There is ice on the planet nearest the Sun

Mercury has ice at its poles

The planet nearest the Sun holds water ice in craters at its poles.

Mercury orbits 58 million kilometres from the Sun on average, and its sunward side reaches between 590 and 725 kelvin, up to about 450 °C. Even so, ice lies in craters at its poles. Radar from Earth pointed to it first: in 1991 the Arecibo telescope found unusually radar-bright patches at the poles. NASA’s MESSENGER probe, which orbited the planet, then gathered the evidence that the patches are ice.

The reason is geometry. Mercury’s axis is tilted by only 0.034 degrees, against 23.44 degrees for Earth. At the poles the Sun therefore never climbs far above the horizon, and the floors of deep craters are never lit. Three papers in Science (volume 339, 2013) reached the same answer by different routes. Neutron measurements near the north pole show a layer rich in hydrogen, more than tens of centimetres thick, beneath a surface layer 10 to 30 centimetres thick that holds less hydrogen. The best match is nearly pure water ice. A laser altimeter found patches that are unusually bright, which fits surface ice, and others that are unusually dark, which fits a layer of organic material lying over ice. Thermal models of the craters showed that the places where ice should be stable match the places that are bright to radar.

From the neutron data the team infers 2 × 10¹⁶ to 10¹⁸ grams of water at the poles in total, which is 20 billion to 1 trillion tonnes. That amount is consistent with delivery by comets or volatile-rich asteroids.

NASA, Mercury Fact Sheet (obliquity 0.034°, sunward surface 590–725 K, semi-major axis 57.9 million km); Lawrence et al., Science 339, 292 (2013) (neutron spectrometer, layer thicknesses, total mass); Neumann et al., Science 339, 296 (2013) (laser altimeter); Paige et al., Science 339, 300 (2013) (thermal models); the MESSENGER team’s release of 29 November 2012 (Arecibo radar, 1991).

The Sun circles a point outside itself

The Sun does not sit still at the centre of the solar system. It circles a point that is usually above its own surface.

Every body in the solar system orbits the common centre of mass, the barycentre. Jupiter alone, about a thousandth of the Sun’s mass at 5.2 times the Earth–Sun distance, puts that point roughly 1.07 solar radii from the Sun’s centre, just clear of the surface. Saturn, Uranus and Neptune pull the Sun around too, and when the giants line up on one side the point moves farther out.

Taking the positions of the Sun from the JPL DE440 ephemeris every five days from 1850 to 2050, the distance from the Sun’s centre to the barycentre ranges from 0.06 to 2.10 solar radii. The farthest was in March 1983. On 63% of the dates sampled, the barycentre lay outside the Sun. Drag the slider to move through time. The crosshair is the barycentre; the grey trace is the path of the Sun’s centre across all 200 years.

Park, Folkner, Williams and Boggs, “The JPL Planetary and Lunar Ephemerides DE440 and DE441”, Astronomical Journal 161, 105 (2021); kernel de440s.bsp; nominal solar radius 695,700 km, IAU 2015 Resolution B3.

Some black holes are less dense than water

A black hole’s size grows with its mass, so a heavy enough one has an average density below water. M87*, one of the heaviest, comes out below air on the usual calculation.

The edge of a black hole, its horizon, sits at a radius of 2GM/c². Double the mass and the radius doubles, but the volume inside grows eightfold. Average density, mass divided by that volume, therefore falls with the square of the mass.

At about 136 million solar masses the average equals water, 1,000 kilograms per cubic metre. The black hole at the centre of the Milky Way, Sagittarius A*, weighs 4.3 million Suns and averages a million kilograms per cubic metre, a thousand times water. M87*, the black hole in the first image ever made of one, weighs about 6.5 billion Suns according to the Event Horizon Telescope, with an uncertainty of 0.7 billion. On that mass its average density is 0.44 kilograms per cubic metre, about 36% of the air at sea level.

That comparison depends on the mass, and the mass of M87* is measured in more than one way. Stellar motions give 5.4 billion Suns, which is 0.64 kilograms per cubic metre. Motions of gas near the centre give 3.5 billion, which is 1.5 and a little denser than air. The average equals air at about 3.9 billion Suns. The calculation also assumes no spin. A spinning black hole has a smaller horizon, and the same convention then gives a higher density.

