# If a planet or star is composed of gas, the center of mass will have zero gravity but immense pressure? I'm trying to understand fusion in stars

I'm trying to understand what drives fusion in stars. Does it happen in the center of the star? This question arises because I always thought a person would be weightless in the center of the earth but started to question the logic of that belief. This site confirmed that I was originally correct. But my doubts occurred because my understanding is that fusion occurs in stars in the center of the star where the gravity would be zero. So I now presume fusion in stars is entirely pressure driven? I guess maybe I'm having trouble understanding how pressure can be high in a zero gravity environment. Another question that occurs to me is: Would the center of a black hole (provided it has any dimensions) also have zero gravity? Or is that why a black hole is described as a singularity and size refers to the event horizon? Thanks for any edification that may come my way!

• Definitely better suited to the Astronomy Stack.
– Ash
Commented Aug 9 at 3:29
• If you reached the first row at a concert, there is no need to push further towards the front. Still, you will be squashed by everybody behind you who certainly is pushing.
– mlk
Commented Aug 9 at 12:44
• Please forgive my ignorance and isn't that missing a step? How could mass not have gravity, however slight? Commented Aug 11 at 19:23

TL;DR: The high pressure in the center comes from the outer regions where there is gravity, not from the zero gravity in the center. And yes, pressure is a factor driving fusion, while gravity is just the thing that indirectly creates the pressure.

There's no direct connection between gravity and pressure.

• You can have pressure without gravity, e.g. in a closed container (e.g. space craft) in a Zero-G environment.
• You can have gravity without pressure, e.g. on the Moon.

If you are in the center of a planet or a star, all its mass particles apply a pulling gravity force on you, but as they are symmetric around you, they cancel out one another, giving a zero-gravity overall result.

Pressure, on the other hand, can be understood when looking at a small part of a body, e.g. in a 1cm cube shape.

There are pushing forces on all surfaces of this cube, and they are roughly equal - otherwise the (non-rigid) material would flow out at the side of least force.

But the forces aren't exactly equal if a gravity source is present, pulling the whole cube "downwards". For an equilibrium, this weight force must be compensated, as otherwise the cube would start moving down. So the pushing force on the lower surface must be larger than the pushing force on the upper surface, by just the weight of the cube.

This means that, the lower you get, the greater the pressure. The increase varies over the "altitude", and can be calculated from the local gravity value and the material's local density, but it will always increase.

Where is the greatest increase in pressure (when going downwards in the star) if we assume a gas-like medium?

• In the outer atmosphere, there is gravity, but close-to-zero density, so a very small pressure increase.
• Somewhere lower, pressure has increased enough to cause a higher density of the gas. So, with the still-high gravity, there is quite some pressure increase.
• The lower you get, the lower the gravity, as more and more of the star's mass gets distributed around you, meaning that more and more of the individual gravity pulls cancel out one another. Because materials compress under pressure, the density will increase, so the decreasing gravity is to some degree compensated by the increasing density. So here is where most of the pressure is created.
• Near the center, we have a very high accumulated pressure, and thus a very high density. But as the resulting gravity is close to zero, the pressure doesn't rise (significantly) any more.
• Gravity is the result of mass that is below you.

(It's an interesting fact that in a sphere, the mass "above" you in the sense of being at greater distance from the centre pulls you in all directions equally and so cancels out)

• Pressure is the result of mass that is above you.

(The mass above you is being pulled towards the centre by the mass that is below it, and so pushes on you.)

So at the centre of a star, with all the mass above you and no mass below you the pressure is at its greatest.

The pressure means that the atomic nuclei are close together and in combination with the high temperatures, there is the possibility that some can overcome the electromagnetic repulsion that they have for each other and fuse together. Fusion is mostly temperature driven, but high pressures help.

