I've been thinking this over myself for a couple of cosmic-level things that I want to build, in particular a more 'accurate' look at the Silver Surfer and Gladiator style characters whose entire concept involves them punching planets into asteroids, so here's a glance at what I've come up with...
So How Are We Going To Do It?
There are two forms of destroying an object; the breaking rules, and the damaging rules.
In the former case the basic idea is that you are not being impeded from destroying the object in question and can simply take a full-round action to attempt to destroy the object. During which it effectively takes a roll of 5 on its toughness. If using a more hand-to-hand method of breaking the object, you can add your super-strength bonus to the damage in question. If your damage bonus is equal or superior to the object in question's toughness, then you automatically break it, and if your damage bonus is five ranks higher than the object's toughness then you can actually go so far as to destroy it entirely.
In the latter case the basic idea is that you attack it like any other object or character, usually in the heat of battle or conflict. This is the kind of situation where you can have the Silver Surfer or Son Goku aiming a blast at a nearby moon and destroying it as a standard action. When using melee attacks, you do not add your bonus to super-strength, and on top of that the object is allowed to roll for resistance. That said, the book does at this point give the option that 'The GM may want to to simply have objects effectively "take 10" on Toughness saves to simplify matters'. This has the effect that you can basically automatically disable or break objects with a damage bonus five ranks higher than the toughness effect, and automatically destroy objects with a damage bonus ten ranks higher than the toughness effect.
Due to the fact that the Earth is really large, as well, I would not allow a super-strength bonus to be added onto the roll, even if only due to issues of leverage. Not unless the character had a significantly large enough number growth ranks that it became believable for them to be within a few categories of the object in question when it comes to size.
But Wait A Minute, How Tough Is The Earth?
This is a question with a surprisingly complex answer, and depends mostly on a few things. The first is the fact that object toughness rules in Mutants & Masterminds 2e are somewhat strange, and the second is the simple question of whatever the hell you think the Earth is actually made out of. I mean, the answer for the latter changes somewhat drastically depending on how you look at it.
For the latter, however, we're going to assume that the Earth is made out of iron for our purposes, since that is the substance with the highest percentage number, at least according to my sources. But due to the more variable material density between the crust, mantle, outer core, and inner core layers, I'm going to assume that the Earth has the same basic toughness as steel.
So that means that the Earth has a basic toughness of around +10, or at least the first inch has that basic toughness, before we start moving our way up the time and value progression table. Which brings me to the not-entirely-complicating factor, that the substance thickness rules work somewhat strangely in Mutants & Masterminds 2e. Rather than increasing the actual toughness rank, it increases the threshold of the toughness save by one rank for each increase along the progression table. For simplicity, and also the special circumstance fact that the Earth is bloody huge, I'm going to be assuming that this is more a straight toughness bonus. Though I will probably be using that as a future rule of thumb for house rulings.
As has been mentioned before, the Earth is approximately five hundred million inches in diameter. Along the time and value progression table, that's around a +26 increase in effective toughness. This leaves us with a basic toughness save of +36. Under the 'breaking object' rules, that's a +41 roll, and the 'damaging object' rules make it a +46.
Putting It Together
Let's have a look at how this goes together;
Damaging the Earth
In order to damage the Earth at all, you need to have a damage bonus which is at most fourteen or fifteen ranks lower than the object's basic roll.
For the breaking object rules, this is around +26-27.
And for the damaging object rules, this is around +31-32.
I think the effect of this would probably be the equivalent of a very large nuclear explosion, possibly much larger than our modern nations can imagine. It'd be the equivalent of Lex Luthor nuking the San Andreas Fault during the 1978 Superman film a hundred times over, and would probably damage things on the other side of the world. To inflict notable amounts of damage on the Earth is the sort of thing that would carry the words 'extinction level event', given the sheer scale of the forces involved. But for an odd outlook, I actually believe these effects would be temporary, and the injured effect on the Earth itself would probably fade after a few minutes or even a few rounds at most, and possibly wouldn't even stack. I would also for the same basic reason ignore the increased damage effects from autofire.
While it might seem odd to claim that the Earth would have regeneration or even immunity to injury in this manner, the simple fact of the matter is that the gravity involved would keep the Earth in one piece.
Breaking or Disabling the Earth
So you want to punch a hole in the Earth, eh? Well, the rules are much as above, but are basically equal to the basic toughness save of the object subtracted by five. Which means you that can just add ten ranks to those which are required for damaging the object.
For the routine-action breaking objects rules, the damage rank required is +36. Actually equal to the object's toughness in general.
For the more standard-action damaging objects rules, the damage rank required is +41.
The effects of breaking or disabling the Earth would be cataclysmic in nature. We're talking about the sort of force that leads to half of the crust being shattered, or the Earth being literally broken in two. To say that nothing on Earth could possibly survive this event is only slightly inaccurate, since the nature of comic-book universes would leave some people on the planet alive, with names like 'Thor' or 'Superman'. But unlike the rules where two disabled results lead to the dead/dying, or in this case 'destroyed', result... I would personally say that while these effects are much less temporary than damaging the Earth, they would still not immediately lead to the Earth's complete destruction if you were to stack them.
Again, the gravity involved would make it impossible for simple 'damage stacking' to work like that. And on top of that I would again ignore the additional damage effects of autofire in this case.
Destroying the Earth Outright
The ranks required for this are five higher than the ones listed previously, or exactly as high as the toughness roll of the object in question.
For the breaking object rules, this means a bonus of +41.
And for the damaging object rules, this means a bonus of +46.
The effects of this would basically be 'commence primary ignition'...
I hope this answers questions.
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