Appearance
11.9 — How We Know Any of This
Nobody has visited a star. Everything known about the universe beyond the solar system arrived as electromagnetic radiation, plus a handful of neutrinos and gravitational waves.
From that thin stream of photons, astronomers have determined the composition, temperature, mass, age, distance, velocity and magnetic field of objects billions of light years away — and have measured the age of the universe to about 1 %.
This chapter is about how.
Telescopes
Two jobs, and the second is usually more important.
Light gathering. The collecting area goes as D^2, so a 10 m telescope gathers 100 times more than a 1 m one and can see objects 100 times fainter — or 5 magnitudes (Chapter 11.1).
Resolution. From Chapter 5.4:
\theta_{\min} = 1.22\frac{\lambda}{D}
Both improve with diameter, which is why telescopes keep getting bigger.
Refractors versus reflectors. A lens must be supported at its rim and suffers chromatic aberration (Chapter 5.2); a mirror can be supported from behind and has none. The largest refractor ever built is the 1.02 m Yerkes telescope of 1897, and nothing larger is practical. Reflectors have no such limit.
Modern designs
Segmented mirrors. Casting a single mirror above about 8 m is impractical. Keck's 10 m mirror is 36 hexagonal segments, each actively positioned to nanometre accuracy. JWST's 6.5 m is 18 segments, folded for launch. The Extremely Large Telescope, under construction in Chile, has 798 segments and a 39 m aperture.
Adaptive optics. The atmosphere limits ground-based resolution to about 1 arcsecond — a factor of 50 worse than a 10 m telescope's diffraction limit.
The fix: measure the distortion hundreds of times a second using a bright reference star, and correct it with a deformable mirror having hundreds or thousands of actuators.
And if no bright star is nearby, create one. A laser tuned to 589 nm excites sodium atoms in a layer at 90 km altitude, producing an artificial star wherever it is pointed. This is why modern observatory photographs show orange beams.
Adaptive optics recovers most of the diffraction limit and is why an 8 m ground telescope can now rival Hubble at infrared wavelengths.
Across the spectrum
Every band shows different physics, and most of them are blocked by the atmosphere.
| Band | What it shows | Where observed |
|---|---|---|
| Radio | Cold hydrogen, pulsars, CMB, jets | Ground |
| Microwave | CMB, molecular clouds | Ground (dry sites), space |
| Infrared | Star formation, dust, cool objects, high redshift | High/dry sites, space |
| Visible | Stars, galaxies | Ground |
| Ultraviolet | Hot young stars, quasars | Space only |
| X-ray | Accretion discs, hot gas, neutron stars | Space only |
| Gamma | Bursts, pulsars, annihilation | Space only |
The atmosphere has two windows — optical and radio — and is opaque almost everywhere else. This is why space astronomy exists, and why the ultraviolet, X-ray and gamma-ray universes were entirely unknown before rockets.
X-ray telescopes cannot use normal mirrors. X-rays pass straight through, or are absorbed. Grazing incidence optics reflect them off nested surfaces at angles under a degree, where the reflectivity becomes high — the same total-external-reflection principle as light in a fibre (Chapter 5.1), operating the other way round. Chandra's mirrors are nested cylinders, polished to within a few atoms of the design shape.
Radio telescopes face the opposite problem: \theta \propto \lambda/D, and radio wavelengths are 10^{5} times longer than optical. A 100 m dish at 21 cm gives 9 arcminutes — worse than the naked eye (Chapter 5.4).
Interferometry
The solution is to combine widely separated telescopes.
Resolution is set by the separation, not the dish size:
\theta = \frac{\lambda}{B}
where B is the baseline.
Worked example: the Very Large Array. 27 dishes spread over 36 km, at 21 cm:
\theta = \frac{0.21}{36{,}000} = 5.8\times10^{-6}\ \text{rad} = 1.2\ \text{arcseconds}
Comparable to a ground optical telescope, from radio waves a million times longer than light.
Very Long Baseline Interferometry goes further, combining telescopes on different continents with atomic clocks recording the signal timing, and correlating the data afterwards.
The Event Horizon Telescope used eight sites from Hawaii to the South Pole, giving an effective baseline of about 10,000 km at 1.3 mm:
\theta = \frac{1.3\times10^{-3}}{10^{7}} = 1.3\times10^{-10}\ \text{rad} = 27\ \mu\text{as}
Twenty-seven microarcseconds — enough to resolve an orange on the Moon.
The 2019 image of M87's black hole and the 2022 image of Sagittarius A* came from this. The data volume was so large — petabytes — that it was flown on hard drives rather than transmitted, and the South Pole data had to wait for the Antarctic summer.
