Gary will immediately collapse into a super-dense ball of whether humans become when they're compacted in that way.

The Earth's suddenly massless material will all speed away at the speed of light - as all massless objects must travel at the speed of light.

What was once Gary and is now super dense something will continue to orbit the Sun on a very slightly different orbit. The moon will orbit Gary with a very slightly disturbed orbit as well. Happily no one will notice as they'll be all randomly heading off into space in bits at the speed of light.

I specifically stated that Gary can safely acquire the mass of other objects

Even so, Gary (and Superman) will also be bathed by the sudden flash radiation of uncountably many zero mass electrons zipping along at the speed of light. Even with zero mass they have charge and Gary unharmed by the mass he's acquired will be ripped apart by this barrage of sort-of-electrons (and protons and every things else). It's instant death one way or another for Gary.

Presumably after Gary actually dies from this weird radiation immunity from sudden swallows of mass ceases ? Not that it matters. because he's dead. If he looses his immunity he's going to superdense ball land (but will be dead during the trip).

Superman will, of course, be unharmed. Krytonite only is his problem. Gary ain't Superman and, like Batman, will be instantly dead. We can only pray for Wonder Woman.

Physicists somewhere else will be happy (and somewhat surprised) to discover the existence of the charged massless elementary particles that were once massive electrons. That's going to really mess up a number of important theories, as we don't think a charged massless particle is possible. Of course we're dead so what we think doesn't matter.

Superman is not going to be affected by any of this unless Gary becomes Kryponite. Superdude might be a bit put out by the disappearance of Lois Lane (as I will be about Wonder Woman) and it's a good job for Gary he's dead already.

Please help put Gary's mind at ease

Good news !

As a superdense ball of something or other Gary no longer has to worry about anything and is, indeed, no longer an identifiable sentient entity. And he should stay that way with Superdude upset about the girlfriend thing.

Before we get to the Earth-situation, let's first explore exactly what Gary's powers entail. We're well outside classical physics now, sailed past classical physics and are now looking at an obscure mathematical description of the universe, called the Plot Field Equations - a description that is only valid at sub-Planck scale.

Let's look at the gold block example and extrapolate from there. The block Gary's holding is obviously the opposite of dark matter. Dark matter is only affected by gravity, not by electromagnetic interactions. Gary's block is affected only by electromagnetic interactions (it's still a solid block, which indicates repulsion from electrons) but not by gravity. Let's call it Light Matter. Due to conservation of mass, Gary acquires the mass from the converted objects.

Light matter is still a solid, and everything not held together by gravity still behaves roughly the same - trees stay tree shaped. Thanks to the intricacies of Plot Field Equations, the gold block nor the tree fly off at light speed. This is because Light Matter resists motion linearly with velocity - an effect quite similar to momentum, but the mass scalar is replaced with the Plot Tensor. Effectively, for most materials (except highly crystalline materials due to the alignment of the Plot Tensor) it feels like a very light block but it will not fall to the Earth.

Now what happens to the Earth if it turns into Light Matter?

The Earth is compressed under it's own mass. First, it will uncompress rapidly. The crust still has Light Momentum, but the compressive force is so massive that the entirety of the crust will be launched into space. Obviously this is not a desirable outcome. Instead, our hero must only acquire the mass of the Earth very briefly to withstand the punch, and then immediately revert. Everything will feel a brief jolt and that's it.

Perhaps this massive jolt is instead absorbed in the Plot Field due to the remnant gravitational waves. Now we're approaching the situation that looks like a proper Super Hero Power.

The first is that the local gravity vector is pointed towards Gary. Gary will soon be pummeled by pebbles, rocks - basically everything's that loose. Everything in the vicinity of Gary will be destroyed. Only sufficiently far, on the other side of the planet, people will not really notice, everything else falls towards Gary

The alternative is to include all objects on Earth as light matter. I'm afraid that means all people near the equator will sail off into space as they slip the bonds of gravity.

All in all, it's a terrible idea Gary. Don't do it. The Plot Field Equations will not save you this time.

