The density of the Sun is $1410~\frac{\text{kg}}{\text{m}^{3}}$ and Mercury's is $5430~\frac{\text{kg}}{\text{m}^{3}}$, but shouldn't the Sun be denser? Because when the Solar System was forming, there was a big disk of debris, and depending on the density of the debris it went closer or further from the centre, which then formed the planets, but the Sun is in the centre, and it's less dense than Mercury, why?

The sun isn't the same density all the way through.

According to MSFC's solar interior page, the core density at the centre of the sun is a whopping 150,000 kg/m$^3$. Surrounding it the radiative zone is around 20,000 - 200 kg/m$^3$ (already less dense than water). Eventually at the edge is the convective zone - the density at the part that we see is much less dense than our own air...

So although the Sun's average density isn't very remarkable, the core is the densest place in the solar system.

Sun - cross section view(Sun cross section from Wikipedia.org)

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    This is another good point. I considered mentioning it myself, but I decided instead to explain why the average density was so low. – called2voyage May 16 '16 at 16:38
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    @Nayuki: "the high temperature further decreases the temperature" – Lightness Races in Orbit May 16 '16 at 23:12
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    Additional note: Outside of the sun's core, most of the outer shells are simply hot hydrogen gas. We know that hydrogen is less dense than the materials in solid planets, and the high temperature further decreases the density. – Nayuki May 16 '16 at 23:33
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    @Nayuki: Wow, you can't just go from "It's hydrogen" to "it's less dense than rock". That's nonsense. Hydrogen under standard conditions (1atm, 293K) is less dense than air. Hydrogen under conditions outside of the core is still much denser than air. See Andy's answer. Dare to follow the links. – AtmosphericPrisonEscape May 17 '16 at 12:51
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    I'm not sure if this actually answers either of two questions – kd88 May 17 '16 at 13:44

Fusion inside of a star affects the sun's density (which does not happen with a planet). It produces an outward pressure that balances against the attraction of gravity, thereby reducing the density as long as the star is burning. Once a star the mass of the sun is no longer able to sustain fusion, what is left is a white dwarf which is in fact much denser than Mercury.

The density of matter depends not only on its composition, but also on temperature and pressure. It's not meaningful to say that substance A is denser than substance B without specifying the conditions under which the comparison is being made.

For a simple everyday example, at room temperature (and pressure) water is significantly denser than air. But heat them both above 100 °C, and the water evaporates and actually becomes considerably less dense than air, even at the same temperature and pressure.

(By the ideal gas law, the density of different gases at a given temperature and pressure is approximately proportional to their average molecular mass. The molecular mass of water is only about half that of diatomic oxygen and nitrogen, which are the main components of air on Earth, and thus water vapor is only about half as dense as air at the same temperature and pressure.)

The surface temperature of Mercury is less than 1000 °C (and the interior temperature should not be much greater), and it mostly consists of metals and silicate minerals (i.e. rock) that are solid or liquid at those temperatures. The Sun's temperature, meanwhile, is over 5000 °C at the surface (photosphere), and a lot hotter deeper inside. If you could heat Mercury up to the same temperature as the Sun, most of the rocks and metals it consists of would evaporate, and would become a lot less dense. So a lot of the density difference simply comes down to the fact that Mercury is a lot cooler than the Sun, and thus able to stay solid.

Another reason why the Sun is less dense than Mercury is that the Sun contains a lot of lightweight hydrogen gas (which has both a very low molecular weight and a very low evaporation point), while Mercury has almost no hydrogen at all. The main reason for this is that the Sun's heat and the solar wind have effectively blown away any hydrogen and other volatile low-density substances that Mercury might once have had (or that might've existed in its general area while the solar system was forming).

The Sun itself can retain hydrogen due to its enormous gravity (but even so, it loses about one billion kilograms of it per second; that's basically what the solar wind I mentioned above mostly is). Mercury, however, is much smaller, and thus its gravity isn't strong enough to hold onto its own hydrogen so close to the Sun.