GRAVITY Collaboration, Astronomy & Astrophysics 657, L12 (2022) (Sgr A*: 4.297 ± 0.012 million solar masses); Event Horizon Telescope Collaboration, Astrophysical Journal Letters 875, L1 (2019) (M87*: 6.5 ± 0.7 billion, from comparing the ring image with simulations); Liepold et al., Astrophysical Journal Letters 945, L35 (2023) (stellar dynamics: 5.37 billion); Walsh et al., Astrophysical Journal 770, 86 (2013) (gas dynamics: 3.5 billion); air at sea level 1.225 kg/m³ in the standard atmosphere (NASA Earth Fact Sheet: 1.217 kg/m³). Density follows from the Schwarzschild radius.

The first planets found beyond the Sun orbit a dead star

In 1992 the first confirmed planets outside the solar system turned up around a pulsar, the collapsed core of a star that exploded.

A pulsar is a neutron star that sends a beam of radio waves across the sky as it spins, like a lighthouse, with extraordinary regularity. In 1992 Aleksander Wolszczan and Dale Frail noticed that the pulses of PSR B1257+12, which spins every 6.2 milliseconds, arrived slightly early and late in a repeating pattern. Two planets tugging the star explained it. Timing alone gave only minimum masses, because the tilt of the orbits was unknown: at least 3.4 times the mass of the Earth for the planet that circles in 66.6 days, and at least 2.8 for the one that circles in 98.2 days. A third, a little heavier than the Moon, followed in 1994.

The tilts were measured in 2003. The two larger planets orbit close to a 3:2 resonance, so they tug on each other and shift the pulse arrival times by microseconds. Maciej Konacki and Wolszczan fitted that effect and obtained true masses and inclinations. The inner planet has 4.3 ± 0.2 Earth masses at an inclination of 53° ± 4°, and the outer planet 3.9 ± 0.2 at 47° ± 3°. Both orbits lie almost in one plane, which supports the idea that the planets formed from a disc of material. The masses assume a pulsar of 1.4 Suns. The third planet, 0.020 Earth masses or about 1.6 Moons, is too small to disturb the others. Its mass is calculated for an assumed orbit in the same plane, at about 50°, and is not a measurement.

The first planet around a Sun-like star came three years after the pulsar planets, with 51 Pegasi b in 1995. How planets formed or survived around a star that exploded as a supernova is still argued.

Wolszczan and Frail, “A planetary system around the millisecond pulsar PSR1257 + 12”, Nature 355, 145 (1992); Wolszczan, Science 264, 538 (1994); Konacki and Wolszczan, “Masses and orbital inclinations of planets in the PSR B1257+12 system”, Astrophysical Journal 591, L147 (2003); Mayor and Queloz, “A Jupiter-mass companion to a solar-type star”, Nature 378, 355 (1995); on formation, Miller and Hamilton, arXiv:astro-ph/0012042.

A heavier white dwarf is a smaller one

Sirius B has 72% more mass than Procyon B and a radius almost 3,000 kilometres smaller. It is smaller than the Earth.

A white dwarf is the burnt-out core of a Sun-like star. Gravity is held off by the pressure of its electrons. The heavier the star, the more tightly the electrons must be packed to carry the weight, so adding mass makes the star shrink. Chandrasekhar derived the relation between mass and radius in the 1930s, and Hamada and Salpeter computed it for cold stars of different compositions in 1961. Two of the best-measured white dwarfs fit it.

Sirius B weighs 1.018 Suns and has a radius of 0.008098 that of the Sun: 5,634 kilometres, less than the Earth’s 6,371. Procyon B weighs 0.592 Suns and has a radius of 0.01232 of the Sun: 8,571 kilometres. Both masses come from the orbits of the stars around their bright companions, so no theory of white dwarfs is assumed. The radii are less direct: they come from fitting model atmospheres to the spectra, the star’s measured brightness and its distance, and the quoted uncertainties are the internal errors of that fit.

Bond et al., Astrophysical Journal 840, 70 (2017) (Sirius B: 1.018 ± 0.011 M☉, 0.008098 ± 0.000046 R☉); Bond et al., Astrophysical Journal 813, 106 (2015) (Procyon B: 0.592 ± 0.006 M☉, 0.01232 ± 0.00032 R☉); Chandrasekhar, Astrophysical Journal 74, 81 (1931); Hamada and Salpeter, Astrophysical Journal 134, 683 (1961).

