The Universe Revision Notes

A galaxy is a massive system consisting of stars, stellar remnants, interstellar gas, dust, and dark matter, all bound together by gravity. Galaxies vary in size and shape, commonly classified as spiral, elliptical, or irregular.

The Milky Way is a spiral galaxy, characterised by a flat, rotating disc containing stars and spiral arms, a central bulge of older stars, and a surrounding halo of stars and globular clusters.

• Galaxies contain billions of stars and other matter.
• Gravity holds all components of a galaxy together.
• Galaxies can be spiral, elliptical, or irregular in shape.

The Milky Way is the galaxy that contains our Solar System. It is a barred spiral galaxy with several spiral arms extending from a central bar-shaped core.

Its diameter is approximately 100,000 light-years. A light-year is the distance light travels in one year, about 9.46 × 10¹² kilometres.

The Milky Way contains over 100 billion stars, along with planets, nebulae, star clusters, and vast clouds of gas and dust.

• Diameter ≈ 100,000 light-years.
• Contains over 100 billion stars.
• Has a spiral structure with arms and a central bulge.

A light-year is the distance travelled by light in one year. Since light travels at approximately 3.00 × 10⁸ metres per second, the calculation is:

Distance in one year = speed of light × number of seconds in one year

= 3.00 × 10⁸ m/s × (365 × 24 × 60 × 60) s ≈ 9.46 × 10¹⁵ metres (or 9.46 × 10¹² kilometres).

• 1 light-year ≈ 9.46 × 10¹² km.
• Used to measure vast distances in space.
• Helps express the size of galaxies and distances between stars.

The Universe contains billions of galaxies, each with billions of stars. The Milky Way is just one galaxy among these countless others.

Galaxies are distributed throughout the Universe, often grouped into clusters and superclusters.

Understanding the Milky Way's size and structure helps place our Solar System in the broader cosmic context.

• The Universe contains billions of galaxies.
• Galaxies group into clusters and superclusters.
• The Milky Way is part of the Local Group of galaxies.

To draw a simple representation of the Milky Way: 1. Draw a large oval to represent the flat disc of the galaxy. 2. Sketch several curved spiral arms extending from the centre outward, resembling a pinwheel shape. 3. Add a small central bulge in the middle of the oval to represent the dense core. 4. Optionally, indicate the position of the Solar System on one of the spiral arms, about two-thirds from the centre.

Label the spiral arms, central bulge, and the approximate location of the Solar System.

• Draw an oval for the disc.
• Add spiral arms curving outward from the centre.
• Include a central bulge.
• Mark the Solar System's position on a spiral arm.

Redshift is the phenomenon where the wavelength of electromagnetic radiation, such as visible light, increases when the source of the radiation is moving away from the observer. This means the light shifts towards the red end of the visible spectrum, which has longer wavelengths.

Electromagnetic radiation from stars and galaxies consists of waves with characteristic wavelengths. When these objects move away from Earth, the waves are stretched, increasing their wavelength and decreasing their frequency.

This effect is analogous to the Doppler effect for sound, where the pitch of a sound decreases if the source moves away from the listener.

• Redshift = increase in wavelength (λ) of electromagnetic waves.
• Occurs when source moves away from observer.
• Wavelength shifts towards red (longer wavelengths).

The increase in wavelength occurs because the source of light is receding relative to the observer. As the source moves away, each successive wave crest is emitted from a position further away, causing the waves to be spaced further apart.

This stretching of waves results in a lower frequency and longer wavelength observed on Earth compared to the wavelength emitted at the source.

The amount of redshift is directly related to the speed at which the object is moving away.

• Wavelength increases due to relative motion away from observer.
• Frequency decreases as wavelength increases.
• Redshift magnitude depends on recessional velocity.

Redshift (z) is quantified by comparing the observed wavelength (λ_observed) to the emitted (rest) wavelength (λ_emitted) using the formula:

z = (λ_observed - λ_emitted) / λ_emitted = Δλ / λ_emitted

where Δλ is the change in wavelength. A positive z indicates redshift (receding source). The recessional velocity (v) of the source can be approximated by: v = z × c, where c is the speed of light (3.0 × 10^8 m/s), valid for relatively low velocities compared to c.