Optical interferometry is far harder, because the light must be combined coherently with path lengths matched to a fraction of a wavelength. The VLT Interferometer in Chile does it, achieving milliarcsecond resolution, and it has imaged the surfaces of nearby giant stars.
Spectroscopy
The single most productive technique in astronomy.
Chapter 5.4 covered diffraction gratings. Spread the light out, and the resulting spectrum carries an extraordinary amount of information.
What a spectrum reveals
Composition. Every element has a unique set of lines (Chapter 7.6), so the spectrum is a chemical fingerprint.
Helium was discovered in the Sun's spectrum in 1868 — an unidentified yellow line during an eclipse — and was not found on Earth until 1895. It is named after Helios.
Temperature. From the continuum shape via Wien's law (Chapter 3.7), and from which ionisation states are present. Hydrogen Balmer lines are strongest at about 10,000 K, because below that too few atoms are in the n=2 state and above it hydrogen is ionised.
Radial velocity. From the Doppler shift (Chapter 2.5), measurable to below 1 m/s.
Rotation. A rotating star has one limb approaching and one receding, so every line is broadened symmetrically. The width gives v\sin i.
Pressure and density. Collisions broaden lines, so a dwarf star's lines are broader than a giant's at the same temperature. This is how luminosity class is determined from a spectrum alone.
Magnetic field. The Zeeman effect splits lines in a magnetic field, by an amount proportional to the field strength. Sunspot fields of 0.3 T were measured this way by Hale in 1908 — the first detection of a magnetic field beyond Earth.
Spectral classification
The sequence O B A F G K M, from hottest to coolest.
| Class | Temperature | Colour | Features | Example |
|---|---|---|---|---|
| O | >30,000 K | Blue | Ionised helium | Zeta Puppis |
| B | 10,000–30,000 | Blue-white | Neutral helium | Rigel |
| A | 7,500–10,000 | White | Strongest hydrogen | Vega, Sirius |
| F | 6,000–7,500 | Yellow-white | Metals appearing | Procyon |
| G | 5,200–6,000 | Yellow | Calcium strong | Sun |
| K | 3,700–5,200 | Orange | Metals dominant | Arcturus |
| M | ❤️,700 | Red | Molecular bands | Betelgeuse |
The letters are not alphabetical because the original classification was by hydrogen line strength, and reordering by temperature scrambled them. Annie Jump Cannon reorganised the sequence at Harvard around 1901, classifying about 350,000 stars by eye, and it is her ordering that survives.
Cecilia Payne showed in her 1925 doctoral thesis that the differences are temperature, not composition, and that stars are overwhelmingly hydrogen and helium. Her advisor persuaded her to describe the result as "almost certainly not real" because it contradicted the consensus that stars had Earth-like composition. She was right, and it is often called the most brilliant PhD thesis in astronomy.
The distance ladder
No single method spans the range. Each works over a limited distance and is calibrated against the one below it.
Rung 1: radar and laser ranging
Bounce a signal and time it.
Venus radar ranging in 1961 fixed the astronomical unit to a few hundred metres, replacing centuries of much cruder determinations.
Lunar laser ranging (Chapter 5.6) gives the Earth–Moon distance to a few millimetres.
Range: solar system only. But it sets the absolute scale for everything above.
Rung 2: parallax
Chapter 11.1 introduced it:
d\ (\text{pc}) = \frac{1}{p\ (\text{arcsec})}
Gaia has measured about 1.5 billion parallaxes with uncertainties down to about 20 microarcseconds, reaching tens of thousands of parsecs.
This is the only geometric method beyond the solar system, and every other rung depends on it.
Rung 3: standard candles
If you know an object's intrinsic luminosity and measure its apparent brightness, the inverse square law gives the distance:
F = \frac{L}{4\pi d^2} \quad\Longrightarrow\quad d = \sqrt{\frac{L}{4\pi F}}
In magnitudes:
d = 10^{(m-M+5)/5}\ \text{pc}
Cepheid variables are the crucial ones.
Henrietta Swan Leavitt, working at Harvard on photographic plates of the Small Magellanic Cloud, found in 1912 that a Cepheid's pulsation period predicts its luminosity.
M_V \approx -2.81\log_{10}P-1.43
Because all the stars in the Cloud are at essentially the same distance, differences in apparent brightness had to be differences in intrinsic luminosity. That is what let her find the relation without knowing any distance at all.
The physics is the kappa mechanism: a layer of partly ionised helium becomes more opaque when compressed, trapping heat, which forces expansion, which lets the heat out, which allows recompression. A thermodynamic engine driving a mechanical oscillation.
Worked example. A Cepheid with a 10-day period and apparent magnitude 15.
