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Title: Methods of Studying Planet Interiors

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This page is about ways of finding planet interiors. For the astronomical objects, see Planet.

Planet Interiors

Artist's depiction of the Interiors of Earth, Mars and Moon

Astronomers use different methods of studying planet interiors to gain a better understanding of how planets are formed and generate more information about the planet, with the process of studying the interiors of planets done through indirect methods so scientists can measure from Earth and due to the inability to directly penetrate to the interior of planets to study them. Methods include using seismology, gravity, oblateness of the planet (which is the bulge at the equator), the magnetic field of the planet, as well as utilising the understanding of our own Earth, as a sort of Rosetta Stone, to better understand other planets. These methods can be used on terrestrial planets such as Earth and its moon but studying gas giants are harder as they do not have distinct layers like the rocky, solid planets.

Seismology

By measuring the path of seismic waves through a planet, it shows which layers of a planet are high and low density, and which of them are solid or molten. Through the existence of sources of energy such as earthquakes or magnetic and electric disturbances the observation and interpretation of seismic waves can provide information on the structure of the deep interiors of planet. Seismic waves are recorded through calculating the time they travel between the source (which can be set up by nature such as an earthquake that excites seismic waves or electromagnetic storms in the upper atmosphere creating electromagnetic sounds, or sometimes planned experiments such as artificial explosions in a region of interest) and the receiver which is the seismographic station. This is all dependent on the physical properties the waves are passing through due to the fact that waves travel at different speeds through different materials and can be reflected by boundaries between the layers.

There are several different kinds of seismic waves that are generated from earthquakes that can be used to measure different parts of the Earth. Compressional (longitudinal) waves go downward through the Earth and are called primary or P waves, while shear (transverse) waves called secondary or S waves travel along the same path as P waves but slower. Both compressional and shear waves can travel through solids but only compressional can through liquids. The time interval between the P wave and the S wave arriving at the seismograph is a measure of the distance of the source, which at distances greater than quarter of the way around the Earth creates a shadow zone that both P and S waves encounter. This shadow zone is the foremost evidence of the Earth's core. There are also other multiply reflected and refract paths that give further information about the interior of the Earth. In addition to these body waves that travel through the Earth there are also surface waves that travel along the surface of the Earth with amplitudes that are the largest at the surface and decrease exponentially with depth. These surface waves are important in studying the crust and upper mantel, especially their lateral variations due to the fact that Earth is the least uniform near the surface. Like body waves there are also two basic kinds, Love waves where particle motion plane is horizontal which means is parallel to the surface, and Rayleigh waves with the particle motion plane being vertical which means is perpendicular to the surface. Very long period surface waves also exist which are called "mantle waves" which have horizontal wavelengths that can exceed 1000 km and maintain substantial amplitudes down to as deep as 600-700 km. Due to their relatively long period of relevance mantle waves can be observed at the same station due to the fact that they travel around the world several times along the same stretch.

Through seismology it generates a density profile of the planet that can be used to guess what the planet is made of. This is due to the fact that for example, rock has a lower density than metal and different metals have different densities. Also materials that are hotter than average are lighter and in a viscous Earth will float to the surface, while colder material is denser and will tend to sink. Meaning that through analysing the seismogram and its data scientists can predict what the planet is made of through comparing its densities to materials we already understand. Keeping in mind the fact that the further in the planet's interior, the higher the temperature and pressure, affecting density.

Seismology provides unrivalled detail about the interior of the planet but data is limited to the distribution of detected earthquakes around the world as well as where seismographic stations are located. Not much can be done about the placement of seismographs around the world expect there may be earthquakes in unexpected areas so generally coverage will improve over time, especially around the Southern Hemisphere where there are several thousand kilometres were no land exists. Seismometers are also needed to on the surface of the planet to measure the tremors through the planet, so current technology can only measure our Earth and its the Moon as well as Mars, but it has difficult to utilising this method for planets further away and especially for gas planets.

Gravity

Through utilising a spacecrafts orbit around the planet, it can show how the planet's gravity affects the spacecraft's orbit. This can determine the planets density profile which shows how dense the different layers of the planet are. Through measuring the radius of each planet at a specified pressure, typically the 1-bar pressure level, by using the occultation technique where the reduction of the radio signal from the spacecraft is measured as it passes behind the planet and combining it with the mass it generates the mean planetary density. If planets did not rotate, they would be a spherical shape and their external gravitational field would be the same as something of the same mass, meaning information about the variation in density through radius could not be calculated. But fortunately the planets do rotate, and the response to their own rotation provides greater information about the planet, with this response being observed in their external gravitational field.

Gravitational data about planets is found through observations of the orbits of natural satellites, the rotational rates of elliptical rings as well as changes in the trajectories of spacecraft. When a spacecraft flies by a planet it samples the gravitational field at different points of its radius, with tracking of the spacecraft's radio signal revealing the Doppler shift due to acceleration in the gravitational field of the planet. By inverting this data it provides an accurate determination of the planet's mass and its gravitational harmonics.