• Redshift formula: z = (λ_observed - λ_emitted) / λ_emitted.
• Recessional velocity: v = z × c (for v << c).
• Units: wavelength in metres (m), velocity in metres per second (m/s).

Observations show that light from distant galaxies is redshifted, indicating they are moving away from Earth. The greater the redshift, the faster the galaxy is receding.

This supports the theory that the Universe is expanding uniformly in all directions, consistent with the Big Bang model.

Redshift measurements allow astronomers to estimate the speed and distance of galaxies, providing insight into the structure and evolution of the Universe.

• Redshift confirms galaxies recede from Earth.
• Supports expanding Universe theory.
• Used to calculate galaxy velocities and distances.

To draw a ray diagram illustrating redshift: start with a source emitting waves of a certain wavelength (λ_emitted) represented by evenly spaced wavefronts.

Show the source moving away from an observer to the right. The wavefronts reaching the observer are spaced further apart (λ_observed > λ_emitted).

Label the wavelengths and indicate the direction of motion and observation.

• Draw wavefronts emitted at equal intervals.
• Show source moving away from observer.
• Observed wavelength longer than emitted wavelength.

Light is an electromagnetic wave characterised by its wavelength (λ) and frequency (f). The wavelength is the distance between successive peaks of the wave and is measured in metres (m). Visible light has wavelengths roughly between 400 nm (violet) and 700 nm (red).

When light from a source is observed, its wavelength can be measured using instruments such as spectrometers. The colour of the light depends on its wavelength: longer wavelengths correspond to redder light, shorter wavelengths to bluer light.

• Wavelength (λ) is measured in metres (m).
• Visible light ranges approximately from 400 nm (violet) to 700 nm (red).

Redshift is the phenomenon where the observed wavelength of light from an object is longer (shifted towards the red end of the spectrum) than the wavelength emitted by the source. This means the light waves are stretched, increasing their wavelength.

Mathematically, redshift (z) is defined as: z = (λ_observed - λ_emitted) / λ_emitted where λ_observed is the wavelength measured on Earth and λ_emitted is the original wavelength emitted by the source.

A positive redshift (z > 0) indicates that the observed wavelength is longer than the emitted wavelength.

• Redshift means an increase in wavelength of light.
• Redshift formula: z = (λ_observed - λ_emitted) / λ_emitted
• Positive z indicates wavelength stretching.

Distant galaxies are moving away from Earth due to the expansion of the Universe. As they recede, the light waves they emit are stretched, increasing their wavelength and causing redshift.

This effect is similar to the Doppler effect for sound, where the frequency of sound waves changes if the source moves relative to the observer.

The greater the speed at which a galaxy moves away, the larger the redshift observed in its light.

• Redshift is caused by galaxies moving away from Earth.
• Light waves are stretched, increasing wavelength.
• Redshift is analogous to the Doppler effect for sound.

Astronomers observe that light from distant galaxies is redshifted compared to light from nearby sources. This observation supports the conclusion that the Universe is expanding.

Redshift measurements allow astronomers to estimate the speed at which galaxies recede from Earth.

The redshift of light from distant galaxies is a fundamental piece of evidence for the Big Bang theory and the expanding Universe model.

• Distant galaxies show redshifted light.
• Redshift indicates galaxies receding from Earth.
• Supports the expanding Universe theory.

To draw a simple diagram illustrating redshift: 1. Draw a horizontal line representing the electromagnetic spectrum with labelled ends: 'Blue (short wavelength)' on the left and 'Red (long wavelength)' on the right. 2. Mark a point labelled 'λ_emitted' near the blue end to represent the original wavelength emitted by a galaxy. 3. Mark a point labelled 'λ_observed' further to the right (towards red) to represent the observed wavelength on Earth. 4. Draw an arrow from 'λ_emitted' to 'λ_observed' showing the increase in wavelength. 5. Label the arrow 'Redshift: wavelength increase due to galaxy recession'.

• Draw spectrum line with blue and red ends.
• Mark emitted and observed wavelengths showing increase.
• Label arrow indicating redshift due to galaxy moving away.

