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I keep hearing and reading statements that refer to the "surface of the Sun" (how hot the surface of the sun is) or the "surface of Jupiter" (when the Shoemaker comets hit Jupiter). I find this to be very confusing and unscientific (especially when stated by astronomers).

If the Sun and Jupiter are basically balls of gas they don't have a surface. It is like saying that the surface of the Earth is somewhere in the upper atmosphere.

Can anyone help me understand how a ball of gas can have a surface.

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  • $\begingroup$ I think that your understanding of this is correct, but they can have defined surfaces for the sake of discussion and to provide an "edge" for things like radio or optical occultations. The pressure and density are changing so rapidly that effectively there is an edge, and that ends up getting imprecisely called a "surface". I think a proper answer will be posted at some point. Possibly helpful; Refraction by Saturn's atmosphere - how dense is it here? $\endgroup$ – uhoh Aug 17 at 6:27
  • $\begingroup$ BTW, the Sun is mostly plasma, which is a bit different to gas. And it gets really dense in the core, around 250 g/cm³, more than 20× the usual density of lead. $\endgroup$ – PM 2Ring Aug 17 at 12:55
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Yes, there is no surface in the sense as we have on the Earth.

However, there is the Barometric High/Pressure formula. It says, that in an ideal gas of atmosphere, the density (and pressure) increases exponentially high the decrease of the height. Its cause is understable even without differentiation: all horizontal layers of the atmosphere holds the mass of all the layers over it.

The result is, that in the atmosphere of the Earth, it is a good estimation of the pressure, that it halves with every $\approx$ 5km of height. Thus, 5km height we have about half of our surface atmosphere density, 10km heigh we have about a fourth, and so on.

In gas planets or stars, where the whole body is gaseous, this barometric formula holds only until the gas loses its ideality, i.e. its density does not grow more linearly with the pressure. In layman terms, it means that its molecules are so close to each other, that doubling the pressure does not halve the volume any more.

This happens typically in very high pressures (some thousand bars). At this point, the gas is already so dense, that we can say, we are already "inside of the body". If the gas is radiating (for example, the thermal radiation due to the $\approx$ 6000K temperature of the Sun), it also means that it is not transparent any more, thus we can not see inside it.

While there is no surface on the Sun (Jupiter, etc), the height difference between the near-total vacuum, and between the point where the atmosphere is not an ideal gas any more, is surprisingly small because of the exponentiality of the barometric formula. For example, the photosphere of the Sun, is only about some hundreds of km high. This is the layer,

  • Which is not enough dense to be able to fade the region below it;
  • But it is already enough dense to be its light enough well visible.

While there is no solid surface, this some hundreds of kms can be considered as "the surface of the Sun", particularly if we compare it to its $\approx$ 1.4million km diameter.

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