Galaxies receding faster than light can still be seen

In the standard model of the universe, every galaxy beyond a redshift of about 1.46 is moving away from Earth faster than light does today. Telescopes see them anyway.

No galaxy outruns light through space. The distance between Earth and a far galaxy grows because space itself is stretching, and special relativity limits speeds within space, not the growth of space. The farther away a galaxy is, the faster the gap widens, in direct proportion to the distance.

Light that left a galaxy while it was already receding faster than light, which in this model means a redshift above about 1.6, began by being carried away from Earth. But the distance at which the recession equals the speed of light grows with time, and eventually the light finds itself inside it and begins to close the gap. The galaxy that sent it is by then still farther off, and still receding faster than light. A galaxy between redshift 1.46 and 1.6 recedes faster than light today, but was just under that speed when its light left, so its light approached from the start.

Davis and Lineweaver, “Expanding Confusion”, Publications of the Astronomical Society of Australia 21, 97 (2004), Sections 1 and 3; the speed at the time of emission is computed here from the same model.

One particle carried the energy of a thrown baseball

On 15 October 1991 a detector in Utah recorded a single cosmic ray with 51 joules of energy. Nobody knows where it came from.

Its energy, (3.2 ± 0.9) × 10²⁰ electronvolts, was far beyond anything a laboratory can make. If the particle was a proton, it weighed some 10²⁶ times less than a baseball. A proton that energetic loses energy quickly to the faint microwave glow left over from the Big Bang. Its attenuation length is under about 30 megaparsecs, 100 million light-years, and the authors conclude that the source should lie within about that distance.

In 2021 the Telescope Array in Utah recorded another, named Amaterasu, at about 40 joules. It points back to a void in the large-scale structure of the Universe. The authors list three possible explanations: a large deflection by magnetic fields, an unidentified source in the nearby universe, or incomplete knowledge of particle physics.

Bird et al., “Detection of a cosmic ray with measured energy well beyond the expected spectral cutoff”, Astrophysical Journal 441, 144 (1995); Telescope Array Collaboration, Science 382, 903 (2023); ball weight, Official Baseball Rules, rule 3.01 (5 to 5¼ ounces).

On one planet iron shows at dusk and not at dawn

On the giant planet WASP-76b, iron absorbs starlight at the evening edge but not at the morning edge. The team that found this concluded that iron condenses on the night side.

WASP-76b is an ultra-hot giant planet: atmospheres of this kind exceed 2,000 kelvin. When it crosses the face of its star, starlight filters through the air at its edges, and the spectrum shows what the air contains.

In 2020 a team using the ESPRESSO spectrograph on the Very Large Telescope saw iron absorption from the evening edge, where air is arriving from the day side, shifted toward the blue by 11 kilometres per second, but none from the morning edge, after the air has crossed the night. The authors conclude that the iron must condense during the journey across the night side. They add that the droplets could be liquid iron, so that it could literally rain iron there. No instrument has seen the droplets: the condensation is a deduction from a missing signal.

The asymmetry itself has held up. A second team found it again in archival HARPS data. Its cause is disputed. Models show that a large temperature difference between the two edges can reproduce the signal without condensation, and that clouds of other materials give reasonable fits where condensation of iron alone does not. A later survey of 14 elements finds those that condense at the highest temperatures strongly depleted, which fits cold-trapping on the night side.

Ehrenreich et al., “Nightside condensation of iron in an ultrahot giant exoplanet”, Nature 580, 597 (2020); Kesseli and Snellen, Astrophysical Journal Letters 908 (2021) (HARPS); Wardenier et al., Monthly Notices of the Royal Astronomical Society 506, 1258 (2021) (temperature asymmetry); Savel et al., Astrophysical Journal 926, 85 (2022) (clouds); Pelletier et al., Nature 619, 491 (2023) (cold-trapping).

One star is more than a thousand times rounder than the Earth

A star 1.6 million kilometres in radius bulges at the equator by only about 3 kilometres. The Earth bulges by 21.

Spinning bodies flatten. The Earth’s equatorial radius exceeds its polar radius by about 1 part in 300. In 2016 Laurent Gizon and colleagues used the vibrations of a star called KIC 11145123, recorded over years by the Kepler space telescope, to measure its shape. It is 2.24 times the Sun’s radius and turns once in 100 days. The equator exceeds the poles by 3 kilometres, give or take 1. That is 1.8 parts in a million, give or take 0.6, and a third of the flattening that rotation alone should produce. The Earth is flattened about 1,900 times more, and the uncertainty on the star puts that ratio anywhere from about 1,400 to 2,800. The authors call it the most spherical natural object measured so far.

