Astrophysics

Planets are celestial bodies that must satisfy the following three criteria:

1. Have sufficient mass that, under their own gravity, they take on a spherical shape.
2. Orbit around a star (or stars)
3. The path of their orbit is virtually clear of all other significant objects.

Planets can be rocky (terrestrial), like Earth, or gaseous, like Jupiter.

In our solar system, the rocky planets orbit the Sun more closely (though this is not always the case in other solar systems). This pattern exists because of how the solar system formed. Closer to the young Sun, temperatures were too high for gases to condense, so only rock and metal remained to build planets. Further out, where it was cooler, vast amounts of hydrogen and helium could accumulate.

It is important to note a planet’s surface gravity depends on both its mass and radius. Jupiter is over 300 times Earth’s mass, yet its surface gravity is only about 2.5 times greater, because its enormous radius works against the effect of its extra mass.

Planetary satellites are objects that orbit a planet. They can either be natural, like the Moon, or artificial, like the International Space Station.

Comets are small objects that are typically made from rock, dust and ice. Due to their small size, they are not spherical. They follow highly elliptical orbits around a star.

Comets are hypothesised to originate from the Oort Cloud, a vast shell of icy debris surrounding the solar system far beyond the orbit of Pluto. Gravitational disturbances can nudge these objects inward toward the Sun. As a comet approaches a star, solar radiation heats its surface, causing ice to sublimate, releasing dust and gas that form the characteristic tail.

Solar systems (also called star systems) consist of at least one star and the objects gravitationally bound to it, such as planets, their satellites and comets.

It is useful to note that some star systems contain more than one star. Binary systems have two stars, while trinary systems have three. In fact, some estimates suggest that over half of all star-like systems in our galaxy are binary or higher-order systems.

Galaxies are vast structures containing stars, gas, dust and dark matter, held together by gravitational attraction. They range enormously in size, from dwarf galaxies containing a few billion stars to the largest galaxies with up to a hundred trillion.

Our solar system lies within one of the arms of a spiral galaxy called the Milky Way, which is estimated to contain 100–400 billion stars.

At the centre of most galaxies is a supermassive black hole, which is thought to play a key role in their formation and evolution.

The Universe contains all matter, energy, space and time, including every galaxy. It is expanding, causing most galaxies to move away from us. The rate of this expansion is accelerating, driven by what physicists call dark energy.

The observable universe is the portion of the universe from which electromagnetic radiation has had time to reach us. Since the universe is estimated to be 13.8 billion years old, light from beyond a certain distance simply hasn’t arrived yet.

The observable universe is approximately 93 billion light-years across, far larger than 13.8 billion light-years because space itself has continued to expand while the light was travelling. Earth is at the centre of the observable universe by definition, since we are the observer.

A star is considered low mass if it has between roughly 0.5 and 10 solar masses. Our Sun falls within this range.

When a low mass star exhausts the hydrogen in its core, hydrostatic equilibrium is disrupted. The core contracts while the outer layers expand and cool, forming a red giant. The star eventually sheds its outer layers as a planetary nebula (unrelated to planets, the name is historical), leaving behind a dense, hot remnant called a white dwarf.

Nebula – stage 1 of star formation

Stars are born in clouds of dust and gas known as stellar nebulae. These clouds are composed primarily of hydrogen and helium, along with heavier elements.

Nebulae are often material leftover from previous supernovae, the explosive deaths of massive stars. This means the atoms in our Sun and solar system were forged inside earlier generations of stars.

Over time, denser regions within the nebula begin to contract under the force of gravity; this process is called gravitational collapse. As the dust and gas are compressed, gravitational potential energy is converted into thermal energy, causing the temperature to rise.

Protostar – stage 2 of star formation

As gravitational collapse continues, the densest regions of the nebula form protostars. These continue to contract and heat up as gravitational potential energy is converted into thermal energy.

