Earth mass

• 1. Introduction

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  Earth mass is the unit astronomers use to weigh everything from nearby planets to distant worlds orbiting other stars. One number sits at the center of that scale: the mass of Earth itself, currently estimated at approximately six ronnagrams, or 6.0 Rg in metric terms. That figure took roughly two centuries of increasingly clever experiments to pin down, and it is still not known with the precision scientists would prefer.

  The challenge is not that Earth is too big to study. It is that measuring Earth's mass means measuring the gravitational constant, the fundamental physical constant known with the least accuracy of any in physics. Gravity is simply too weak, at laboratory scales, to pin down precisely. So the planet beneath your feet remains, in a precise mathematical sense, the least-well-measured object astronomers routinely work with.

  What does that mass actually consist of? How did the first experimenters coax a number out of mountains and mines and pendulums? And how much does Earth's mass change from year to year, right now, as you listen? Those are the threads this documentary will follow.

• 2. A Scale for the Solar System

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  Jupiter tips the scale at 317.8 Earth masses. Saturn comes in at 95.2. Neptune, Uranus, Venus, Mars, Mercury and Pluto each get their own entry in the table that astronomers use to compare planets, all expressed as multiples or fractions of one Earth mass. At the other end of the scale, Eris, a dwarf planet beyond Neptune, weighs just 0.0027 Earth masses, barely a sliver.

  The Sun sits at the top: 332,946 Earth masses. That ratio captures how dominant the Sun is in the solar system's budget of matter. The Moon, often thought of as Earth's companion, accounts for only about 1.2% of Earth's mass. Because of that, the mass of the Earth-Moon system together is close to 6.0457 in the standard units.

  Beyond our solar system, the same scale has become the go-to measure for rocky worlds discovered around other stars, called exoplanets. Gliese 667 Cc, a planet orbiting a distant star, weighs roughly 3.8 Earth masses. Kepler-442b, another exoplanet, falls somewhere between 1.0 and 8.2 Earth masses depending on the measurement. The Earth mass unit allows direct comparison across vast distances, anchoring every planetary discovery to something tangible.

  Astronomers prefer this unit not just for elegance. The geocentric gravitational constant, the product of Earth's mass and the universal gravitational constant, is known with a relative uncertainty of just 2 parts in a very large number. That precision comes from laser ranging data collected by satellites such as LAGEOS-1. The absolute mass in kilograms is far less certain, so scientists work in ratios and avoid the messier figure whenever they can.

• 3. What Earth Is Made Of

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  Iron and oxygen each account for roughly 32% of Earth's total mass. Magnesium and silicon each contribute about 15%. Calcium, aluminium and nickel each come in around 1.5%. Together, those seven elements account for the overwhelming majority of the planet's weight.

  The distribution of that mass is uneven. Earth's core takes up only 15% of the planet's volume but holds more than 30% of its mass. The mantle, by contrast, fills 84% of the volume and holds close to 70% of the mass. The crust, the thin shell on which all of human civilization sits, accounts for less than 1% of Earth's total mass.

  Density swings dramatically from layer to layer. The upper crust runs at less than 2,700 kilograms per cubic meter. At the inner core, the figure climbs to as much as 13,000. About 90% of Earth's mass comes from two broad chemical families: the iron-nickel alloy in the core, and the silicon dioxides and magnesium oxide that dominate the mantle and crust.

  Some components are almost vanishingly small. Carbon accounts for 0.03% of Earth's mass. Water, despite covering most of the surface, makes up just 0.02%. The entire atmosphere contributes about one part per million. It was Charles Hutton, analyzing the results of the Schiehallion experiment in 1778, who first recognized that the Earth's interior must be substantially metallic. He estimated that the metallic portion occupied about 65% of Earth's diameter, a figure not far from the modern value of 55%.

• 4. Mountains, Mines, and Pendulums

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  Pierre Bouguer and Charles Marie de La Condamine led an expedition between 1737 and 1740 that carried pendulums up the flanks of Pichincha Volcano and mount Chimborazo in Ecuador and Peru. The goal was to measure how much gravity changed with elevation, which could reveal the density hiding inside the planet. Bouguer reported in a 1749 paper that the deflection they detected was 8 seconds of arc. That was not precise enough to pin down Earth's mean density, but it was enough to prove, at minimum, that the planet was not hollow.