The authors suspect a weak magnetic field is making the star look rounder, which in a star of this kind would itself need explaining. Scale each to a ball one metre across and the star’s equator stands out by 0.9 micrometres, less than a thousandth of a millimetre. The Earth’s would be 1.7 millimetres.

Gizon et al., “Shape of a slowly rotating star measured by asteroseismology”, Science Advances 2, e1601777 (2016); Earth flattening 1/298.257 (WGS 84; the NASA Earth Fact Sheet gives 0.003353).

The Milky Way is not flat

The Milky Way’s disc is bent: one side of its edge curls up and the opposite side curls down, in an S.

The Milky Way is usually drawn as a flat disc. In 2019 Dorota Skowron and colleagues mapped it in three dimensions with 2,431 classical Cepheids, young stars whose pulsation rate reveals their true brightness and therefore their distance. The map shows the disc is flat out to about 8 kiloparsecs (26,000 light-years) from the centre, then bends progressively out of plane. The authors fitted a smooth surface to the Cepheids as a guide to the eye. At 15 kiloparsecs (49,000 light-years) from the centre that surface lies up to 0.74 kiloparsecs, about 2,400 light-years, above or below the middle. The warp continues out to about 20 kiloparsecs.

The warp had been seen before in gas, dust and older stars, mostly from star counts. The Cepheid map shows it in three dimensions, from stars whose distances were measured one by one.

Skowron et al., “A three-dimensional map of the Milky Way using classical Cepheid variable stars”, Science 365, 478 (2019).

Where each claim comes from

Every fact above ends with its references. Primary papers are linked where they are open to read. The ten results are not all the same kind of result:

1. Mercury. Neutron, radar and laser measurements point to ice, and thermal models calculate where ice is stable. The total mass is inferred.
2. Barycentre. Computed from a published ephemeris.
3. Black holes. The masses are measured. The average density is calculated from them by a convention.
4. Pulsar planets. Measured from pulse timing. The true masses also rest on an assumed pulsar mass.
5. White dwarfs. Masses measured from orbits. Radii come from model-atmosphere fits to spectra.
6. Recession speed. Calculated in a model of the universe.
7. Cosmic ray. One event, measured. The distance limit is a calculation that assumes a proton.
8. WASP-76b. The missing iron signal is measured. Its cause is inferred and disputed.
9. The round star. Measured from oscillations.
10. The warp. Distances are measured. The height at a given radius comes from a fitted surface.

What is estimated or still open

• Mercury’s ice. The three instruments agree that ice is there. How much is not settled: the total of 20 billion to 1 trillion tonnes is inferred from neutron data near the north pole, and its range spans a factor of fifty.
• Barycentre. The distances are computed from a published ephemeris, not measured directly. They use the nominal solar radius of 695,700 km.
• Black hole density. The averages divide each mass by the volume inside its horizon. They say how large the horizon is, not what lies inside. For M87* they depend on which mass is used, and they assume no spin.
• Pulsar planets. The masses of the two larger planets are measured, on the assumption that the pulsar weighs 1.4 Suns. Each orbit has a mirror-image solution with the same mass. The innermost planet’s mass is calculated for an assumed orbit in the same plane. How planets formed or survived near a supernova remnant is still argued.
• White dwarfs. Composition and temperature shift the exact radius, and the radii depend on atmosphere models. The pair shown matches theory for carbon–oxygen cores.
• Recession speed. The redshifts of 1.46 and 1.6 hold for the matter and dark-energy content assumed. Other measured values move them a little.
• The 1991 cosmic ray. Its energy is uncertain by about 0.9 × 10²⁰ eV. The 30 megaparsec scale applies if it was a proton; its identity is not known.
• WASP-76b. The missing iron at the morning edge is measured. Whether it condenses, or the morning edge is simply cooler or cloudier, is disputed; no droplets have been seen.
• The round star. The 3 kilometres carries an uncertainty of 1. The magnetic-field explanation is the authors’ conjecture.
• The warp. The diagram is a sketch, and the 0.74 kiloparsecs is the height of a fitted surface. Cepheids show a smaller warp than older stars do, so the height depends on which stars are used.