Redshift is the increase in the wavelength of electromagnetic radiation, such as visible light, observed from an object moving away from the observer. In astronomy, redshift is observed when light from distant galaxies shifts towards the red (longer wavelength) end of the visible spectrum.

This effect is explained by the Doppler effect for light: when a light source moves away from an observer, the wavelengths of emitted light are stretched, increasing their wavelength and shifting the light towards red.

The redshift (z) can be quantified by the formula: z = (λ_observed - λ_emitted) / λ_emitted, where λ_observed is the wavelength measured on Earth and λ_emitted is the wavelength emitted by the source.

• Redshift means light wavelength increases (shifts to red).
• Caused by galaxies moving away (Doppler effect).
• z = (λ_observed - λ_emitted) / λ_emitted quantifies redshift.

Astronomers observe that light from distant galaxies is redshifted compared to light from nearby stars or galaxies. The greater the distance to a galaxy, the larger the redshift observed.

This implies that distant galaxies are receding from Earth at higher speeds. The redshift is measured by comparing known spectral lines (such as hydrogen emission lines) from the galaxy with their wavelengths measured on Earth.

The velocity (v) at which a galaxy recedes can be approximated by v = z × c, where c is the speed of light (approximately 3.0 × 10^8 m/s), valid for small redshifts.

• Distant galaxies show larger redshifts than nearby ones.
• Redshift measured by comparing spectral lines.
• Recession velocity v ≈ z × c for small z.

The observation that all distant galaxies are moving away from Earth, with velocity proportional to their distance, indicates that the Universe itself is expanding uniformly in all directions.

This expansion means that space itself is stretching, causing the wavelengths of light traveling through space to increase, resulting in redshift.

The linear relationship between recession velocity and distance is expressed by Hubble's Law: v = H₀ × d, where H₀ is the Hubble constant, v is the recession velocity, and d is the distance to the galaxy.

• All distant galaxies recede, showing Universe expansion.
• Space expansion stretches light wavelengths, causing redshift.
• Hubble's Law: v = H₀ × d relates velocity and distance.

The expanding Universe supports the Big Bang Theory, which proposes that the Universe began from a hot, dense initial state and has been expanding ever since.

Redshift observations provide empirical evidence for this expansion, consistent with predictions of the Big Bang model.

The Big Bang Theory explains the observed redshift as a consequence of the Universe's expansion, rather than galaxies moving through static space.

• Expansion evidence supports Big Bang Theory.
• Big Bang describes Universe origin as expansion from dense state.
• Redshift matches predictions of expanding Universe model.

To draw a diagram illustrating redshift and Universe expansion:

1. Draw a horizontal axis labelled 'Distance from Earth (light years)'.

2. Draw a vertical axis labelled 'Recession velocity (km/s)'. Mark origin at zero for both axes. 3. Plot points showing increasing velocity with increasing distance, forming a straight line through the origin, representing Hubble's Law. 4. Indicate a galaxy at a certain distance with a spectral line shifted towards red compared to a reference line at Earth. 5. Label the redshifted wavelength and the emitted wavelength to show the increase in wavelength.

• Axes: Distance (light years) vs Recession velocity (km/s).
• Straight line graph through origin shows v ∝ d (Hubble's Law).
• Spectral lines illustrate redshift (longer wavelength).

Cosmic Microwave Background Radiation (CMBR) is electromagnetic radiation that fills the Universe and is detected in every direction in space. It is a form of microwave radiation with a very specific frequency range, corresponding to a temperature of approximately 2.7 kelvin (K).

CMBR is the remnant thermal radiation left over from the early stages of the Universe, shortly after the Big Bang. It is essentially the cooled and stretched radiation from the hot, dense state of the Universe about 380,000 years after the Big Bang, when the Universe became transparent to radiation.

• CMBR is microwave radiation with a blackbody spectrum at about 2.7 K.
• It has a peak frequency near 160.2 GHz (wavelength ~1.9 mm).
• It is uniform and isotropic, meaning it is detected equally in all directions.