For nuclear fusion to begin, both temperature and pressure in the core must become high enough for hydrogen nuclei (protons) to overcome the electromagnetic repulsion between them. Since protons are all positively charged, they naturally repel each other. Only at extreme temperatures (~15 million °C) do they move fast enough to get close enough for the strong nuclear force to bind them together, fusing hydrogen into helium.

Main sequence phase – stage 3 of star formation

Once nuclear fusion is sustained, the outward radiation pressure produced by hydrogen fusion in the core balances the inward pull of gravity. This balance is called hydrostatic equilibrium.

The star has now entered the main sequence phase, where it will spend the majority of its life. This process of fusing hydrogen into helium in the core is known as core hydrogen burning (though no combustion is involved, the term ‘burning’ is used loosely in astrophysics).

More massive stars have hotter cores, which means they fuse hydrogen at a much faster rate. Counterintuitively, this means they exhaust their fuel supply and leave the main sequence sooner than less massive stars. Our Sun will spend roughly 10 billion years on the main sequence; a star ten times its mass may last only 20 million.

Red giant phase – stage 4 of star formation

Over time, the hydrogen in the core becomes depleted. The outward radiation pressure from fusion decreases, and hydrostatic equilibrium is lost. Gravity now dominates, causing the core to contract and heat up.

This rising core temperature heats the surrounding layers, causing them to expand dramatically. As the outer layers expand, the same amount of energy is spread over a much larger surface area. This reduces the surface temperature, shifting the star’s colour toward red (cooler stars emit longer wavelength light). The star has become a red giant.

Shell hydrogen burning phase – stage 5 of star formation

Although hydrogen in the core is depleted, significant hydrogen remains in the surrounding layers. Previously, these regions were not hot enough for fusion to occur.

As the core contracts and heats up, it transfers thermal energy to the layer (or shell) immediately surrounding it. Eventually, temperatures in this shell become sufficient for hydrogen fusion to begin. This process is called shell hydrogen burning. This is quite different from a main-sequence star, where fusion occurs only at the centre.

Core helium burning phase – stage 6 of star formation

As the core continues to contract, its temperature rises further. Eventually it becomes hot enough (approximately 100 million °C) for helium nuclei to fuse into carbon and oxygen. This process is called core helium burning.

Core helium burning restores outward radiation pressure in the core, temporarily re-establishing hydrostatic equilibrium. Meanwhile, shell hydrogen burning continues in the layer surrounding the core.

The combined energy output from both the core and the shell pushes the outer layers further outward, increasing the star’s size.

Shell helium burning phase – stage 7 of star formation

Eventually, the helium in the core is exhausted and fusion stops. Once again, hydrostatic equilibrium is lost. Gravity dominates, and the core contracts and heats up further.

This heat is transferred outward to the surrounding shell, which becomes hot enough for the helium within it to begin fusing into carbon and oxygen. This is called shell helium burning.

Beyond this, a further outer shell also becomes hot enough for hydrogen fusion to occur. The star now has a layered structure: a carbon-oxygen core, a helium-burning shell, and a hydrogen-burning shell.

For a low mass star, this is as far as fusion progresses. The core will never reach the temperatures needed to fuse carbon into heavier elements, so the star’s nuclear fuel is now effectively finite.

Core stops collapsing – stage 8 of star formation

In low mass stars, the carbon-oxygen core will never reach the temperatures required to fuse heavier elements. This is because heavier nuclei carry greater positive charge, meaning the electromagnetic repulsion between them is stronger, requiring more energy to overcome.

Without fusion to provide outward pressure, gravity continues to compress the core until it is roughly the size of Earth, incredibly dense, with a teaspoon of material weighing several tonnes.

At this point, electrons within the core resist being compressed any further. This outward force is called electron degeneracy pressure, and it is sufficient to halt gravitational collapse, establishing a new and final equilibrium.

