eduKate Learning Manual · Astronomy × Cosmology × Physics · Secondary → JC · Measure Distance → Measure Redshift → Find Relation → Infer Expansion
Wait, What? The Farther Away a Galaxy Is, the Faster It Usually Recedes — Without Earth Being the Centre
Look across the large-scale Universe and a striking pattern appears: sufficiently distant galaxies tend to have larger cosmological redshifts. In the nearby Hubble-flow regime, recession speed is approximately proportional to distance.
At first this sounds as though galaxies were blasted outward from one location and we happen to sit near the middle. That is the wrong picture.
The deeper model is that the scale of space between gravitationally unbound galaxies changes with cosmic time. If space expands uniformly, every sufficiently separated observer can see distant galaxies receding, with greater separation accumulating a larger recession rate.
Measure galaxy distance → measure spectral redshift → compare many galaxies → larger distances show larger recession → infer a changing cosmic scale factor → local linear approximation becomes v ≈ H₀d.
The Big Question
How can every distant galaxy appear to recede from us without placing us at the centre of the Universe?
Quick Answer
On sufficiently large scales, the Universe is well described as homogeneous and isotropic. Distances between comoving locations grow with a cosmic scale factor a(t). The recession rate between nearby comoving galaxies is approximately:
v = H(t)d
At the present epoch, H(t) is H₀, the Hubble constant. This does not describe every galaxy’s local motion and is not a universal special-relativistic velocity formula for arbitrarily large redshift. It is the low-redshift expression of cosmological expansion.
What You Will Learn
- what astronomers actually measure when they say a galaxy is redshifted
- how distance is measured independently of redshift
- why v ≈ H₀d is a local cosmological relation
- why expansion has no ordinary centre inside space
- how peculiar velocity creates scatter for nearby galaxies
- why cosmological redshift is deeper than a simple Doppler shift
- how the cosmic distance ladder works
- why H₀ is measured in km s⁻¹ Mpc⁻¹
- what the current Hubble-tension problem is — and what it does not yet prove
- how the law connects to the age and history of the Universe
Part 1 — Redshift Is a Measured Change in Wavelength
A galaxy spectrum contains absorption and emission features whose laboratory wavelengths are known. If a spectral line emitted at wavelength λemit is observed at λobs, redshift is:
z = (λobs − λemit)/λemit
Equivalently:
1 + z = λobs/λemit
Positive z means the observed wavelength is longer. NASA describes distant-galaxy light as being cosmologically redshifted as the Universe expands.
Part 2 — For Small Redshift, Redshift Behaves Like a Recession Speed
At sufficiently small z:
v ≈ cz
This lets astronomers plot approximate recession velocity against independently measured galaxy distance.
At large redshift, however, converting z into “velocity” requires a cosmological model. The simple cz relation eventually fails, and recession speeds defined from cosmic expansion need not behave like ordinary local velocities in special relativity.
Part 3 — The Hubble–Lemaître Relation
In the nearby smooth Hubble flow:
v ≈ H₀d
where:
- v = recession speed in the low-redshift approximation;
- d = distance;
- H₀ = present-day Hubble expansion rate.
The usual unit for H₀ is kilometres per second per megaparsec, km s⁻¹ Mpc⁻¹. This says how much additional recession rate appears for each megaparsec of separation in the local Hubble flow.
A Quantitative Window
If we use H₀ = 70 km s⁻¹ Mpc⁻¹ as a convenient illustrative value, a galaxy at 100 Mpc has:
v ≈ (70)(100) = 7000 km s⁻¹
A galaxy at 200 Mpc would have approximately 14,000 km s⁻¹ in the same low-redshift linear model.
The numerical value 70 is used here for reasoning, not as a declaration that the present Hubble constant is exactly known.
Part 4 — Why There Is No Ordinary Centre
Imagine points marked on an expanding grid. If every grid spacing grows by the same fraction, any point sees every other point move farther away. More distant points gain more new spacing between them per unit time, so their recession rate is larger.
No marked point on the grid must be the centre of the expansion.
The familiar balloon-surface analogy can help if used carefully: galaxies are represented by points on the two-dimensional surface, and as the surface stretches each point sees others recede. The centre of the three-dimensional balloon is not a place on the surface and therefore is not the cosmological centre in the analogy.
The analogy breaks if learners imagine galaxies physically embedded in rubber or the Universe expanding into pre-existing empty space. The mathematical lesson is uniform scale change, not balloon mechanics.
Part 5 — Derive Hubble Flow From the Scale Factor
Let a comoving coordinate separation be χ. Physical distance is:
d(t) = a(t)χ
Differentiate with respect to time:
ḋ = āχ
Since d = aχ:
ḋ = (ā/a)d
Define:
H(t) = ā/a
Then:
vrec = H(t)d
This shows why a linear distance–recession relation emerges naturally from uniform expansion.