CMBR is detected using sensitive microwave receivers on satellites, balloons, and ground-based telescopes. Instruments measure the intensity of microwave radiation across different frequencies to map the CMBR spectrum.

The radiation is observed as a nearly perfect blackbody spectrum, confirming its thermal origin. The uniformity of the CMBR across the sky supports the idea that it comes from the early Universe.

The frequency of CMBR lies in the microwave region of the electromagnetic spectrum, typically from about 30 GHz to 300 GHz.

• Detection requires microwave antennas and radiometers.
• Measurements confirm a blackbody spectrum at 2.7 K.
• CMBR frequency corresponds to microwaves (~160 GHz peak).

Shortly after the Big Bang, the Universe was extremely hot and dense, filled with a plasma of photons, electrons, and protons. Photons were constantly scattered by free electrons, making the Universe opaque.

As the Universe expanded and cooled, it reached a temperature where electrons and protons combined to form neutral hydrogen atoms (recombination). At this point, photons decoupled from matter and began to travel freely through space.

These photons have been travelling ever since, their wavelengths stretched by the expansion of the Universe, shifting their radiation into the microwave region observed today as CMBR.

• CMBR originates from the recombination era (~380,000 years after Big Bang).
• Photons decoupled from matter and have been travelling freely since.
• Expansion of the Universe stretched photon wavelengths into microwaves.

CMBR provides strong evidence supporting the Big Bang theory, as it matches predictions of radiation left over from the early hot Universe.

Its uniformity and spectrum help scientists understand the conditions of the early Universe and the subsequent expansion and evolution of cosmic structures.

Small fluctuations in the CMBR intensity correspond to the seeds of galaxies and large-scale structures observed today.

• CMBR confirms the Universe began in a hot, dense state.
• Its uniformity supports the cosmological principle (homogeneity and isotropy).
• Fluctuations in CMBR relate to formation of galaxies and clusters.

The Cosmic Microwave Background Radiation (CMBR) is the residual thermal radiation left over from the early stages of the Universe, specifically from the time shortly after the Big Bang, approximately 380,000 years after the Universe began.

At this early time, the Universe was extremely hot and dense, filled with a plasma of photons, electrons, and protons. Photons were constantly scattered by free electrons, making the Universe opaque to radiation.

As the Universe expanded and cooled, it reached a temperature (~3000 K) at which electrons and protons combined to form neutral hydrogen atoms, a process called recombination. This made the Universe transparent to radiation, allowing photons to travel freely through space. These photons constitute the CMBR.

• CMBR formed about 380,000 years after the Big Bang.
• Originated when the Universe became transparent to radiation (recombination).
• Represents the oldest electromagnetic radiation detectable.

The Universe has been expanding since the Big Bang, causing the space between galaxies to increase over time.

As space expands, the wavelength of the CMBR photons stretches, increasing their wavelength and decreasing their frequency and energy. This phenomenon is known as cosmological redshift.

Originally, the CMBR was in the visible or infrared region of the electromagnetic spectrum at a temperature of about 3000 K. Due to expansion, its temperature has cooled to approximately 2.7 K, corresponding to microwave wavelengths (~1 mm).

• Expansion stretches photon wavelengths (redshift).
• CMBR wavelength shifted from visible/infrared to microwave region.
• Current CMBR temperature is about 2.7 K.

The electromagnetic spectrum ranges from gamma rays (short wavelength, high frequency) to radio waves (long wavelength, low frequency).

The CMBR is now observed in the microwave region, with wavelengths roughly between 1 mm and 1 cm.

This shift from higher-energy radiation to microwaves is direct evidence of the Universe's expansion since the Big Bang.

• Microwaves have longer wavelengths than visible light.
• CMBR peak wavelength corresponds to a blackbody spectrum at 2.7 K.
• The shift in wavelength is due to the Doppler effect caused by cosmic expansion.

The CMBR provides a snapshot of the early Universe and is a cornerstone of the Big Bang theory.

Its uniformity across the sky supports the idea that the Universe began in a hot, dense state and has been expanding and cooling ever since.

Measurements of the CMBR's temperature fluctuations give information about the Universe's composition, age, and development.