A better idea would be to only transfer the momentum rather than the mass. I suppose certain solutions of the Plot Field Equations allow for such a violation of Einstein's equivalence principle. The mass of objects on top of the Earth should be plenty to avoid random debris in space knocking Earth off of it's trajectory. A large meteoroid impact will however literally knock the Earth from its socks. Also, Gary will continue moving in whatever direction be was before (remember, any gravitational or other forces are insignificant compared to his momentum). Hopefully for Gary, that's up into space (if he brought a parachute) and not plowing straight into the Earth.

Silly Gary.

He will launch off the surface of the planet immediately and then go back to normal.

Assumptions:

1. Inertia is a property of matter, not mass.


2. "The earth" is defined as everything that lies within the exosphere


3. He has to contact a solid in order for his ability to work. (gas doesn't count as an object)


4. Gary is protected from the effect of his own power. (I mean, the Flash doesn't break his bones while running, or when punching at supersonic speeds, this is pretty much a given for super powers)

Results:

1. The Earth is spinning, usually Gary is held down to the surface by gravity, but now that the earth has no mass (as now only Gary does) the earth isn't holding him down anymore. If Gary were near the equator, he'd lift off the surface by his own momentum at an apparent acceleration of 0.003 G (though it's really just the earth rotating out from beneath him) as he nears the arctic circle it will reduce to about half of that, so he's going to loose contact with the ground, at which point he'll have to break the connection (as he won't be touching the ground anymore). Then everything would immediately return to normal.


2. The earth is also moving around the sun at a speed of about 67,000 mph, however, this isn't going to have a very big effect on Gary, as he is only going to have about 0.0005 G of apparent acceleration due to the sun's gravity (the direction depending on what time of day it is. He probably won't even notice as #1 will dominate him floating.


3. Superman, wouldn't have any mass either, as he's within the exosphere, so something strange and confusing would happen to his fist as it collides with Gary's face.


4. Everything on earth, the water, etc. wouldn't move toward Gary at all because, they didn't have mass to be attracted to him by gravity.


5. The orbit of the moon will be altered a little as the center of mass that it's orbiting has been moved by one Earth radius ~4,000 miles, but that's not really significant as the difference between the moon's largest distance from earth and its smallest is over 25,000 miles.


6. The earth's orbit will change because of the time spent without the sun pulling it back, but as it was a short time and was only missing that 0.0005 G of acceleration it also will fall within the normal orbital variation.

Even assuming Gary's body is somehow immune to the large list of physics-related problems that immediately spring to mind for super-concentrated masses, it doesn't look good for anyone involved.

Think of the Earth + Gary as a single system. That system has the same total mass as it always had, only the center of mass has moved. At astronomical scales, that's not far enough to seriously perturb the orbit of the planet or the moon. You might shave a few fractions of a second off of the next leap year, but nothing catastrophic here. Just don't keep it like this for a long time.

The problems are on the smaller scales. Particularly, imagine if you were on the opposite side of the planet from Gary. The mass of the Earth+Gary system is the same, but your distance from the center of mass is now roughly twice as far as it was a moment ago. That's a sudden and instantaneous drop in the gravitational force applied. You were standing on the ground, which means the force of gravity pulling you down compressed the ground, and this was balanced by the recoil forces of the ground pushing back up on you. Assuming the Earth remains a solid, there will be an instant where the recoil force will remain the same, but the gravitational force will be reduced. The net effect would be like placing an action figure on a table and then bumping the underside of the table. The poor guy would pop up in the air and fall back down. Whether this equates to an awkward stumble or a three-story toss is left to the storyteller. At a minimum, you'll have lots of fragile knick-knacks broken.

If the Earth does not remain a solid (if it becomes "Earth-colored air" like your gold block example), then the poor folks on the other side of the planet are in a really rough spot. They'll be accelerated towards the center of gravity of the Earth+Gary system, and with no solid ground to hold them up, they'll move into the interior of the planet. When Gary puts the mass back, they'll be stuck underground, inside the planet. Not only would this be an irritating inconvenience, you'd have all sorts of problems with two things trying to occupy the same space at the same time.

