Unit 5: Astrophysics and Cosmology

This guide covers sub-topic 5.6 Astrophysics and Cosmology, the fourth and final sub-topic in Unit 5: Thermodynamics, Radiation, Oscillations and Cosmology, completing the content of the Pearson Edexcel International Advanced Level in Physics (YPH11), Issue 3 specification.

Before studying this

This topic follows sub-topics 5.3-5.5, and draws on Unit 4’s electric field content (sub-topic 4.4) for comparison with gravitational fields, and on Unit 2’s wave content (sub-topic 2.3) for the underlying concepts of frequency, wavelength and wave speed — the Doppler effect itself is new material, introduced here in sub-topic 5.6.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 5.6

Candidates will be assessed on their ability to: understand that a gravitational field (force field) is defined as a region where a mass experiences a force; understand that gravitational field strength is defined as g = F/m; use the equation F = Gm₁m₂/r² (Newton’s law of universal gravitation); derive and use the equation g = Gm/r² for the gravitational field due to a point mass; use the equation Vgrav = −Gm/r for a radial gravitational field; compare electric fields with gravitational fields; apply Newton’s laws of motion and universal gravitation to orbital motion; understand what is meant by a black body radiator and interpret radiation curves for such a radiator; use the Stefan-Boltzmann law equation L = σAT⁴ for black body radiators; use Wien’s law equation λmaxT = 2.898 × 10⁻³ m K for black body radiators; use the equation intensity I = L/4πd², where L is luminosity and d is distance from the source; understand how astronomical distances can be determined using trigonometric parallax; understand how astronomical distances can be determined using measurements of intensity received from standard candles (objects of known luminosity); sketch and interpret a simple Hertzsprung-Russell diagram that relates stellar luminosity to surface temperature; understand how to relate the Hertzsprung-Russell diagram to the life cycle of stars; understand how the movement of a source of waves relative to an observer/detector gives rise to a shift in frequency (Doppler effect); use the equations for redshift, z ≈ Δf/f ≈ Δλ/λ ≈ v/c for a source of electromagnetic radiation moving relative to an observer, and v = H₀d for objects at cosmological distances; and understand the controversy over the age and ultimate fate of the universe associated with the value of the Hubble constant and the possible existence of dark matter.

Gravitational fields

A gravitational field is a region where a mass experiences a force. Gravitational field strength is g = F/m. Newton’s law of universal gravitation gives the force between two point masses:

F = Gm1 m2 / r²

and the field due to a single point mass is g = Gm/r². The gravitational potential in a radial field is Vgrav = −Gm/r (negative, since gravitational potential energy increases towards zero as distance from the mass increases towards infinity). Gravitational fields are structurally similar to electric fields — both follow an inverse-square law and both have radial and uniform forms — but gravitational forces are always attractive, while electric forces can be attractive or repulsive. Newton’s laws of motion combined with universal gravitation are applied to orbital motion, for example deriving orbital speed or period for a satellite in circular orbit.

Black body radiation and standard candles

A black body radiator absorbs and re-emits all radiation incident on it; its emission spectrum (radiation curve) depends only on its temperature. The Stefan-Boltzmann law gives total power radiated:

L = σAT⁴

Wien’s law gives the wavelength of peak emission:

λmax T = 2.898 × 10⁻³ m K

The intensity of radiation received at distance d from a source of luminosity L is:

I = L / 4πd²

Astronomical distances can be measured using trigonometric parallax (the apparent shift in a nearby star’s position against distant background stars, as Earth orbits the Sun, for relatively close stars) or using standard candles — objects of known luminosity, such as certain supernovae — where measured intensity and known luminosity give distance via the inverse-square relationship above.

The Hertzsprung-Russell diagram and stellar life cycles

The Hertzsprung-Russell diagram plots stellar luminosity against surface temperature, revealing patterns such as the main sequence, red giants and white dwarfs. This diagram can be related to the life cycle of stars — a star’s position on the diagram, and how it moves across it over time, reflects its stage of nuclear fusion and eventual fate (depending on initial mass, this may include red giant, white dwarf, supernova, neutron star or black hole stages).

Redshift and cosmology

The Doppler effect describes the shift in observed frequency (or wavelength) of waves caused by relative motion between source and observer. For light from receding astronomical sources, this produces redshift z:

z ≈ Δf/f ≈ Δλ/λ ≈ v/c

At cosmological distances, recession velocity relates to distance via Hubble’s law:

v = H0 d

where H₀ is the Hubble constant. There is ongoing scientific controversy over the precise value of the Hubble constant, and what this implies for the age and ultimate fate of the universe, connected to the possible existence of dark matter (unseen mass inferred from its gravitational effects on visible matter and radiation).

Worked example. A star has a surface temperature of 5800 K. Find the wavelength at which it emits most strongly, using Wien’s law.

λmax = (2.898 × 10⁻³) / T = (2.898 × 10⁻³) / 5800 = 5.00 × 10⁻⁷ m (500 nm — in the visible spectrum, consistent with a Sun-like star).

Common mistakes

Confusing gravitational potential (always negative, Vgrav = −Gm/r) with gravitational field strength (g = Gm/r², always positive in magnitude). Forgetting that redshift z is dimensionless (a ratio), not a wavelength or frequency itself. Assuming Hubble’s law applies at all distances — it specifically describes the relationship for objects at cosmological distances, where recession dominates local gravitational effects. Misreading a Hertzsprung-Russell diagram’s axes — luminosity typically increases upward and temperature typically decreases left-to-right (the reverse of a conventional numerical axis).

Quick revision checklist

• Use g = F/m, F = Gm1m2/r², g = Gm/r², and Vgrav = −Gm/r.
• Compare gravitational and electric fields, and apply Newton’s laws to orbital motion.
• Define a black body radiator and use L = σAT⁴ and λmaxT = 2.898×10⁻³ m K.
• Use I = L/4πd² and describe how parallax and standard candles determine astronomical distance.
• Sketch and interpret a Hertzsprung-Russell diagram, and relate it to stellar life cycles.
• Explain the Doppler effect and use z ≈ Δf/f ≈ Δλ/λ ≈ v/c and v = H0d.
• Describe the Hubble constant controversy and its link to the age/fate of the universe and dark matter.

Related resources

• Unit 5: Oscillations — the previous sub-topic
• Unit 4: Electric and Magnetic Fields — compare electric and gravitational fields
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.