• CMBR is strong evidence for the Big Bang theory.
• Uniformity indicates a homogeneous early Universe.
• Temperature fluctuations inform cosmological models.

Redshift occurs when light waves emitted by a source are stretched to longer wavelengths as the source moves away from an observer. This is analogous to the Doppler effect for sound but applies to electromagnetic waves such as visible light.

When a galaxy moves away from Earth, the wavelengths of the light it emits are increased, shifting the light towards the red end of the visible spectrum. This shift is called redshift.

The amount of redshift is directly related to the speed at which the galaxy is receding from Earth. The faster the galaxy moves away, the greater the increase in wavelength observed.

• Redshift means an increase in wavelength (λ) of light.
• It is caused by the relative motion of the galaxy moving away from Earth.

The speed of a receding galaxy can be calculated using the formula derived from the Doppler effect for light:

\[ v = c \times \frac{\Delta \lambda}{\lambda_0} \]

where: \( v \) is the speed of the galaxy (in metres per second, m/s), \( c \) is the speed of light in vacuum (approximately \( 3.0 \times 10^8 \, \text{m/s} \)), \( \Delta \lambda = \lambda_{observed} - \lambda_0 \) is the change in wavelength (in metres, m), and \( \lambda_0 \) is the original (rest) wavelength of the light emitted by the galaxy (in metres, m).

• \( v \) = speed of galaxy (m/s)
• \( c \) = speed of light (\( 3.0 \times 10^8 \, \text{m/s} \))
• \( \Delta \lambda \) = observed wavelength minus original wavelength (m)

Suppose the original wavelength of a spectral line emitted by a star in a galaxy is \( 500 \text{ nm} \) (nanometres), but the observed wavelength on Earth is \( 505 \text{ nm} \). Calculate the speed at which the galaxy is receding.

Step 1: Calculate the change in wavelength: \( \Delta \lambda = 505 \text{ nm} - 500 \text{ nm} = 5 \text{ nm} \).

Step 2: Convert nanometres to metres: \( 1 \text{ nm} = 1 \times 10^{-9} \text{ m} \), so \( \Delta \lambda = 5 \times 10^{-9} \text{ m} \), \( \lambda_0 = 500 \times 10^{-9} \text{ m} \). Step 3: Substitute values into the formula: \[ v = 3.0 \times 10^8 \times \frac{5 \times 10^{-9}}{500 \times 10^{-9}} = 3.0 \times 10^8 \times 0.01 = 3.0 \times 10^6 \, \text{m/s} \] Step 4: Express the answer in km/s: \[ 3.0 \times 10^6 \, \text{m/s} = 3000 \text{ km/s} \] Therefore, the galaxy is receding at 3000 km/s.

• Calculate \( \Delta \lambda = \lambda_{observed} - \lambda_0 \)
• Convert wavelengths to metres
• Substitute into \( v = c \times \frac{\Delta \lambda}{\lambda_0} \)

Wavelengths must be in consistent units, typically metres, before substitution into the formula.

Speed of light \( c \) is always \( 3.0 \times 10^8 \, \text{m/s} \).

A common error is to forget to convert nanometres (nm) to metres (m), leading to incorrect speed values that are too large by a factor of \( 10^9 \). Another mistake is to use the observed wavelength as the original wavelength or vice versa, reversing the sign of \( \Delta \lambda \).

• Always convert wavelengths to metres before calculation.
• Use \( c = 3.0 \times 10^8 \, \text{m/s} \).

To draw a simple diagram illustrating redshift: 1. Draw a horizontal arrow pointing right labelled 'Galaxy moving away from Earth'. 2. Draw a wave representing light emitted from the galaxy with wavelength \( \lambda_0 \) near the galaxy. 3. Draw the same wave near Earth but stretched to a longer wavelength \( \lambda_{observed} \). 4. Label the increase in wavelength as \( \Delta \lambda \). 5. Indicate that the shift towards longer wavelengths corresponds to redshift.