Gary is in a particularly rough spot, though. Gravity normally pulls him towards the ground, and that force results in friction between his feet and the ground. That friction is what allows him to stand in place when a force pushes on him. Once the mass gets redistributed, the Earth has zero mass. There's no longer any force to generate friction between him and the Earth. Without anything holding him in place, the impact of Superman's punch would send him sailing off into the distance. He'd lose contact with the Earth, his powers would no longer work, the mass would return to normal, and he'd fall to the ground with a lot of horizontal momentum. When he hit the ground his powers would re-activate and the Earth would go massless again. Gary's velocity vector at that point has a downward component, so his momentum carries him into the interior of the Earth. There's nothing here with mass to impede his motion, so he continues on that vector until he crosses back out of the planet somewhere else, loses contact with the Earth, gravity returns, he falls back towards the Earth, his powers re-activate, etc, etc. It might actually take Gary a rather long time before he comes to a halt. He's now like a stone skipping across a pond, if that stone could skip on the top and bottom surfaces of the water.

Luckily, there's an easier solution to all of this. If you're going to get in a fight with Superman, let him punch you. Block the punch and the instant he makes contact with you, take away all of Superman's mass. A punch thrown by a massless assailant will have zero kinetic energy behind it. Kinetic energy must be conserved so it will be absorbed into Gary along with the mass but when it's evenly distributed throughout his body, it's nothing he can't handle (that's one way bullet-proof vests work).

So if your character is taking all the mass of the whole planet, then I assume that his powers can absorb the mass of things touching the things he's touching, so part of this depends on what still has mass once he's absorbed the mass of the planet.

As a human is much smaller than the Earth, the distance between Gary's surface and his center of mass will mean a much higher gravitational force.

Anything left with it's own mass (including atmosphere if it still has mass) will start falling towards Gary. Things with mass near Gary will be crushed and anything with mass on the other side of the planet will effectively be launched into orbit around Gary, as he's effectively just doubled their distance to the center of gravity they were falling towards previously.

I'm assuming that the things without mass can't be crushed in this state as the gold cube didn't implode previously, but anything not fixed down, while not affected by Gary's gravitational field, will now be free to drift off into space unless trapped by other forces heading towards Gary.

Gary will implode.

Gary is effectively super massive and his new gravitation will wreak havoc on his surroundings but will first compress him and kill him pretty much instantly. If the mass remains in him possibly the earth reforms with him as the new core though the result won't be anything like the earth we have today.

The earth no longer has gravity and things farther away from Gary go flying off into space. The moons orbit is permanently altered and it goes flying off into space. The world probably ends as the inner core of the earth now that gravity is no longer holding it together is going to expand greatly causing super earthquakes at a minimum.

I would be hard pressed to imagine Gary could survive even a nanosecond with that much gravity in him.

I will provide a more optimistic, less killy scenario. One of the problems with the proposed power is that it only works with "an object Gary is touching". (Now strictly speaking, you can't 'touch' anything because at a molecular level, nothing is touching anything) The thing is "Earth" is not a simple object, it is a large collection of objects, one of which is Tectonic plates. So Gary's power should be limited to one tectonic plate worth of mass. This would be enough to give Gary the inertia he wants while stealing roughly ~(1/7)% of the Earth's mass (There are 7 plates and the crust is 1% of Earth's total mass).

Now, it could also be argued that "loose dirt" is not one object so Gary would need his feet on limestone or something, or be limited to just the mass of the pavement he is standing on.

Of course this assumes he remembered to take his shoes of before the fight.

Also that superman doesn't just, you know, laser-eye, blizzard breath, simply tie up, punch harder, Phantom Zone, or lets the over-enthusiastic police taz Gary. (On second thought, Gary's first mistake was fighting Superman)

Gary is dead, and everyone else, is dead. Upon absorbing the mass of the Earth, Gary suddenly has a density of approximately 5.97*10^24 kg/m^3 or 5.97*10^21 g/cm^3. For reference, the core of the sun has a density of roughly 150 g/cm^3.

As such, Gary would potentially trigger nuclear fusion and the resultant heating would likely cause him to explode like a nuclear bomb.

Ignoring this, Gary has bigger problems. The surface of Gary would suddenly have a gravitational acceleration of 1.59*10^15 m/s^2. This would be immediately catastrophic, even without mass, the Earth would be pulled inwards onto Gary, wrapping around him to place him at the center. This would liquify the entire planet and destroy everything on its surface.