# How big a nuke would be needed to break Phobos out of orbit?

Phobos

• Orbital period: 8 hours
• Equatorial rotation velocity: 11.0 km/h (6.8 mph) (at longest axis)

With an 8 hour orbit around Mars it must be going at a fair clip already which got me to wondering, why not use it as a generation ship, if we can kick it out of orbit we might even be able to do it in a way where we slingshot it around a couple of other planets on the way out .. that might give us a respectable speed .. & there's plenty of room inside for some really big sealed habitats.

So assuming it's optimally positioned on the surface for the purpose.

How big a nuke would we need to break it out of its orbit of Mars?

Presumably a large concave pit in the appropriate spot is needed to guide the blast for best effect.

• Recommend closing due to the inappropriateness of the concept. I recommend asking for a calculation of the total energy needed to be applied along a vector to move a satellite of this mass. A "nuke" dumps energy in a rather uniform 4*pi steradians (excepting some relatively small "directed energy" items which will be useless against anything bigger than a very small asteroid), so most of the energy won't even change the kinetic energy Phobos has. Dec 6 '19 at 14:14
• This is a hellishly difficult question to ask, due to the range of different ways a chunk of rock might respond to a really energetic dose of x-rays. Also, if I'm not misunderstanding, as you lift it out of Mars' gravity well, it'll slow right down (because Kepler hates you) so it isn't immediately obvious that there's any benefit over phobos vs some other rock potatoid in the asteroid belt. Dec 6 '19 at 14:16
• @CarlWitthoft you could always bury it, of course. Doesn't make modelling what happens next any easier, but there'll be less wastage (in exchange for more mess). Dec 6 '19 at 14:19
• Although an object in a close circular orbit will be moving faster than one in a distant circular orbit around the same body, it still takes more energy to get it out of orbit and away to infinity, so Phobos is basically the worst possible choice for this. A main belt asteroid, a distant Moon of Neptune or a KBO like the one photographed by New Frontiers would all be better choices. Dec 6 '19 at 14:19

Simply to lift get Phobos out of Mars orbit you would need to increase its orbital velocity by a factor of $$\sqrt{2}$$ (this is generally true for any object in circular orbit). Phobos orbits at about 2.1 km/s (Wikipedia) relative to Mars, so this is a delta-V of $$2.1 \times (\sqrt{2} -1)$$ which is about $$0.9 km/s$$. It's mass, same source is about $$10^{16}kg$$ so the energy needed is $$0.5\times 10^{16}\times 900^2 J$$ which is $$4\times 10^{21}J$$. So, assuming perfect efficiency and no wastage at all (which you will certainly not get with a nuke) you must release at least this much energy. A ton of TNT equivalent is just over $$4GJ$$ so this is just about $$10^{12}$$ tons TNT equivalent, or a million megatons.

• @Pelinore little rock? I feel like you need to recalibrate your sense of size ;-) Dec 6 '19 at 14:41
• @Pelinore and everest is less than 9km high... you could be up and back in time for tea and medals. Dec 6 '19 at 14:46
• @uhoh you're missing the kinetic energy of its current orbit. Dec 6 '19 at 14:48
• @uhoh fair point. The KE of Phobos on an escape trajectory as measured by an observer left behing in Phobos old circular orbit is the number I computed. The change in KE of Phobos as observed by an observer at rest at the centre of mass of Mars is half the number you calculated. I think to reconcile these we have to think about what happened to the reaction mass and how much energy each observer thinks it had to start with, and thinks it has at the end. Dec 6 '19 at 14:56
• I'm still pondering this and fyi I've just asked When is it okay to use energy arguments in orbital mechanics?
– uhoh
Dec 7 '19 at 2:19

It can't be done. Unless it's really, really solid (and that's not likely!) trying to shove it that hard will break it up instead. You would need to use a bunch of bombs to move it more gently.

• Yes I noticed that a few hours back, my attention is shifting to Deimos now, nothing I've found so far suggests that's an accretion of loose rocks too but I'm still looking? the questions still good for the orbital mechanics of moving that much mass from that orbit, but your right, a single blast big enough likely breaks Phobos up. Dec 8 '19 at 3:05
• @Pelinore I would be very surprised if any moon of any planet anywhere can be shoved out of orbit with one boom. You move such things around with a bunch of smaller bombs, not with one big boom. Dec 8 '19 at 3:16