For planets, one thing leads to another

One of the biggest benefits of being a journalist is that you become aware of interesting things from various fields. As a science journalist, the ambit is narrowed but the interestingness, not at all. And one of the most interesting things I’ve come across is a relationship between the rate at which planets rotate – the equatorial rotation velocity – and their mass. It seems the lighter the planet, the lower its equatorial rotation velocity. This holds true for all the planets in the Solar System, as well as large asteroids and Kuiper belt objects such as Pluto. The plot below shows logarithm of planet mass (kg) on the x-axis and logarithm of equatorial rotation velocity (km/h) on the y-axis.

The blue line running through the points is a local regression fit and represents a statistical connection. However, there are four prominent outliers. They represent Mercury, Venus, Earth and Mars, the System’s rocky, inner planets. Their spin-mass correlation deviates from the normal because they are close to the Sun, whose gravitational pull exerts a tidal force on the planets that slows them down. Earth and Mars are also influenced by the gravitational effects of their moons. Anyway, I’ve already written at length about this fascinating connection. What I want to highlight here are more such connections.

And before that, a note: it’s probably obvious that they exist because the connection between mass and equatorial velocity could just as well be a connection between mass and a string of other properties that eventually influence the equatorial velocity. This thought was what led me to explore more connections.

Mass and rotation period

The rotation period of a planet describes the time taken for the planet to rotate once around its axis. If mass and equatorial velocity are related, then mass and rotation period can be related, too, if there is a connect between mass and planetary radius, which in turn implies there is a connect between radius and density, which in turn implies that planets that can get only so big and so dense before they become implausible, presumably – a conclusion borne out by a study released on May 26.

Image: A log-log plot between planetary mass and rotation period.

Density and rotation period

If a planet can only get so big before it becomes puffy, and its mass is related to its rotation period, then its density and rotation period must be connected, too. The chart below shows that that hypothesis is indeed borne out (it’s not my hypothesis, FYI): log(density) increases as log(rotation period) does, so denser planets rotate faster. However, the plot shows significant variation. How do you explain that?

Image: A log-log plot between density and rotation period.

Turn to the Solar System’s early days. The Sun has formed and there is a huge disk of gas, rocks, dust and other debris floating around it. It exerts a gravitational pull that draws heavier things in the disk toward itself. As it becomes more energetic, however, it exerts a radiation pressure that pushes lighter things in the disk away. Thus, the outermost areas of the disk are mostly dust while the inner areas are heavier and denser. It’s possible that this natural stratification could have created different bands of material in the disk of different densities. These different kinds of materials could have formed different kinds of planets, each now falling on a specific part of the log(density) v. log(rotation period) plot.

Mass and density

Of course mass and density are related: the relation is called volume. But what’s interesting is that the volume isn’t arbitrary among the Solar System’s planets. It rises and then dips, which means heavier planets are less dense and, thus, more voluminous. For example, Jupiter is the heaviest planet in the Solar System – it weighs as much as 317 Earths. Its volume is more than 1,300-times Earth’s. However, its density – 1.33 g/cm3 versus Earth’s 5.52 g/cm3 – shouldn’t be surprising because it’s made of mostly hydrogen and helium. Which is just what we deduced based on the mass-period connection.

Image: A log-log plot between mass and density.

One way to find out if there’s any merit in this exercise is to conduct a detailed study. Another way is to perform a regression analysis. I’m not smart enough to do that, but I’ll blog in detail about that when I am.