impact time, then we do ourselves the double favour of warning ourselves of impending danger, and giving ourselves plenty of time to shift the trajectory into a 'miss.'

A change in speed of the asteroid 20 years before impact of just 50 m/hr, could result in a shift in trajectory of approximately 8800 km, which could potentially be a miss. The same menuver performed at 1 million km (10 thousand seconds or less than 3 hours before impact) out would require a delta-v of about 880 meters per second--which is clearly not possible without using nuclear explosives. And this would almost certainly result in the gross fragmentation of the body--which may be good or bad, depending on the number and size of the individual fragments. Certainly bad for anything that happened to be in orbit about Earth at the time!

A 50 m/hr delta-v is still a very substantial velocity change for the asteroid. If we were to use nuclear thermal rockets, using liquid hydrogen and operating at a specific impulse of 1000 seconds, we could achieve the desired impulse by expending:

dM=mi*(1-exp(V/Ce)) where mi=initial total mass of asteroid and propulsion system, which we can approximate by saying the propulsion system is of negligeable mass compared to the asteroid, so mi=33 million tons. V=desired velocity increment in meters per second. Ce=exhaust velocity of rocket in meters per second, found by multiplying the Isp by Earth's gravitational acceleration constant of 9.80665 m/s^2.

Putting it all together we get:

dM=33*10^6 tons *(1-EXP((50 m/hr*1hr/3600 seconds)/(1000*sec*9.80665*m/s^2)))
dM=46,700 kg. This is the amount of liquid hydrogen propellant required to give this asteroid a velocity increment of only 50 m/hr. This seems rather doable. If the Isp was instead 10,000 seconds as for an Ion engine, then how much propellant would be required?

dM=4674 kg, which also seems doable. Even though these are substantial amounts, the numbers seem plausible.

How about power levels? Well, in the first case, let's suppose we have an NTR which is capable of processing about 25 kg/sec of propellant. This results in a burn duration of about 1870 seconds, or about 1/2 hour. Now with 1000 seconds of specific impulse, estimate the kinetic power of the exhaust jet:

P=1/2*25*kg/sec*(1000*sec*9.80665*m/sec^2)^2

which comes to about: P=1202 MW. This is Jet Power--the actual mechanical power carried off by the stream of gas exhiting the nozzle. For most efficient rocket engines the Jet Power is created with much better than 50% efficiency, so a concervative design would pin the available reactor power at about 2.4 GW, which is on par with the Phoebe-2 Reactor system of the original Project Rover/NERVA programs. Incidentaly the thrust level achieved by this engine would be about:
F=(25*kg/sec)*(1000*sec*9.80665*m/sec^2)
F=245 kN of force (which is about 55000 lb-force) which is also in the ball park of a Nerva engine from the 1960's.

For the second example using Ion engines, we'll start with the reactor and work backwards. Let's say we have a good 5 Megawatt thermal reactor which produces a modest 1.5 MW of electric power. Now assuming power conversion of 89% then the available delivered electric power to the ion thruster is about 1.5MW*.89=1.34 MWe.
Modern ion thrusters are about 45% efficient, so the conversion of this electric power to Jet Power (kinetic power of exhaust stream) is about: 1.34 MWe*.45=0.603 MW

The jet power equation is: P=1/2*mdot*v^2, where v=the exhaust velocity in meters per second, and mdot is the time derivitive of mass (otherwise known as the propellant consumption rate!) then solving for mdot gives:

mdot=2*P/v^2

And in the case of the ion engine: P=603,000 Watts (jet power), v=10,000 sec*9.80665*m/sec^2 gives us a propellant consumption rate of:

mdot=1.254*10^-4 kg/sec of propellant, or about 10.84 kilograms per day.

The estimated burntime is thus about:

T=mp/mdot, where mp is the mass of propellant available.

Using mp=4674 kg, mdot=1.254*10^-4 kg/sec, gives us a burntime of:

T=3.727*10^7 seconds, or about 1.2 yr. Which seems doable as well!

While an NTR system is probably achievable sooner, the delivery of 45 metric tons of propellants to an asteroid millions of kilometers away is no small engineering feat. Such a combined system will probably approach 60 to 70 tons, minumum. This would require orbital assembly, and multiple launches to ferry up parts. Thus it seems that the ion thruster system--which at first appears to be more technically challenging, appears to be the winner simply by virtue of the fact that the size of such a system is surprisingly modest. Utilizing something like a Prometheus propulsion system with expanded propellant capacity, and ample jettisionable ion thruster spares seems at first 'glance' to have the ballpark capability to be used as an ansteroid deflection system. And at first, I admit that I was skeptical. I thought for sure NTR would have it beat hands down. I think it can be done with ion thrusters!




-- Edited by GoogleNaut at 19:35, 2005-10-30

With either a nuclear heat engine or a solar panel you are obliged to expose a lot of surface, either to reject waste heat or capture sunlight. The difference is that rejecting waste heat can be done at more than 1 kW/m^2.

But there's another kind of solar panel that can do a lot in space, and that is a thin reflective film. Googlenaut mentioned applying a 50-metre-per-hour delta 'V' to a 33-million-tonne rubble pile, momentum change 4.6e+8 N·s. Draping an aluminized mylar strip 10 metres by 10 km over the pile so that two 5-km tails hang from it in the direction away from the sun ... well if they hang straight away they don't do much, but spin is likely to prevent that. Say they hang 45° away from the antisunward direction. Then from the sun their projected area is 70710 m^2 and they harvest the starward momentum of ... supposing their service starts at a point as far from the Sun as Mars is ... 16 MW of sunlight. Divide by 'c' to get momentum transfer rate, 0.052 N.

That's going to take 280 years to accumulate the 4.6e+8 N·s. Well, using wider, longer strips, and more of them, it wouldn't necessarily be a joke. It has no moving parts.

--- Graham Cowan, former hydrogen fan
boron as energy carrier: real-car range, nuclear cachet