White dwarf and planetary nebula formation – stage 9 of star formation

As the core contracts, the helium-burning shell becomes increasingly unstable. The star begins to pulsate, and these pulsations eject the outer layers of the star into space, forming an expanding cloud of gas and dust called a planetary nebula (the name is historical; it has nothing to do with planets).

This material enriches the surrounding interstellar medium with heavier elements such as carbon and oxygen, which may eventually form part of new stellar nebulae, beginning the cycle again.

The exposed remnant left behind is a white dwarf: an extremely hot, dense core in which no nuclear fusion occurs.

A star is considered high mass if it has a mass greater than approximately 10 solar masses. Unlike low mass stars, high mass stars have cores hot enough to fuse elements far beyond carbon and oxygen, progressing through successive stages of fusion up to iron.

Stars with between 10 and 40 solar masses will expand into red supergiants before ending their lives in a violent explosion called a supernova. The remnant left behind is either a neutron star or a black hole, depending on the remaining core mass, these are not represented on an HR diagram.

It is useful to note these supernovae are responsible for distributing heavy elements throughout the interstellar medium, the same material that forms new stellar nebulae. Every element heavier than iron found on Earth was produced during a supernova explosion.

Red supergiant phase

High mass stars spend far less time on the main sequence than low mass stars because their hotter cores fuse hydrogen at a much faster rate. Initially, they follow the same sequence of core and shell burning.

However, due to their greater mass, their cores reach temperatures high enough to fuse elements progressively heavier than carbon and oxygen, including magnesium, silicon, and ultimately iron. This produces a layered structure, with the heaviest elements closest to the centre.

Iron is the critical turning point. Iron has the highest binding energy per nucleon of any element (a measure of how tightly its nucleus is held together), making it the most stable nucleus.

Fusing lighter elements into heavier ones up to iron releases energy. Fusing elements heavier than iron absorbs energy. Once an iron core forms, no further fusion process can provide the outward pressure needed to resist gravitational collapse. The star is now on the brink of catastrophe.

Supernova

Once an iron core forms, it can no longer sustain fusion that releases energy. Without outward pressure, gravity causes the core to collapse in on itself within seconds.

The outer layers fall inward at enormous speed, strike the incompressible core, and rebound, generating a powerful shockwave that tears the star apart. This explosion is a supernova.

During this process, the extreme temperature and pressure provide enough energy to fuse elements heavier than iron, including gold, uranium, and many others. These elements are flung out into space, enriching the interstellar medium.

The diagram above shows the stratified layers of fusion within a high-mass star just before it goes supernova. Each layer fuses progressively heavier elements toward the centre, with the iron core at the heart.

A supernova produces a dramatic increase in luminosity, briefly outshining an entire galaxy. The remnant left behind will become either a neutron star or a black hole.

The remnant a high-mass star leaves behind depends on its core mass after the supernova.

If the core mass exceeds:

• approximately 1.4 solar masses (Chandrasekhar limit), the electrostatic repulsion between electrons (electron degeneracy pressure) is insufficient to resist gravitational collapse. The core continues to compress, forcing electrons and protons together to form neutrons via a nuclear reaction. The collapse is then halted by neutron degeneracy pressure, producing a neutron star, an object roughly 20 km across but extraordinarily dense.

• approximately 3 solar masses, even neutron degeneracy pressure is overcome. No known force can halt the collapse, and a black hole forms.

Degeneracy pressure is a quantum mechanical effect, despite the name, ‘degenerate’ here simply means matter compressed to an extreme degree. When particles are packed this tightly, they resist further compression, creating an outward pressure that opposes gravity.

A white dwarf is the stellar remnant of a low mass star. Once the outer layers have been expelled as a planetary nebula, what remains is the exposed core, composed primarily of carbon and oxygen, supported against gravity by electron degeneracy pressure. No nuclear fusion takes place.