Oblateness

Every planet bulges a bit at the equator due to their rotation causing centrifugal force to act on itself. This bulge is called the planet's oblateness, with the density profile of the planet shown through the strength of the olbateness. A planet's response to its own rotation is characterised by how much distortion there is on the surface of constant total potential. This amount of distortion, known as the level surface, is dependant on the distribution of mass inside the planet, the mean radius of the level surface as well as the rotational rate. This distortion, otherwise known as oblateless of the outermost level surface is measured from direct observations of the planet, whether through direct telescopic measurement or from observations of spacecraft. Gravitational harmonics provide information on how a planets shape responds to its own rotating-frame forces from its own spin, which depend on the distribution in mass of a particular planet. Interpretation of these harmonics require accurate knowledge of the rate the planet rotates, this is calculated from the rotation rate of each planet's magnetic field. This approach works assuming the field's rotation follows the rotation of the bulk of the interior and convective motions deep in the electrically conducting interior of the planet generate magnetic fields.

Magnetic Fields

There are two methods that can estimate the radius of a planet's electrically conducting core through the spatial structures of its magnetic field, which is spherical and concentric with the planet's surface These include 'the frozen flux method' and 'the flat spectrum method'. The frozen flux method bases its concept on the electrical conductivity of the planet's core being so large compared to the exterior of the core that the exterior can be considered an electrical insulator. The field that then emerges from the core surface is advected by motions on the core-mantle boundary which matches smoothly to the net unsigned flux, $\mathrm {N} (r,t)$, which is the potential field outside the core. This concept is calculated through$\mathrm {N} (r,t)=\phi |Br(r,\theta ,\phi ,t)|dS$, where $Br(r,\theta ,\phi ,t)$is the radial component of the magnetic field and $dS=r^{2}sin\theta d\theta d\phi$, with $\theta$being the colatitude and $\phi$being the longitude, this integral equation is taken over the entire surface of the sphere of radius $r$where the centre of the planet is the origin and it is independent of time $t$. The magnetic field is assumed from observations above the surface of the planet and is fitted to a potential field that vanishes at great distances from the planet. This is possible as the main magnetic field is created within the planet core and the core exterior acts as an insulator, the potential field obtained by the observations can then be used to evaluate $\mathrm {N} (r,t)$for any $r$. For the flat spectrum method it originates from the potential field as $V=a\sum _{l=1}^{\chi }\sum _{m=0}^{l}\left({\frac {a}{r}}\right)^{l+1}[g(t)cosm\phi ++h(t)sinm\phi ]P(\theta )$ where it utilises the mean square of the field intensity over a spherical surface of radius $r$, permeability of free space, the mean energy density at the surface of the planet and by excluding mantle conduction with external sources if gives an arbitrary $r$.The level this provides is the flat-spectrum estimate of the core radius.

Rosetta Stone

Utilising what we already know is also effective in analysing what planets are made of, such as knowing what kind of building blocks are used to create planets and previous studies have shown only a limited number of elements are needed to describe the total mass of the planet. Due to the intimacy of the human species to Earth, large amount of research has been done on the planet throughout history, trying to discover and understand the planetary body and how it works. This knowledge can be used as a basis information towards understanding planets other than earth. So beyond just being a home Earth is also a crucial Rosetta Stone into measuring and interpreting the process, internal structure and the overall histories of other planets in the solar system and further, the galaxy.

Studying Gas Giants

It is hard to analyse the interiors of gas giants due to the fact that they don't have distinct layers like terrestrial planets and the cloudy faces of these planets tell little about its interiors. Instead these interiors are studied through theoretical predictions from analysis of the mass, radius, shape and gravitational fields of the planets. The study of how planetary materials at high densities and pressures behave also provide experimental and theory based framework to base planetary interior models upon These interior models create a window into the internal structure of these planets that help better understand planet formation processes in our solar system and others.

There is several observational data that can provide information on the composition and structure of these giant planets. The easiest to obtain quantities include the mass, which is known from the orbits of natural satellites, radius, which is the polar and equatorial radii as well as the rotational period which is from remote and in situ observations of the magnetic fields on these planets. These fundamental observations combined with an understanding of high-pressure behaviour in matter allowed for the conclusion in the 1940's that Jupiter and Saturn were predominantly hydrogen. More detailed interior models have since been created through direct measurement of the planets' high-order gravity fields, heat flow, interior rotational states, as well as atmospheric elemental composition detected through spacecraft and ground-based spectroscopes. These models have allowed the separation of the giant planets into two broad categories, with Jupiter and Saturn as predominantly hydrogen-helium gas giants that have enhanced abundance of heavier elements and dense cores. While Uranus and Neptune are ice giants with hydrogen-helium envelopes that have dense cores.