The Cosmic Distance Ladder – How We Measure the Universe

Stand on one side of a deep river gorge and try to work out how far it is to a tree on the far bank. You can't stretch a tape measure across a hundred metres of air and rushing water. But pace out a measured line along your own side, note the angle to the tree from each end, and a little trigonometry gives you the distance without ever crossing.

That trick is where one of astronomy's greatest achievements begins: working out how far away almost everything is, from the Moon to galaxies whose light set out before Earth existed. No single method covers all of that. Instead astronomers use a chain of techniques called the cosmic distance ladder, each rung calibrated against the one below. At the top sits one of physics' liveliest unsolved arguments.

The Bottom Rung: Radar Off Venus

The most trustworthy rung uses radar, pointed at planets. Send out a burst of radio waves, time how long the echo takes to come back, and because radio waves travel at the speed of light, the timing converts directly into distance.

Bounced off Venus, Mars, Mercury and asteroids for decades, radar pins down solar system distances with extraordinary precision, and crucially fixes the size of Earth's orbit. The average distance between Earth and the Sun, about 150 million kilometres, is called the astronomical unit, and it becomes the baseline for the next rung.

Parallax: The Finger Trick, Scaled Up

Look at a finger held in front of your face with one eye, then the other, and it jumps against the background. That is parallax, and the closer the object, the bigger the jump.

Astronomers do the same with stars, using Earth's positions six months apart on opposite sides of its orbit as their two eyes. A nearby star seen in January and again in July shifts slightly against far more distant stars. Since radar has told us the width of Earth's orbit, that shift gives the distance by pure geometry, with no assumptions about the star itself.

The shifts are minute, less than one arcsecond even for the nearest stars, roughly the width of a human hair seen from several kilometres away. Then the European Space Agency's Gaia spacecraft, launched in 2013, measured the positions of well over a billion stars from above the blur of Earth's atmosphere. Gaia pushed reliable parallaxes out to many thousands of light years, and its measurements now anchor nearly every distance further out.

Henrietta Leavitt's Pulsating Stars

Further out, no shift can be detected, so the next rung uses a different idea. If you know how bright a candle is up close, you can judge how far away one is at night by how faint it looks. Objects of known true brightness are called standard candles.

The first powerful one came from Cepheid variables, stars that swell and shrink so their brightness rises and falls over days to months. In the early twentieth century, Henrietta Leavitt at Harvard College Observatory studied many of them in the Small Magellanic Cloud, a neighbouring galaxy easy to spot in a dark Australian sky. Since those stars all sat at roughly the same distance, differences in apparent brightness were real. Leavitt found a consistent pattern: the longer a Cepheid takes to pulse, the more luminous it is.

Calibrated with nearby Cepheids measured by parallax, that pattern became a tool reaching millions of light years. In the 1920s Edwin Hubble used Cepheids to show that fuzzy patches such as the Andromeda nebula were not clouds inside the Milky Way but separate galaxies far beyond it.

Exploding White Dwarfs

In more distant galaxies, single Cepheids become too faint to pick out. The rung that reaches billions of light years is a Type Ia supernova. It begins with a white dwarf, the dense leftover core of a Sun-like star, orbiting close to a companion. The white dwarf pulls material from its partner, or sometimes merges with another white dwarf, until it nears a critical mass called the Chandrasekhar limit, after astrophysicist Subrahmanyan Chandrasekhar. Then it detonates in a thermonuclear blast that can briefly outshine its whole galaxy. Because conditions are so similar each time, the peak brightness is remarkably consistent.

Here is the defining feature of the ladder: supernovae aren't trusted on their own. Astronomers first found Type Ia supernovae in galaxies close enough to contain measurable Cepheids, then used those Cepheids to work out how bright a typical Type Ia really is. Every rung borrows its calibration from the one below, all the way down to radar, so a small error near the bottom can ripple upward through everything built on it. Independent side rungs, such as the Tully-Fisher relation linking a spiral galaxy's spin to its brightness, help catch hidden mistakes.

Redshift and the Expanding Universe

When a galaxy moves away from us, its light is stretched toward the red end of the spectrum, a little like an ambulance siren dropping in pitch as it drives off. In the late 1920s Hubble found that the more distant a galaxy, the faster it seemed to be receding, a straight-line relationship the Belgian physicist Georges Lemaître had also reached. That is what you'd expect if space itself is expanding, like dots spreading on an inflating balloon. The number linking distance to recession speed, the Hubble constant, tells us how fast the universe is expanding today and feeds into estimates of its age and size.

In the late 1990s, two teams used Type Ia supernovae to show that very distant galaxies were fainter, and so further away, than expected: the expansion is speeding up. One team was led by Brian Schmidt at the Australian National University's Mount Stromlo Observatory, who shared the 2011 Nobel Prize in Physics for the discovery. The cause has been named dark energy, explored in Dark Energy – Why the Universe Is Flying Apart.

The Hubble Tension

Two broad ways of measuring the Hubble constant have refused to agree for about a decade.

• From the ground up. Cepheids and Type Ia supernovae in nearby galaxies give distances and redshifts directly. A long-running collaboration called SH0ES has refined this method, which gives roughly 73 kilometres per second per megaparsec.
• From the top down. The cosmic microwave background, the afterglow from about 380,000 years after the Big Bang, was mapped in fine detail by ESA's Planck satellite. Run forward with a well-tested model of cosmic history, it predicts roughly 67.

That gap, a little under ten per cent, sits well outside what either method's stated precision should allow. It may be a subtle, undiscovered error in one method, perhaps in how Cepheids are calibrated. Or, as cosmologists increasingly take seriously, both may be right and our standard picture of the universe is missing something, possibly to do with dark energy. Nobody yet knows, and independent methods such as gravitational lensing are being brought in to help settle it. The early-universe side is told in The Cosmic Microwave Background – The Universe's Baby Photo.

A Ladder Still Being Built

The distance ladder is the gorge trick, reinvented again and again, each rung leaning on the one before, carrying us from radar echoes off Venus to galaxies whose light left them before the Sun formed. It works astonishingly well. That its two grandest measurements still disagree isn't a failure. It is a sign that something real is still waiting in the gap between two carefully measured numbers.