Key properties:

• Approximately the size of Earth (diameter of a few thousand kilometres)
• Extremely dense. A teaspoon of white dwarf material would weigh several tonnes
• Very hot initially, but with no energy source it slowly radiates away its thermal energy

It is useful to note that over trillions of years, a white dwarf is theorised to cool into a black dwarf. A cold, dark remnant. None yet exists, as the universe is not old enough.

When nuclear fusion in a star’s core stops, so does the outward radiation pressure. The star becomes unstable as it collapses under its own gravity.

In a low mass star, this collapse is eventually halted by electron degeneracy pressure:

1. As the core collapses, electrons are forced closer and closer together.
2. They fill the available energy levels of the atoms in the core, starting with the lowest.
3. Eventually, all energy levels are filled. The Pauli exclusion principle states that no more than two electrons can occupy the same orbital, so the electrons have nowhere left to go.
4. This resistance to further compression creates an outward pressure, electron degeneracy pressure , that halts gravitational collapse.

A half-empty plastic bottle with the lid on can be squeezed into a smaller volume. However, a bottle completely filled with water becomes almost impossible to compress; the water has nowhere to go and resists the inward force. Electron degeneracy pressure works on a similar principle, with electrons resisting compression once all available states are occupied.

A neutron star is the stellar remnant formed when a star’s core mass exceeds the Chandrasekhar limit (approximately 1.4 solar masses). The collapse forces electrons and protons together to form neutrons, and is halted by neutron degeneracy pressure. The result is an object composed almost entirely of neutrons, with roughly the same density as an atomic nucleus.

Key properties:

• Approximately in diameter, despite containing more mass than the Sun
• Extremely dense. Approximately compared to for iron.
• Can spin up to 600 times per second due to conservation of angular momentum. When the core shrinks, its rotation rate increases dramatically.
• Emit beams of radio waves from their magnetic poles. As the star spins, these beams sweep across space like a lighthouse. When detected from Earth, this pulsing signal gives them the name pulsars.

Black holes

• If the core of the collapsing star is greater than three solar masses, then the immense gravity causes the core to collapse into a black hole.
• The gravitational field around a black hole is so strong that not even light can escape from it.
• The boundary where the escape velocity equals the speed of light, is known as the event horizon or Schwarzschild radius.
  • Outside the event horizon the escape velocity is less than so light can escape and anything outside this boundary can be observed.
  • Inside the event horizon the escape velocity is greater than Light cannot escape and anything inside this boundary cannot be observed and is unknown: this is what causes the ‘black hole’.
• There is still matter within the event horizon but light from it will never reach us.

The flat disc of matter surrounding the ‘black hole’ that we can see is known as the accretion disc. The material in the accretion disc slowly dissipates energy and spirals into the black hole.

If stars and planets get too close to the black hole, the intense gravitational forces will stretch them and eventually cause them to break apart. As this material spirals towards the black hole, the intense frictional and gravitational forces squash it and raise its temperature, making it extremely bright.

The black hole shadow is actually a magnified image of the black hole’s event horizon, appearing roughly twice its size due to gravitational lensing.

Hertzsprung-Russell diagrams are graphs which plot the temperature of a star against its luminosity:

• X axis: surface temperature is measured in kelvin, with hotter stars on the left.

• Y axis: luminosity compared to our sun, with brighter stars towards the top.

When astronomers first plotted the stars, they had clustered them together in four groups:

• Main sequence
• White dwarfs
• Giants
• Supergiants

Most stars in the universe are on the main sequence. This is where stars spend most of their lives, in their stable core hydrogen-burning phase. When a star leaves the main sequence, it becomes either a white dwarf, a giant, or a supergiant, depending on its mass:

• Brighter stars have a proportionally higher surface temperature.

• The coolest stars are red, while the hottest stars are blue.

A continuous spectrum is a type of light spectrum where you can observe all possible frequencies of light, spread smoothly over a wide range. It’s like seeing the full range of colours in a rainbow without any gaps.