M_V = -2.81\log_{10}(10)-1.43 = -2.81-1.43 = -4.24
d = 10^{(15+4.24+5)/5} = 10^{24.24/5} = 10^{4.848} = 70{,}500\ \text{pc} = 230{,}000\ \text{ly}
Range: up to about 30 Mpc with Hubble, which reaches the nearest galaxy clusters.
Type Ia supernovae are the next rung.
A white dwarf accreting from a companion reaches the Chandrasekhar limit of 1.44 solar masses (Chapter 7.7) and detonates. Because the trigger mass is always the same, the peak luminosity is nearly the same — about 10^{10} solar luminosities.
The remaining scatter is removed by the Phillips relation: brighter supernovae decline more slowly, and correcting for the decline rate reduces the scatter to about 10 %.
Range: over 1000 Mpc, because they briefly outshine their entire host galaxy.
And these are what found dark energy (Chapter 12.7).
Rung 4: redshift
For the most distant objects, use the expansion itself:
v = H_0d
with H_0 \approx 70 km/s/Mpc.
Range: to the edge of the observable universe.
Calibrated by every rung below it, which is why an error anywhere propagates all the way up.
The Hubble tension
And that is exactly the current problem.
Two independent routes to H_0 disagree.
The distance ladder — parallax to Cepheids to Type Ia supernovae — gives:
H_0 = 73.0 \pm 1.0\ \text{km/s/Mpc}
The cosmic microwave background, interpreted through the standard cosmological model, gives:
H_0 = 67.4 \pm 0.5\ \text{km/s/Mpc}
A difference of about 5 sigma, which by the standards of Chapter 8.6 is a discovery-level discrepancy.
Either there is an unidentified systematic error in one method, or the standard cosmological model is missing something. JWST has now re-measured the Cepheids with better resolution and confirmed the ladder result, which makes a Cepheid crowding error less likely. The tension is unresolved and it is one of the most active problems in cosmology (Chapter 12.5).
Measuring masses
The only way to weigh anything distant is to watch something orbit it (Chapter 11.3).
M = \frac{4\pi^2a^3}{GT^2}
Binary stars give stellar masses directly, and about half of all stars are in binaries.
Galaxy rotation curves give the mass inside a given radius — and gave the first strong evidence for dark matter (Chapter 12.4).
Velocity dispersion in clusters does the same for the largest structures, and Zwicky's 1933 application of it to the Coma Cluster was the first dark matter detection of all.
Gravitational lensing weighs mass by how much it bends light (Chapter 6.6), and works even when nothing is orbiting.
And the black hole at the galactic centre was weighed by tracking individual stars orbiting it for 25 years. The star S2 has a 16-year orbit and has now been followed through more than one complete circuit, giving 4.3\times10^{6} solar masses within a region smaller than Neptune's orbit. Ghez and Genzel shared the 2020 Nobel Prize for it.
New windows
Neutrinos (Chapter 8.5) pass through everything and point back at their sources.
Gravitational waves (Chapter 6.10) carry information from places light cannot escape.
Cosmic rays are charged, so magnetic fields scramble their directions and they cannot be traced to sources — except at the very highest energies, where the deflection becomes small.
Multi-messenger astronomy combines them, and GW170817 was the first full example: gravitational waves, gamma rays, and follow-up across the entire electromagnetic spectrum from one event.
What Part 11 established
The sky's motions — days, seasons, eclipses, precession — all follow from a tilted, spinning, orbiting Earth, and were measured to arcminute precision long before anyone knew what they meant.
Kepler's laws and Newton's law are equivalent, each derivable from the other, and the derivation shows that the closed ellipse exists only because the exponent is exactly 2.
The vis-viva equation gives speed anywhere in any orbit, and from it the geostationary altitude of 35,786 km falls out in three lines.
Delta-v is the currency of spaceflight, transfers and plane changes are priced in it, and the Oberth effect means where you burn matters as much as how much.
Three bodies cannot be solved, and out of that come the five Lagrange points, gravity assists that cost nothing, and a solar system that is chaotic on a 5-million-year timescale and stable enough for life anyway.
The rocket equation is exponential, which forces staging, and it is why space is expensive in a way no engineering improvement can fix.
Landing a booster was solved by reformulating the mathematics, not by better hardware.
And everything known beyond the solar system came from analysing light, through a ladder of distance methods whose current 5-sigma disagreement may be pointing at new physics.
What the next Part fixes
The mechanics of orbits says nothing about what the objects are. Part 12 asks how a star works, why it must eventually die, what it leaves behind, and what happens when gravity wins completely. Then it goes larger: galaxies, the evidence that most of the matter in them is something nobody has identified, the expansion of the universe and the equations that govern it, the Big Bang and how much of it is actually established, the 68 % of the universe that is accelerating its expansion for reasons unknown, an honest examination of what science fiction gets right and wrong, and finally the questions that sit at the edge of what physics can address at all.