The percentages are shares of the universe's total energy density today, measured mainly from the cosmic microwave background by the Planck satellite. They are not fixed. As space expands, matter thins out and the dark energy density stays about constant, so its share has been growing, and matter dominated the universe until roughly 4 billion years ago. Dark matter was first inferred in the 1930s from galaxy clusters moving too fast, and made convincing in the 1970s by Vera Rubin's rotation curves. Dark energy came from two supernova teams in 1998, who found distant explosions dimmer than a decelerating universe predicts.

The 10³⁶ comes from comparing the electric and gravitational forces between two protons, and it holds at any distance because both fall as 1/r². Gravity still rules the sky because matter is nearly neutral, so electric pulls cancel while every mass adds. The weak force is short ranged because its carriers are heavy, about 80 and 91 times a proton.

The rows are evenly spaced but the temperatures are not. From the Sun's surface to its core is a factor of about 2,700, and the top row is roughly 15 billion times boiling water. Absolute zero stays at the bottom because it cannot be reached by any finite number of cooling steps, the third law of thermodynamics.

Since 2019 the kilogram, ampere, kelvin and mole are defined by fixing h, e, k and N, so those four carry no measurement uncertainty at all. G is the outlier: its uncertainty is about 22 parts per million and repeat experiments still disagree by more than their stated errors. Alpha, the electron mass, the permittivity and the permeability are still measured and keep small uncertainties.

An electron trapped in a square box, shown as a probability cloud. Each colour is twice as dense as the one below it. Exact Schrödinger solution, one full cycle takes about 11 femtoseconds in a 1 nm box.

This is an atomic-resolution image of a single hexabenzocoronene molecule (a ~1.4 nm nanographene) captured by IBM using non-contact atomic force microscopy with a CO-functionalized tip. The bright lines show individual carbon-carbon bonds and atoms. Higher-order bonds appear brighter and slightly shorter. The image is a force map, taken in ultrahigh vacuum at ~5 K. Credit: IBM Research.

Henrietta Swan Leavitt spent years comparing glass photographs of the night sky, looking for stars whose brightness changed. At the Harvard College Observatory, she studied Cepheid variables in the Magellanic Clouds. In 1912, she reported a remarkably simple pattern: the brighter a Cepheid truly was, the longer its cycle of brightening and dimming. That relationship transformed a blinking star into a cosmic measuring tool. Once astronomers calibrated it, they could compare a Cepheid’s true brightness with how faint it looked from Earth and estimate its distance. Edwin Hubble later used Cepheids to show that the Andromeda “nebula” lay far beyond the Milky Way. The same distance ladder helped reveal an expanding universe. Leavitt died in 1921, before the full scale of her discovery became clear. Her patient work with tiny points on fragile plates gave astronomy a way to measure distances which was instrumental for us to understand our place in the universe.

Each speed is measured against a different reference, which is the point. Speed only means something relative to something else, and the cosmic microwave background is the closest thing the universe offers to a rest frame. The 14.5 billion light year distance is not the edge of the visible universe. The observable universe reaches about 46 billion light years.

Venus is hot because of a carbon dioxide atmosphere about 90 times thicker than Earth's, which traps sunlight. Saturn would only float in a bathtub big enough to hold it, and none exists. The Moon drifts because of tides, as Earth's rotation slows while the Moon moves outward.

The way out is time. The universe is about 13.8 billion years old, so light from beyond the cosmic horizon has not had time to arrive, and stars have only existed for a limited stretch. Expansion also stretches starlight to longer wavelengths, which dims it.

At 72 °C water boils but cooks food slowly, so mountaineers and high altitude kitchens use pressure cookers, which raise the boiling point to about 120 °C. Boiling temperature also shifts with the weather. A deep low pressure system can lower it by a degree or two.

Light reaches the observer almost instantly, covering 1 km in about 3 millionths of a second, while sound takes nearly 3 seconds. Sound travels more slowly in cold air, about 331 m/s at 0 °C, so the rule shifts a little. Thunder is usually inaudible beyond about 15 km because sound bends upward away from the ground.

Several of these needed little more than a stick, a ramp, a pendulum or a torsion balance. The last three show physics moving from the classical picture to the quantum one, since atoms turned out to have a tiny nucleus, spin took only two values and electrons behaved as waves.

Cecilia Payne looked at the dark lines in starlight and reached a conclusion astronomy was not ready to accept. For her 1925 doctoral thesis, she combined quantum theory with thousands of stellar spectra recorded at Harvard College Observatory. The pattern of absorption lines revealed not only temperature but abundance. Her calculations showed that hydrogen and helium were enormously more common in stars than heavier elements. The accepted view held that stars had roughly the same elemental composition as Earth. Princeton astronomer Henry Norris Russell urged caution, and Payne weakened the conclusion in her published thesis, calling the hydrogen and helium abundances almost certainly unreal. They were real. A few years later, Russell reached the same conclusion through other evidence and acknowledged her work. Stars, including the Sun, are overwhelmingly made of hydrogen and helium. Payne’s analysis had identified the basic chemical composition of the universe. Her thesis was later praised as one of the most brilliant ever written in astronomy. Recognition inside Harvard came slowly. She spent years in poorly defined positions before becoming the university’s first woman promoted to full professor from within its Faculty of Arts and Sciences and its first woman to chair a department.

Three black holes and three stars, released at rest. Every star is torn apart and the black holes merge into one of 116 Suns. One run out of 600.

Cosmic distances form a ladder. Parallax fixes nearby stars, such as Proxima Centauri at 4.25 light years. Type Ia supernovae peak at nearly the same brightness, so m − M = 5 log10(d/10 pc) gives their distance, and their recession speeds give v = H₀d. Early-universe data give H₀ = 67.4 km/s/Mpc and local ladders about 73.0. With the quoted uncertainties that is nearly 5σ apart, and it is unresolved.

Entropy counts arrangements: S = k_B ln W. A hundred coins show 50 heads in about 10^29 ways and 100 heads in exactly one way, so mixed outcomes win by sheer number. Gas molecules splitting between two halves of a box obey the same counting. All N molecules in one half has probability 2^-N. For a mole that is about 10^(-1.8 × 10^23), so the second law is statistical but effectively absolute.

In 1676 Rømer saw Jupiter's moon Io appear late when Earth was far from Jupiter. His timing implied about 22 minutes for light to cross Earth's orbit, against the modern 16.6, and so roughly 2.3 × 10^5 km/s. Wheels, mirrors, radio and lasers then sharpened c. Since 1983 it has been defined as exactly 299,792,458 m/s, and the metre follows from it. Relative error fell about 40 million times from 1676 to 1972.

Galileo showed that fall distance grows as t². Newton showed that the pull falls as 1/r², which fits the Moon: at 60 Earth radii its acceleration is about 1/3600 of g. Cavendish then weighed the Earth, finding it 5.45 times denser than water. Einstein's 1915 theory bends starlight by 1.75 arcseconds at the Sun's edge, confirmed in 1919. LIGO detected two merging black holes in 2015, with a strain near 10^-21.

A black hole is not perfectly black. Quantum effects at the horizon give it a temperature T = ħc³/(8πGMk_B), lower for heavier holes. For a solar mass it is about 62 nanokelvin, far below the 2.7 K microwave background, so stellar black holes currently gain more energy than they lose. Only holes under about 0.6 Moon masses are warmer than that background. Evaporation time scales as M³, roughly 10^67 years for the Sun. Hawking radiation has not been observed.