Black holes are rather special, as they don't contain any "matter". In fact it's not really known what they do contain, since we don't really know how gravity works on very small scales. The model of a black hole in Relativity has a "singularity" at zero radius. A singularity isn't a physical object, but a feature of the solution to an equation where it has an infinite value. In a black hole, all the mass is always below you and no mass is above you.

So in a black hole, the pressure is always zero, and gravity increases as your distance from the centre decreases.

But the singularity probably isn't physically real, and probably "something quantum" happens. It's not at all clear if notions like "pressure" or even "gravity" make sense at such scales.

• I would say, rather, that gravity is a force exerted by all mass around you. "Below" is defined by the direction of the net gravitational force that you experience. Commented Aug 9 at 17:03
• By "below" I mean "closer to the centre of a spherically symmetrical blob of matter. And I'm going to wave my hands and say "shell theorem" a few times. In this limited sense, (and as briefly mentioned in my answer) the mass that is above you doesn't exert a net force on you. I think the "above"/"below" contrast is useful to explain why there is lots of pressure at the centre of a star, but no net gravitational force. And why there is lots of gravity ont he surface of the Earth, but not much pressure. Commented Aug 9 at 17:12
• Definitely an aside: recently read an interesting article by Carlo Rovelli about black holes becoming white holes and that tiny white holes might be dark matter. Commented Aug 9 at 21:39

Gravity is not zero anywhere. In the center of a star it's balanced out, but even in your description it's not complete balance - it's just infinitesimally off balance from other planets, stars, etc. Just as gravity is balanced - in all directions - so is pressure. Pressure and gravity are different. In this case gravity is the cause of the pressure due to it's effect on the matter in the star.

• Zero gravity may not occur at the exact center of a body due to external influences, but that doesn't mean it is zero nowhere. Commented Aug 9 at 16:29
• @NuclearHoagie how gravity can be zero? Since it decrease with the square of distance can be really small but never zero. What am I missing?
– Mark
Commented Aug 11 at 21:15
• @Mark There's always gravity, but net gravity can balance out to exactly zero. The intermediate value theorem suggests that a continuous field which points in every direction somewhere must go to 0 somewhere. You can't have a continuous gravitational field that points in opposite directions at the North and South Poles, and not find somewhere in between where the gravity is exactly 0 (try and draw it, it would require discontinuity). Commented Aug 12 at 13:32

"Hydrostatic equilibrium" is how the force of gravity is balanced not by the mere presence of pressure itself but by pressure gradient. The center ends up having immense pressure due to the necessary pressure gradient: if I tell you a mountain must have a slope, that mountain will end up being tall. As other answers mentioned, this is because pressure holds up all the mass above.

It's important to understand that a "gradient", a "slope", and a "difference" are all related. And "differences" lead to net force: if all forces balance out, there is no net force.

Consider your body. There is atmospheric pressure all around you. But there is no acceleration of your skin outwards or inwards. And no net force: why? Because there is no pressure gradient, no pressure difference: you are in balance.

Consider a balloon. There's a huge amount of pressure (the whole atmosphere) pushing down. So how can it float? Because there's a slightly larger amount of pressure pushing it up. The bottom of the balloon experiences a slightly higher pressure than the top. There is a difference in pressure due to height. The higher up you go in Earth's atmosphere, the less pressure there is. This is because Earth's atmosphere is roughly in hydrostatic equilibrium: there are pressure gradients which balance out the force of gravity.

An analogous example

Imagine 3 balls in a line which all pull towards each other, but also are gravitationally attracted to the Earth. The one in the middle has 0 net pull due to balls: it is balanced on either end. You are allowed to put the balls on a mountain and try to balance the forces so that the balls do not move.

Here, the slope of the ground will determine the force the balls will feel towards the Earth. The balls would roll down the slope, if not for the pull of the other balls.

You can imagine that you'll put the center ball on the peak of the mountain: that's where it should be balanced. Here, the height of the mountain is analogous to pressure, and the slope of the mountain is analogous to the pressure gradient.

My balls on a mountain:

> ooo
> /-\