For example: If you were to look at the spectrum of light produced by a white-hot filament, you would see a continuous blend of colours from red to violet without any missing sections.

Even though the Sun’s light appears white, its spectrum is not continuous.

When we examine it closely, we see dark lines in the Sun’s absorption spectrum called absorption lines where some frequencies are missing. These gaps are caused by elements in the Sun’s outer layers absorbing certain specific wavelengths of light.

Photons generated by nuclear fusion in a star’s core move outward over thousands of years, passing through the various layers of plasma and gas in the star as they do.

These photons encompass all frequencies of the electromagnetic spectrum, forming what is called a continuous spectrum.

As the photons travel through the gas layers, they are absorbed by ions or atoms in the gas, exciting the electrons. These excited atoms then re-emit photons, but in random directions and often at different frequencies than which they were absorbed.

Spectroscopy is used to analyse the light emitted by stars. The outer atmospheres of stars are not hot enough to produce an emission line spectrum. Instead, stars emit an absorption line spectrum. An absorption line appears when light from a source passes through a cooler gas and is observed by a detector.

An absorption line spectrum is essentially the opposite of an emission spectrum, dark lines are superimposed on a continuous background. These dark lines correspond to specific wavelengths of light that are absorbed by the gas as photons excite the atoms.

Each element has a unique set of energy levels, meaning the pattern of spectral lines is unique for each gas.

An example of the absorption spectrum for hydrogen is shown above. The different dark lines indicate the wavelengths of light that are absorbed when electrons are excited within a hydrogen atom.

The absorption lines (unique pattern of dark lines) in a star’s spectrum acts like a fingerprint for the elements present in the star. By analysing the absorption spectrum, scientists can determine the chemical composition of a star, even if it is located far away.

If a particular element is present in a star, its characteristic absorption lines will appear in the star’s spectrum. By comparing the emission line spectra of elements confirmed in a laboratory, such as hydrogen and helium with the absorption line spectrum of the Sun, we can verify the Sun’s chemical makeup.

It is important to note that when provided with an absorption spectrum of a star, you can be asked to identify a star with a similar chemical composition. Pay close attention to the spacing and pattern of the dark lines to match the spectrum to the corresponding element.

Continuous spectra

• A continuous emission spectrum is one that contains light across all wavelengths of the electromagnetic spectrum.
• This type of spectrum is produced by hot, dense objects, such as the cores of stars.
• Photons emitted from these sources include all possible wavelengths and frequencies, creating a seamless spectrum without gaps.

Emission line spectra

• An emission line spectrum occurs when electrons transition from higher to lower energy levels, releasing photons.
• Each transition corresponds to a specific wavelength, producing coloured lines on a black background.
• This type of spectrum is characteristic of hot, low-pressure gases.

Absorption spectra

• Absorption spectra arise when an atom absorbs specific wavelengths of light, resulting in missing lines.
• When a continuous spectrum passes through a cool, low-pressure gas, specific wavelengths of light are absorbed, leading to a spectrum with missing wavelengths.
• This spectrum consists of a continuous background with dark lines where certain wavelengths have been absorbed.

The missing wavelengths in an absorption spectrum correspond exactly to the wavelengths emitted in the emission spectrum of the same element. When electrons return to lower energy levels, they emit photons in all directions, which is why some wavelengths appear absent.

The three kinds of spectra you should be familiar with:

• Continuous spectra: Contains all possible wavelengths and frequencies
• Emission line spectra: Discrete coloured lines on a dark background
• Absorption line spectra: Discrete dark lines on a continuous background

The key differences between how these spectra are produced and what they look like are shown in the image below:

A black body radiator is a theoretical object that absorbs and emits radiation at all wavelengths. While true black bodies are ideal and do not exist in reality, stars provide the closest real-world approximation.

The spectrum of radiation emitted by a black body is determined solely by its temperature.

