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by Iason Saganas (LMU München) & Ludwig Scheibe (TU Berlin), July 2024

Most people know of tides from the seas on Earth, with sometimes significant differences between low tide and high tide. But tidal forces play a significant role in planetary science as well. Tidal forces can lead to a change in the planet’s orbit around its star (“migration”) which is an important aspect in studying how planetary systems evolve long-term.

For planets close to their star – or, equivalently, moons close to their planet – tidal forces change their rotation, so that they may end up having a permanent day- and night-side – a process called tidal locking. Also, if the tides are strong enough, they can be an additional source of internal heating in a moon or planet, which might make an otherwise uninhabitable body able to support life. But what are tidal forces exactly, and how do they cause these things? Let’s find out.

Consider a moon accompanying its host planet. On its orbit, the moon is pulled towards the planet by the force of gravity. But at the same time, the moon’s gravity is also pulling on the planet. Since the strength of gravity depends on the distance, not every point on the planet experiences the moon’s pull at the same strength. Since the planet is extended in space – i.e. has an actual volume – it “feels” gravity more strongly on one side than the other.

SPP 1992 Iason Saganas / Ludwig Scheibe

Specifically, on the side of the planet facing the companion, gravity is stronger than on the opposite side, and the planet is “squished” toward the direction of the moon. Conversely, on the side facing away from the companion, gravity is weaker, and a squish of the same side happens in the opposite direction. So-called “tidal bulges” form, as the planet is elongated and assumes an elliptical, rather than spherical shape. On Earth, these bulges are primarily observed in water and are the reason for high tide, but to a certain extent, the whole planet is deformed in this way.

SPP 1992 Iason Saganas / Ludwig Scheibe

However, in addition to the planet and the moon orbiting each other, they also rotate around their own axes. This, together with the fact that the formation of the bulges is not instantaneous, means that the moon-facing tidal bulge does not form directly at the point in direct connection between moon and planet (“under” the tide-raising satellite you might say). Instead, the bulge is shifted either forward or backward relative to the satellite’s position, depending on the system’s initial conditions. We call this tidal lag.

SPP 1992 Iason Saganas / Ludwig Scheibe

SPP 1992 Iason Saganas / Ludwig Scheibe

The moon and the tidal bulge attract each other. In the example shown in this picture, the tidal bulge is carried ahead of the moon. This happens when the initial orbital period of the moon, that means the time it takes for the moon to make one full orbit, is longer than the rotation period of the planet around its own axis. Due to the gravitational attraction, the satellite forces the spinning planet to slow down, so as to catch up with the tidal bulge.

Effectively, a cosmic wrench, the size of a planet, is implemented by this interplay.

Due to the law of the conservation of angular momentum, if the planet slows down, that loss in angular momentum has to be gained somewhere else; In fact, the moon itself gains this angular momentum by sapping it out and absorbing it into its orbital motion. As a result, by Kepler’s Third Law, the moon widens its orbit around the planet, increasing their mutual separation.

Conversely, in the opposite case when the tidal bulge is “behind” the moon in the rotation, the process happens in reverse: The moon speeds up the planet’s rotation. Again, due to the conservation of angular momentum, that means that the orbit of the moon slows down and that its orbital distance shortens.

This is the underlying mechanism of a process called tidal migration. This happens right now, for our Earth-Moon system. Due to tidal migration, the Moon pushes itself away from us at a rate of about 3.8 cm per year (this can be measured with lasers). That rate is not enough for the moon to escape earth’s gravitational influence before both getting obliterated by the sun’s red giant phase in about 5 billion years.

While these processes are explained here using a planet and its moon, the same principle applies for a star that is orbited by a planet, in which case the planet takes the role of the satellite. Thus, tidal migration can happen in this case as well, where a planet’s orbit around the star gradually widens or narrows. This has been observed in a few cases by very carefully measuring the times of transit for a planet. In the case of the hot Jupiter WASP-12 b, scientists found that its 1.1-day-orbit shortens by about 30 milliseconds each Earth year, as the planet very slowly moves towards its star. On human time scales, that is an imperceptibly tiny effect, but over the billions of years that planetary systems exist, this kind of tidal migration has an important effect on the way these systems evolve.

Furthermore, the deformation caused by the tides cause friction within the planet’s material, which in turn is a source of heating in the interior. This is important for a planet’s or a moon’s long-term thermal evolution. For example, it can lead to a moon having liquid water under its surface despite being outside the classical habitable zone, which in turn might make it suitable for life. This is suspected for example for some of the moons of Jupiter and Saturn here in the Solar System.

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Oben sieht man, wie das licht eines Sterns durch ein stilisiertes Prisma in seine Farben aufgebrochen wird. Daneben das ungestörte Sternenlichtspektrum in Diagrammform. Unten fällt das Sternenlicht erst durch die Atmosphäre eines Sterns, bevor es durch das Prisma aufgefächert wird. Einige Linien in dem Farbspektrum sind schwarz. Danabene das auf diese Art beeinflusste Sternenpektrum in Diagrammform, mit gut sichtbaren Absorptionslineien.

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