(Basically the same thing happened to Venus, Earth and Mars, which is why these inner planets didn't turn into huge balls of hydrogen gas like Jupiter and Saturn did. However, Earth and Venus were both big enough, and located far enough from the Sun, that they could hang on to other slightly less volatile substances like water and air. Mars is located even further from the Sun, but is also a lot smaller than Earth, which is the main reason why it today has only a very thin atmosphere of carbon dioxide, and very little if any water.)

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    Excellent unique point about the hydrogen being blown away by the solar wind. Because one would indeed expect the solar system during formation behaving along the lines of a single entity like a planet: lighter elements should tend to be on the outside, and hence the sun being composed of more heavy elements. Or maybe all bodies should be of similar composition. The solar system cannot be understood without understanding its history. – Peter A. Schneider May 19 '16 at 15:00

I'd say the most important answer is because the volume of stars is counted differently than for (inner) planets.
For the former, most of the gas surrounding the dense core is counted. The latter don't have significant enough amounts of it.

This is even more pronounced with larger stars.
VY Canis Majoris: "With an average density of 0.000005 to 0.000010 kg/m3, the star is a hundred thousand times less dense than the atmosphere of Earth (air) at sea level. It is also undergoing strong mass loss with the outer layers of the star no longer gravitationally bound"
Yeah, less density than the air outside the ISS, and still a part of the star's volume.
enter image description here The star is farting gas like nobody's business, and a huge part of that still counts into its diameter. The Sun is no different.

Obviously we're not using the same metric, so there is no point comparing the values.

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    You make an excellent point -- what we see as 'the sun' in visible light (the photosphere) would've been considered atmosphere on a planet, and not have counted as part of the volume for computing the density of the planet. – Joe May 17 '16 at 15:13

All the other answers address the density of the sun, but I feel that none of them actually addresses the OP's misconception. OP seems to think denser material should sink, but this is not the case. Thus Pluto is denser than Uranus, but orbits further out. There is nothing strange about this.

The reason is that orbital energy is conserved indefinitely unless there is some kind of interaction. A planet feels "weightless" just like an astronaut in a space station, because it is in freefall towards the centre of mass of the solar system. Unless it interacts with another body, matter, regardless of its density, will continue to orbit at the same distance from the centre of mass of the solar system, as a consequence of conservation of energy.

Density only becomes an issue when objects come into physical contact, and a body receives a push from another body.

Thus in an orbiting spacecraft, dense objects just float around "weightlessly" and do not "fall" to the "bottom." Both the air and the objects in the spaceship are experiencing gravity, but they are falling at the same rate, so they do not push each other.

When the spacecraft is on the ground, the Earth's surface pushes up on the spacecraft, and prevents it from accelerating towards the centre of the earth. Under these circumstances, the denser objects, if unconstrained, will fall towards the floor of the spacecraft, displacing the less dense air. When they hit the floor, they receive a push from it, preventing their continued fall.

In space objects do not push each other by physical contact, so density makes no difference. A trillion tons of iron and a trillion tons of silica may have different volumes, but they have the same mass, therefore so long as their interactions with the rest of the solar system are purely gravitational, both will behave identically.

On the other hand, matter that has coalesced into a planet, sun, or moon will become stratified by density. In the case of a moon or rocky planet this is almost entirely due to the denser materials sinking and forcing the more voluminous ones to rise. In the case of the sun or a gas giant the core will also be denser due to compression. In addition to contact forces, friction is also present. Note also that friction is necessary for orbital decay: without it satellites will orbit at the same height indefinitely.

Simple answer. The sun is mostly hydrogen with an atomic weight of 1. Mercury is mostly (70%) metal such as iron (with an atomic weight of 55). Iron has a head start on density. For hydrogen to equal iron in density, 55 hydrogen atoms would have to be compressed in the space of a single iron atom. This happens in the core of the sun, but not in the entire sun.

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