The intensity–wavelength graph for black bodies shows the relationship between the temperature and the peak wavelength of emitted radiation for different objects. As the temperature in kelvin rises, the peak wavelength reduces, and the intensity increases.

Based on Wein’s displacement law:

• Hotter objects emit radiation with shorter peak wavelengths, meaning they appear white or blue.

• Cooler objects have longer peak wavelengths, giving them a red or yellow appearance.

• Hotter objects also emit greater intensity at each wavelength compared to cooler ones.

Recall how wavelength varies along the electromagnetic spectrum, so reducing wavelength means the radiation moves from the radio end of the spectrum towards the gamma end of the spectrum. Within the visible light region, a lower wavelength means light moves from red to violet.

The gravitational field strength decreases as the distance from the mass increases. It follows an inverse-square relationship:

This relationship holds true for all gravitational fields, regardless of the mass generating it. For example, doubling the distance from a mass decreases the gravitational field strength by a factor of four.

Gravitational field strength, (at a given distance) is directly proportional to the mass of the object.

Larger masses produce stronger gravitational fields at the same distance. For example, a person standing on the Earth’s surface experiences a gravitational force of towards the centre of the Earth.

On the other hand, the gravitational force between two electrons is a factor of less than the Coulomb force of repulsion between them, so can be ignored.

The higher the mass and the smaller the radius of a celestial body, the greater the gravitational field strength at its surface.

Different celestial bodies have different values of , which refers to the gravitational field strength at the body’s surface. The gravitational field strength on a planet determines the force acting on an object or person due to gravity. The stronger the gravitational field strength, the heavier the object will feel, and the more force is needed to lift it.

Newton’s shell theorem states that a spherical shell of mass exerts the same gravitational pull on external objects as if all its mass were concentrated at its centre.

Calculations related to gravitational fields of spherical objects can be simplified by treating their mass as concentrated at a single point at their centre – this is the point mass approximation.

This approximation holds for spherically symmetric objects where the mass distribution is uniform.

The point mass approximation is commonly used for planets, stars, and other celestial bodies to calculate gravitational effects on nearby objects.

For example, the Earth can be approximated to a point mass of at the centre.

Without this approximation, finding the gravitational force acting on an object due to the Earth would require summing up the effects from each point on the Earth, which would be extremely difficult.

The point mass approximation applies only at distances greater than the radius of the spherical mass.

Inside the spherical mass, the gravitational field strength is influenced by the mass distribution.

Inside a spherical mass, the gravitational field strength at a point depends on the amount of mass inside within the radius equal to the distance at that point.

As you move away from the centre, more mass is enclosed within that radius, so the gravitational field strength actually increases.

This increase turns out to be directly proportional to the distance from the centre, which explains why the beginning of the graph above is a straight-line.

At distances greater than the radius of the mass, the inverse-square relationship is observed.

In a gravitational field, the field lines:

• represent the direction and strength of a gravitational field,

• indicate the force on a mass at each point in a gravitational field,

• always point inward towards the mass, as gravity is always an attractive force, and

• never cross each other.

If the gravitational field lines are closer together, the field is stronger at that point. When the gravitational field lines are spaced further apart, the field is weaker. Gravitational field-line diagrams show that the field strength decreases with distance from the centre of mass.

A spherical mass produces a radial, symmetrical gravitational field, equivalent to a point mass at its centre. Non-spherical masses only approximate this pattern at large distances; close to the object, the field lines follow the actual shape of the mass distribution.

In a uniform gravitational field, the field lines are parallel and equidistant, indicating a constant gravitational field strength over the region.

The gravitational field close to the surface of a planet is approximately uniform. The gravitational field strength remains approximately constant over relatively small distances from the surface.

Although the planet’s gravitational field is radial, the distance between the test mass (the object experiencing gravity) and the centre of the planet does not change much relatively when you are near the surface of a planet.