• Arrow showing galaxy receding from Earth
• Wave with original wavelength near galaxy

A supernova is a powerful and luminous explosion of a star, often outshining an entire galaxy for a short period. Certain types of supernovae, especially Type Ia, have a consistent intrinsic brightness (absolute magnitude). Because their absolute brightness is known, they serve as 'standard candles' in astronomy, meaning their observed brightness can be used to determine their distance from Earth.

• Supernovae are extremely bright stellar explosions.
• Type Ia supernovae have a known, consistent absolute brightness.
• They can be observed in distant galaxies, providing a reference point for distance measurement.

Brightness is the amount of light energy received per unit area per second, measured in watts per square metre (W/m²). Absolute brightness (or luminosity) is the total energy emitted by the supernova per second, measured in watts (W). Apparent brightness is how bright the supernova appears from Earth.

The inverse square law states that apparent brightness decreases with the square of the distance from the source. Mathematically:

\[ \text{Apparent Brightness} = \frac{\text{Absolute Brightness}}{4 \pi d^2} \] where \( d \) is the distance to the supernova in metres.

• Brightness is energy per unit area per second (W/m²).
• Absolute brightness is total emitted power (W).
• Apparent brightness decreases as distance squared increases.
• Inverse square law formula relates brightness and distance.

Rearranging the inverse square law to find distance:

\[ d = \sqrt{\frac{\text{Absolute Brightness}}{4 \pi \times \text{Apparent Brightness}}} \]

By measuring the apparent brightness of the supernova from Earth and knowing its absolute brightness, astronomers calculate the distance to the supernova and thus to its host galaxy.

• Measure apparent brightness using telescopes.
• Use known absolute brightness of the supernova type.
• Calculate distance using the rearranged inverse square law.
• Distance units are typically in metres or light-years (1 light-year ≈ 9.46 × 10¹⁵ m).

Suppose a Type Ia supernova has an absolute brightness of \( 3.0 \times 10^{36} \) W. If its apparent brightness measured on Earth is \( 1.0 \times 10^{-14} \) W/m², calculate the distance to the supernova.

Using the formula: \[ d = \sqrt{\frac{3.0 \times 10^{36}}{4 \pi \times 1.0 \times 10^{-14}}} \]

Calculate denominator: \( 4 \pi \times 1.0 \times 10^{-14} = 1.26 \times 10^{-13} \) W/m². Then: \[ d = \sqrt{\frac{3.0 \times 10^{36}}{1.26 \times 10^{-13}}} = \sqrt{2.38 \times 10^{49}} = 4.88 \times 10^{24} \text{ m} \] This distance is approximately 515 million light-years.

• Use correct units for brightness and distance.
• Calculate denominator carefully including \( 4 \pi \).
• Take square root of the quotient.
• Convert metres to light-years if needed.

Measuring supernova brightness requires sensitive telescopes and detectors. Dust and gas between galaxies can absorb or scatter light, affecting apparent brightness and causing uncertainty. Calibration of absolute brightness is based on nearby supernovae with independently known distances.

Despite limitations, supernovae provide one of the most reliable methods for measuring cosmic distances beyond the reach of parallax or Cepheid variables.

• Use calibrated instruments for brightness measurement.
• Account for interstellar absorption and redshift effects.
• Repeat observations to reduce uncertainty.
• Combine with other distance measurement methods for accuracy.

The Hubble constant, denoted as H₀ (H-naught), is a fundamental parameter in cosmology that describes the rate at which the universe is expanding.

It is defined as the ratio of the recession velocity (v) of a galaxy to its distance (d) from Earth:

The equation is expressed as v = H₀d, where: v is the velocity at which the galaxy is moving away from Earth (in metres per second, m/s), d is the distance to the galaxy (in metres, m), and H₀ is the Hubble constant (in reciprocal seconds, s⁻¹).

• Hubble constant (H₀) = velocity (v) / distance (d)
• Units of H₀ are s⁻¹ (e.g., m/s per m)
• v = H₀ × d relates galaxy speed and distance

The Hubble constant represents how fast galaxies recede per unit distance due to the expansion of space itself.

For example, if H₀ = 2.2 × 10⁻¹⁸ s⁻¹, a galaxy 1 × 10²⁴ m away would recede at v = H₀ × d = 2.2 × 10⁻¹⁸ × 1 × 10²⁴ = 2.2 × 10⁶ m/s.