Part 6 — Galaxies Also Have Peculiar Velocities
Galaxies do not merely ride the cosmic expansion. They also fall toward nearby masses and orbit within groups and clusters.
The observed radial velocity can be thought of approximately as:
vobs ≈ H₀d + vpec
where vpec is the galaxy’s local peculiar motion relative to the smooth Hubble flow.
For a nearby galaxy, a few hundred km s⁻¹ of peculiar motion can be a large fraction of H₀d. This is why local distance–redshift plots have scatter and why astronomers use sufficiently distant samples to measure H₀.
Part 7 — Not Everything Expands With the Universe
Solar systems, planets, people and many galaxies do not steadily expand with the Hubble flow. Local electromagnetic or gravitational binding dominates over the extremely weak expansion across such scales.
Even the Milky Way and Andromeda are moving toward each other because their mutual gravitational dynamics overcome the local Hubble recession.
Cosmic expansion is primarily a large-scale relation among sufficiently separated, gravitationally unbound structures.
Part 8 — How Do We Know the Distances?
Redshift alone cannot establish a distance–redshift law if redshift is also used to define the distance. The original scientific problem therefore requires independent distance measurements.
Modern measurements build a cosmic distance ladder:
- parallax: geometric calibration for nearby stars;
- Cepheid variables: pulsation period relates to intrinsic luminosity;
- Type Ia supernovae: calibrated luminous explosions extend the ladder to much greater distances.
NASA describes Hubble and Webb observations as cross-checking Cepheids and supernovae to strengthen the distance ladder.
The Historical Carrier — Slipher, Lemaître and Hubble
Vesto Slipher measured large spectral shifts of spiral nebulae before their true extragalactic distances were known. Georges Lemaître combined relativistic cosmology with available observations and in 1927 derived an expanding-universe relation between distance and recession. Edwin Hubble’s 1929 observational paper established a clearer empirical distance–velocity relation using galaxy distance estimates.
NASA’s historical account notes that Lemaître reached the expanding-universe interpretation before Hubble’s 1929 publication. The International Astronomical Union later recommended the name Hubble–Lemaître law to reflect that history.
The scientific lesson is distributed discovery: spectra, distances, theory and improved calibration were assembled across researchers rather than appearing fully formed in one observation.
Part 9 — Cosmological Redshift Is Not Just a Simple Doppler Shift
For nearby galaxies, the Doppler analogy works reasonably well. At cosmological distances, the deeper description is that the scale factor changes while light travels.
The relation between emitted and observed wavelength is:
1 + z = a(tobs)/a(temit)
The photon wavelength is stretched by the expansion history between emission and observation.
This is why simply inserting very large cosmological redshifts into the non-relativistic Doppler formula is wrong.
Part 10 — H₀ Is Present-Day Expansion, Not a Constant Through All Cosmic History
The notation can mislead. H₀ is called the Hubble constant because it is the present value of the Hubble parameter. The expansion rate H(t) changes over cosmic time as matter, radiation and dark energy affect the dynamics.
At earlier epochs the Hubble parameter was different. Cosmology therefore studies the full expansion history, not just one present-day number.
Part 11 — The Hubble Time
The inverse of H₀ has units of time. For H₀ ≈ 70 km s⁻¹ Mpc⁻¹:
1/H₀ ≈ 14 billion years
This Hubble time is close to the actual cosmic age but is not automatically equal to it. The age depends on how H(t) changed across history. A Universe that always expanded at the present rate would have one age; a Universe that decelerated and later accelerated has another.
Part 12 — The Current Hubble Tension
Different methods currently infer somewhat different present-day expansion rates.
NASA’s Hubble science summary describes late-Universe distance-ladder measurements in the broad region of roughly 70–76 km s⁻¹ Mpc⁻¹, while values inferred from early-Universe cosmic-microwave-background data within the standard cosmological model are around 67–68 km s⁻¹ Mpc⁻¹.
Hubble and Webb observations have strengthened confidence that simple Cepheid-crowding errors do not trivially erase the discrepancy. NASA’s 2025 Webb science review continued to list the Hubble tension among active cosmological puzzles.
But the correct scientific statement is:
The tension is evidence of a persistent measurement/model discrepancy. It is not yet proof of one specific new particle, field or theory of gravity.
RFE Stress Test — Expansion or Bad Distance Calibration?
A redshift–distance trend could be misleading if distances are systematically wrong. That is why modern work uses multiple independent or partially independent routes:
- parallax anchors;
- Cepheid variables;
- Type Ia supernovae;
- maser distances;
- gravitationally lensed time delays;
- standard-ruler methods such as baryon acoustic oscillations;
- cosmic microwave background fits.
Agreement across methods strengthens expansion evidence. Disagreement among precise methods becomes a new scientific problem rather than something to hide.
Observation vs Inference
Observation: galaxy spectra are redshifted, and independently estimated distances correlate with redshift.
Inference: large-scale recession increases with distance.
