How heavy is Earth and how much weight could it sustain before caving in?
Herman D’Hondt
Mascot, Australia
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Let’s start by realising that there is a difference between mass and weight. Mass is an inherent property of things and reflects how much “stuff” there is in something. Weight, on the other hand, is the force an object feels under the influence of gravity.
Thanks to Albert Einstein’s insights, we now know that gravity is equivalent to acceleration, so an accelerated mass will experience weight because of that. Mass is expressed in kilograms, weight in newtons (N), or kg × m/s2. The acceleration caused by Earth’s gravity is 1g, or about 9.8 m/s2, giving a 75-kilogram person a weight of 735 N. Under an acceleration of 2g, the same person would weigh 1470 N.
The total mass of Earth is approximately 6 × 1024 kg. Under normal conditions, adding more mass to it won’t significantly affect it. However, under extreme conditions, it can be made to collapse, by either adding enough mass, or compressing it enough.
In the 1930s, Subrahmanyan Chandrasekhar calculated that, if an object becomes heavier than about 1.4 times the mass of the sun, the pressure caused by gravity becomes stronger than the nuclear forces that prevent atoms from collapsing.
Any object more massive than that will become a black hole, as will Earth if about 460,000 Earths (2.8 × 1030 kg) are piled on top of each other.
Alternatively, if Earth is compressed to about the size of a marble, the pressure overcomes the nuclear forces and, again, we have created an Earth-mass black hole. I will leave the design of the pressurising system as an exercise for the student.
Eric Kvaalen
Les-Essarts-le-Roi, France
Earth has a mass of about 6 million million million million kilograms.
If more mass were added to it, it would at first get bigger. But the pressure in the deep interior would get higher and higher, and this would compress the material (rock or metal core). Eventually, it would reach the point where Earth would no longer get bigger as one adds mass, it would just have a higher and higher average density. After this, adding mass would actually cause Earth to shrink. This is seen in white dwarf stars – the more massive they are, the smaller they are. But the shrinkage would take place gradually as more mass is added. Earth wouldn’t yet collapse.
As more mass was added, Earth would pass the Chandrasekhar limit of 1.4 solar masses, at which point the electrons in the deep parts of the planet would combine with the protons, forming neutrons. This would be a collapse, forming something similar to a neutron star.
Mike Follows
Sutton Coldfield, West Midlands, UK
The mass of Earth is about 6 × 1024 kilograms. Its weight depends on the local gravitational field strength, which is about 6 millinewtons per kg, due mainly to the gravitational pull of the sun. This gives it a weight just shy of 4 × 1022 N.
Increasing its mass might eventually turn Earth into a star. However, a star normally starts by fusing hydrogen in its core, before “burning” progressively heavier elements. But the core of an “Earth star” would be composed of heavier elements like carbon, oxygen, silicon and iron.
If extra mass were added in the form of hydrogen, any hydrogen fusion would need to take place in a shell surrounding this core. Iron can’t undergo fusion, but the other elements could fuse if sufficient mass were added to make the core hot enough. Perhaps as you read this there is a planet out there that is capturing hydrogen gas blown into its gravitational well by a local supernova.
Hillary Shaw
Newport, Shropshire, UK
Subsiding would be a better descriptor than “caving in”. Some 40 kilometres below us, the planet is no longer solid but a viscous magma. Very viscous – about 10,000 to 100 million times the viscosity of water. If you started piling space rocks at one point on our crust, the land would slowly subside, at around 1 metre for every 2.5 metres height of rocks you piled up. Adjustment would take millennia, as we see in the Baltic Sea region today, where the land is still rising after the ice cover disappeared thousands of years ago.
If you could pile, say, a 100-kilometre-high rock tower, measuring 10 metres on each side (and keep it balanced upright), it would, in short order, sink down until it reached magmatic regions, under enormous pressure. Then it might come right back up again, accompanied by lava and gases. I hope you took out volcano damage insurance for the area you did this experiment in.
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