(in Earth Atmospheres)
Compared to Earth
2 900 000
3 600 000
Now, if everything were as simple and easy as possible, the g2 values in the third column would be the same as the calculated values in the last column. And, to a center extent, that is exactly the case, because, as it happens, these four planets have fairly similar structures, with dense, metal-rich cores, and less-dense, rocky mantles. In fact, because Venus is thought to have a structure almost identical to that of the Earth, the gravity curve for Venus is thought to be nearly identical to that of the Earth, and so the two values, "simple" and "accurate", are identical (the fact that the Earth's values are identical is meaningless, because we are using it as the unit of comparison). However, for Mercury and Mars, the "accurate" values are a little lower than the "simple" values, so it is worth discussing the reason for this, and examining Figure 1 one more time.
Note that the gravity curves for Mercury (in blue) and Mars (in green) are quite different from those for the Earth and Venus (in red). Mercury has an unusually large metallic core, which is thought to make up about 75% of the radius, and 60% of the mass, of the planet, and so the peak gravity, which occurs at the core-mantle boundary, is further out than in the Earth. As a result, the curve for Mercury, although looking similar to that for the Earth, lies well below the curve for the Earth throughout much of the interior of the two planets. This means that the gravity inside Mercury is, on the average, lower, compared to its surface gravity, than the gravity inside the Earth is, compared to its surface gravity. As a result, merely squaring the surface gravity gives too large a result for Mercury (about 20% too large, as you can see from the table).
Similarly, Mars has an unusually small, low-mass core, and although, at its core-mantle boundary, the gravity is larger than for a uniform planet, it is still considerably less than at the surface, which makes its average internal gravity less than you would expect, if it were just a smaller version of the Earth, and makes the "simple" calculation just about as accurate (and inaccurate) as the one for Mercury.
Now, please note that although the simple calculation (squaring gR) is a bit "off" for Mercury and Mars, the error involved is very small compared to the huge difference between the actual values, and the values for the Earth and Venus. The Earth and Venus have large surface gravities, large internal gravities, and large internal pressures, while Mercury and Mars have small surface gravities, small internal gravities, and small internal pressures. And insofar as the large difference between Venus and the Earth, on the one hand, and Mars and Mercury, on the other hand, has any effect on their structures, even the simple calculations will give at least an approximate indication of what is going on. As a result, we would probably be perfectly justified in using a similar approach to estimating the internal gravities and pressures of other objects, as well. Insofar as they were similar to the Terrestrial planets, the results of the calculations would be expected to be more accurate, and insofar as they were different from the Terrestrial planets, the results of the calculations would be expected to be less accurate, but in any event, the results should at least be in the right ball park, so to speak.
The Internal Pressures of the Jovian Planets and Pluto
With this in mind, let's see what we would get for the internal pressures of the Jovian planets, using estimates based on the squares of their surface gravities (unfortunately, accurate estimates of the internal structures of these planets are harder to obtain, but I have listed the best values which I could find, or estimate):
(in Earth Atmospheres)
|Ratio of Pressure|
to Earth's Internal Pressure
|3 600 000|
(50 to 100) 000 000
(5 to 8) 000 000?
(4 to 5.5) 000 000?
(5.5 to 7) 000 000?
(9 to 11) 000?
15 to 30
1.5 to 2.5?
1.1 to 1.5?
1.5 to 2?
.0025 to .0030?
Note that the pressures inside the Jovian planets are considerably greater than those which would be expected on the basis of the "uniform" planet calculations. This is because, according to detailed calculations, these planets must be considerably compressed in their centers, so that as you go inwards, their gravities are much larger, in comparison to their surface gravities, than for the Terrestrial planets. Figure 4, below, shows approximate estimates of the internal gravities for Jupiter and Saturn, compared to those for the Terrestrial planets (in order to make the graph reasonably small, it has been vertically compressed by a factor of two, compared to Figure 1). As you can see, both Jupiter and Saturn are thought to be very compressed in the center, making their central gravities much higher, at various internal positions, compared to the corresponding values for the Terrestrial planets. This makes both their internal gravities and internal pressures considerably higher than we might otherwise expect. For Jupiter, the gravity and pressure are many times greater than for an uncompressed planet, while for Saturn, since its gravity and compression are less, the differences are not as great. Uranus and Neptune, although not shown in the graph, would be still less compressed, but still considerably more compressed than the Terrestrial planets.
Figure 4: Gravities inside the Jovian planets are much greater, proportionately, than inside the Terrestrial planets.
(Note: The gravity inside Jupiter cannot be greater than the 1/r2 law shown by the dots, but the straight-line approximation to its internal gravity is only an approximation, and the actual gravity would be somewhat lower, particularly in the outer layers.)
(To Be Continued)
(Topics still to be covered --
(How the internal pressures can be used to estimate the structures of the planets
(How the estimated structures can be used to correct the crude estimates