Cosmological inference: the relationship is naturally explained by a changing cosmic scale factor in an expanding Universe.
Common Misconceptions and How to Repair Them
- “The Big Bang exploded from one point into empty space.” Repair: standard cosmology describes expansion of spatial separations throughout the observable Universe.
- “Earth is at the centre because everything recedes from us.” Repair: homogeneous expansion produces the same large-scale relation for any comoving observer.
- “Every galaxy recedes.” Repair: local peculiar velocities can overwhelm Hubble flow; Andromeda approaches the Milky Way.
- “Redshift is always ordinary Doppler motion through static space.” Repair: cosmological redshift reflects scale-factor change over light travel time.
- “H₀ has always had the same value.” Repair: H₀ is today’s value; H(t) changes with cosmic epoch.
- “The Hubble tension proves new physics.” Repair: it is an unresolved discrepancy that may involve physics, modelling, calibration or combinations thereof.
Checkpoint Questions
- How is redshift defined?
- Why must galaxy distance be measured independently to establish the law?
- What does H₀ measure?
- Why can every observer see distant galaxies recede without being at a centre?
- What is peculiar velocity?
- Why is cz only a low-redshift approximation?
- What exactly is the Hubble tension?
Apply It — A Nearby Galaxy Breaks the Rule
A nearby galaxy is blueshifted. Does that falsify cosmic expansion?
No. Its local peculiar velocity can exceed H₀d at small d. The Hubble–Lemaître relation emerges statistically across sufficiently large separations where local gravitational motions become small relative to the expansion term.
Unfamiliar Transfer — Why More Distance Creates More Recession
Imagine two galaxies separated by one unit of cosmic grid and another pair separated by ten units. If every unit grows by 1% during a time interval, the first separation gains 0.01 unit while the second gains 0.10 unit. Same fractional expansion, ten times the absolute separation change.
This is the deep reason a uniform fractional scale change generates recession rate proportional to distance.
Answer Key
1. z = (λobs − λemit)/λemit. 2. Otherwise redshift would be used to prove a relation defined from redshift itself. 3. Present-day fractional expansion rate per distance scale. 4. Every comoving separation grows proportionally in a homogeneous expansion. 5. Local motion relative to smooth Hubble flow. 6. Large-z cosmology requires the scale-factor/metric model. 7. A persistent difference between late- and early-Universe determinations of present expansion under current models.
Can You Explain WHY?
Explain why v ≈ H₀d does not imply an explosion from Earth. A strong answer should connect scale factor → uniform fractional expansion → physical separation → derivative of distance → Hubble parameter → no preferred comoving centre → peculiar-velocity boundary.
Singapore Secondary and JC Science Bridge
Secondary Physics supplies waves, spectra, velocity and graphs. JC Physics adds relativity, gravitation and quantitative modelling. Hubble–Lemaître reasoning then demands an important scientific move: distinguish the data relationship from the cosmological model that explains it.
Deep Science Windows
- Friedmann equations: general relativity links H(t) to matter, radiation, curvature and dark energy.
- Cosmic acceleration: Type Ia supernovae revealed that late-time expansion is accelerating.
- Baryon acoustic oscillations: a standard ruler traces expansion across cosmic history.
- Cosmic microwave background: early-Universe structure constrains cosmological parameters and predicts a model-dependent H₀.
- Hubble tension: precision disagreement between inference routes is an active test of both measurement systems and cosmological theory.
Evidence Boundaries
The simple law v = H₀d is a low-redshift approximation. At high redshift, distance has several cosmological definitions and the relation between z, distance and recession depends on the expansion history. The balloon analogy is useful only for homogeneous scaling; it should not be mistaken for literal material space expanding into an external room.
Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK
- KNOW: galaxy redshift grows statistically with distance in the expanding Universe.
- CONNECT: d = aχ gives v = Hd for comoving separations.
- EXPLAIN: uniform fractional expansion produces larger absolute recession at larger distance without a centre.
- APPLY: use v ≈ H₀d only in its low-redshift regime.
- CHECK: separate peculiar velocities, distance-systematics, large-z cosmology and unresolved Hubble-tension claims.
Teaching Guide for Parents, Tutors and Teachers
Why this opening works: “everything recedes but we are not the centre” creates a genuine geometric contradiction that forces the learner to replace explosion thinking with scale-factor thinking.
- Central reasoning model: distance + redshift → proportionality → scale factor → expansion without centre.
- Teaching sequence: spectral redshift → independent distance → v = H₀d → grid analogy → scale-factor derivation → peculiar velocities → current tension.
- Diagnostic question: “Would an observer in another distant galaxy also see us receding?”
- If stuck: use points on an expanding coordinate grid, not an explosion drawing.
- Ready for more: introduce Friedmann equations, distance measures, BAO and cosmological parameter inference.
Quiet Teaching Standard: do not let “farther = faster” remain a graph slogan. Require the learner to derive it from uniform fractional expansion and state where the low-z law fails.