  The more famous attempt came two decades later. Nevil Maskelyne, the Astronomer Royal, proposed to the Royal Society in 1772 that a proper mountain experiment would honor the nation that carried it out. The Royal Society formed a Committee of Attraction whose members included Joseph Banks and Benjamin Franklin. The committee sent the surveyor Charles Mason to scout for an ideal mountain.

  After a summer-long search in 1773, Mason settled on Schiehallion, a peak in the central Scottish Highlands. It stood isolated from neighboring hills, its symmetrical east-west ridge simplified the geometry, and its steep slopes let the instruments be placed close to the mountain's center of mass. Maskelyne, Hutton and Reuben Burrow ran the experiment, completing it by 1776.

  George Biddell Airy pursued a different approach entirely, descending into mines rather than climbing mountains. His first trials in Cornwall between 1826 and 1828 ended in disaster, ruined by fire and flood. He finally succeeded in 1854 with measurements taken in a coal mine in Harton, South Shields, arriving at a density of 6.6. Later, Robert von Sterneck repeated similar experiments in mines of Saxony and Bohemia, gathering values between 5.0 and 6.3 across different depths. Those varied readings planted the seed of the concept known as isostasy.

• 5. Cavendish and the Laboratory

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  Henry Cavendish, in 1798, was the first person to measure the gravitational attraction between two bodies directly inside a laboratory. His experiment combined Newton's second law of motion with Newton's law of universal gravitation to extract Earth's mass without involving any mountain or mine at all.

  Cavendish found a mean density of 5.45, sitting about 1% below the modern accepted value of 5,515 kilograms per cubic meter. That accuracy, achieved with equipment available at the end of the 18th century, was a remarkable result. By the 1890s, continued refinements had pushed uncertainty down to about 0.2%. By 1930, it had dropped further to 0.1%.

  Isaac Newton had actually contemplated the mountain-deflection experiment in his Principia, but concluded pessimistically that the effect would be too small to detect. He did, however, estimate on general grounds that Earth's density would be five or six times that of water. The modern figure is 5.515, making Newton's intuition surprisingly close despite his lacking any reliable measurements to work from.

  High-precision repetitions of the Cavendish experiment remain the method of choice today. Results reported since the 1980s fall between 6.672 and 6.676 for the gravitational constant, with some measurements from that period yielding results that are mutually exclusive with each other. The 2014 CODATA recommended value sits close to 6.674, carrying a relative uncertainty below 10 to the negative fourth power. The Astronomical Almanac Online, as of 2016, recommends a standard uncertainty of 1 for the Earth mass figure itself.

• 6. A Planet Slowly Changing

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  Earth is not a fixed quantity. Micrometeorites and cosmic dust fall in continuously, while hydrogen and helium bleed away into space. The combined effect is a net loss estimated at roughly 5.5 times ten to the seventh kilograms per year. In practical terms that is about 45,000 tons gained annually from infalling material against 100,000 tons lost through atmospheric escape.

  Hydrogen escapes fastest, at around 95,000 tons per year. Helium leaves at about 1,600 tons per year. These gases are light enough that Earth's gravity cannot hold onto them permanently at the top of the atmosphere.

  At the far extreme of mass gain, the Chicxulub impactor provides the sharpest contrast available. That single event, with a midpoint mass estimate of 2.3 times ten to the fifteenth kilograms, added approximately 900 million times the annual dustfall amount to Earth's mass in a single strike.

  Human spaceflight contributes a small but measurable loss on the other side. Spacecraft placed on escape trajectories permanently remove mass from the Earth-Moon system. Since the mid-20th century, that cumulative loss has been estimated at 65 kilograms per year on average, and Earth lost about 3,473 tons in the first 53 years of the space age. The trend is currently decreasing as mission profiles have changed.

  Nuclear processes inside Earth add a further wrinkle. The combination of nuclear fission and natural radioactive decay converts a small amount of mass into energy, at an estimated 16 tons per year. All of these changes, taken together, fall well within the existing measurement uncertainty of 0.01%, leaving the official Earth mass figure unaffected.