The units of H₀ can be understood as velocity divided by distance, resulting in s⁻¹. It is often expressed in kilometres per second per megaparsec (km/s/Mpc) in astronomy, but SI units are preferred for calculations.

• H₀ units: s⁻¹ (e.g., m/s per m)
• Typical value: approximately 2.2 × 10⁻¹⁸ s⁻¹
• Velocity increases linearly with distance

The equation v = H₀d can be rearranged to find either velocity or distance:

To find velocity: v = H₀ × d, where d is known; to find distance: d = v / H₀, where v is known.

Example calculation: Calculate the recession velocity of a galaxy 5 × 10²³ m away, given H₀ = 2.2 × 10⁻¹⁸ s⁻¹: v = 2.2 × 10⁻¹⁸ × 5 × 10²³ = 1.1 × 10⁶ m/s (1,100,000 m/s).

• Rearrangement: d = v / H₀
• Substitute values carefully with correct units
• Check units to ensure velocity in m/s and distance in m

The Hubble constant provides evidence that the universe is expanding, as more distant galaxies move away faster.

It allows astronomers to estimate the age of the universe by taking the reciprocal of H₀, giving an approximate time since all matter was concentrated at a single point.

For example, age ≈ 1 / H₀ = 1 / (2.2 × 10⁻¹⁸ s⁻¹) ≈ 4.5 × 10¹⁷ s, which is about 14 billion years.

• Expansion rate of universe quantified by H₀
• Age of universe estimated as 1 / H₀
• Supports Big Bang theory

Draw a graph with distance (d) on the horizontal axis (in metres or megaparsecs) and velocity (v) on the vertical axis (in m/s or km/s).

Plot points for several galaxies showing their recession velocities versus distances.

The graph should be a straight line passing through the origin, with gradient equal to the Hubble constant H₀.

• X-axis: Distance (m or Mpc)
• Y-axis: Velocity (m/s or km/s)
• Gradient = H₀
• Straight line through origin

The Hubble constant, denoted as H₀, is a fundamental parameter in cosmology that measures the rate at which the Universe is expanding.

It is defined as the ratio of the recessional velocity (v) of a galaxy to its distance (d) from Earth: v = H₀ × d.

Here, v is measured in metres per second (m/s), d in metres (m), and H₀ has units of reciprocal seconds (s⁻¹). This means H₀ represents the fractional increase in distance per unit time, indicating how fast galaxies move away from each other due to cosmic expansion.

• Hubble constant (H₀) units: s⁻¹ (inverse seconds).
• Equation: v = H₀ × d, where v is recessional velocity (m/s), d is distance (m).
• H₀ quantifies the expansion rate of the Universe.

The current syllabus estimate for the Hubble constant is H₀ ≈ 2.2 × 10⁻¹⁸ s⁻¹.

This value is derived from astronomical observations of distant galaxies and their redshifts, which indicate how fast they are moving away from Earth.

The small magnitude of H₀ reflects the vast scale and slow expansion rate when expressed per second.

• H₀ ≈ 2.2 × 10⁻¹⁸ s⁻¹ (syllabus estimate).
• Determined from redshift measurements and galaxy distances.
• Represents the Universe's expansion rate at the present epoch.

The age of the Universe can be estimated by taking the reciprocal of the Hubble constant: Age ≈ 1/H₀.

This approximation assumes a constant expansion rate over time and that all matter was once concentrated at a single point (the Big Bang).

Using the syllabus value, Age ≈ 1 / (2.2 × 10⁻¹⁸ s⁻¹) ≈ 4.55 × 10¹⁷ seconds, which converts to about 14.4 billion years (using 1 year ≈ 3.15 × 10⁷ seconds).

• Age of Universe ≈ 1 / H₀.
• Calculation: 1 / (2.2 × 10⁻¹⁸ s⁻¹) = 4.55 × 10¹⁷ s.
• Convert seconds to years: 4.55 × 10¹⁷ s ÷ 3.15 × 10⁷ s/year ≈ 14.4 billion years.

Given a galaxy at a distance d = 1.0 × 10²⁴ m, calculate its recessional velocity using H₀ = 2.2 × 10⁻¹⁸ s⁻¹.

Formula: v = H₀ × d = (2.2 × 10⁻¹⁸ s⁻¹) × (1.0 × 10²⁴ m) = 2.2 × 10⁶ m/s.

Therefore, the galaxy is moving away at 2.2 million metres per second (about 2200 km/s).

• Formula: v = H₀ × d.
• Substitution: v = 2.2 × 10⁻¹⁸ × 1.0 × 10²⁴ = 2.2 × 10⁶ m/s.
• Answer: 2.2 × 10⁶ m/s (2200 km/s).
• Common error: forgetting to convert units or misplacing powers of ten.

The Hubble constant shows that the Universe is expanding uniformly, with more distant galaxies receding faster.

This supports the Big Bang theory, which states that the Universe began from a very dense, hot state and has been expanding ever since.

The value of H₀ is crucial for cosmology, affecting estimates of the Universe's size, age, and fate.

• Hubble's law: velocity proportional to distance.
• Supports the expanding Universe model.
• H₀ helps estimate Universe's age and expansion history.

The Hubble constant, denoted as H₀, is a measure of the rate at which the Universe is expanding. It is defined by the equation v = H₀d, where v is the recessional velocity of a galaxy moving away from Earth, and d is its distance from Earth.

The units of H₀ are typically given in s⁻¹ (per second) when expressed in SI units, or in km/s per megaparsec (km/s/Mpc) in astronomy. For physics calculations, the SI unit s⁻¹ is preferred.

The current estimate for the Hubble constant is approximately 2.2 × 10⁻¹⁸ s⁻¹. This means that for every second, the recessional velocity of galaxies increases proportionally to their distance by this factor.

• Hubble constant (H₀) relates velocity and distance: v = H₀d
• Units of H₀ in SI: s⁻¹
• Current estimate: H₀ ≈ 2.2 × 10⁻¹⁸ s⁻¹

The age of the Universe (t) can be estimated by taking the reciprocal of the Hubble constant: t ≈ 1/H₀.

This estimation assumes that the Universe has been expanding at a constant rate since the Big Bang, which is a simplification but provides a useful approximation.

Since H₀ has units of s⁻¹, its reciprocal has units of seconds, giving an estimate of the Universe's age in seconds, which can be converted into years for practical understanding.

• Age of Universe t ≈ 1/H₀
• Assumes constant expansion rate
• Units: seconds (convert to years)

Given H₀ = 2.2 × 10⁻¹⁸ s⁻¹, calculate the age of the Universe.

Formula: t = 1/H₀ = 1 / (2.2 × 10⁻¹⁸ s⁻¹) = 4.55 × 10¹⁷ s.

Convert seconds to years: 1 year ≈ 3.15 × 10⁷ s, so t = (4.55 × 10¹⁷ s) / (3.15 × 10⁷ s/year) ≈ 1.44 × 10¹⁰ years, or approximately 14.4 billion years, consistent with current scientific estimates.

• t = 1 / H₀ = 4.55 × 10¹⁷ s
• Convert to years: t ≈ 14.4 billion years
• Calculation assumes constant expansion

The estimation t ≈ 1/H₀ assumes a constant rate of expansion, which is an oversimplification because the expansion rate has changed over time due to gravitational effects and dark energy.

More accurate models use cosmological parameters and observations to refine the age estimate.

Despite simplifications, this method provides a useful order-of-magnitude estimate for the Universe's age.

• Assumes constant expansion rate
• Does not account for acceleration or deceleration
• Useful for approximate age estimation

To visualise the Hubble constant, draw a graph with distance (d) on the x-axis (units: metres or megaparsecs) and recessional velocity (v) on the y-axis (units: m/s or km/s).

Plot points representing galaxies at various distances and their measured velocities.

The graph should be a straight line passing through the origin, with gradient equal to H₀, illustrating the linear relationship v = H₀d.

• x-axis: Distance (m or Mpc)
• y-axis: Velocity (m/s or km/s)
• Gradient = H₀ (rate of expansion)