this question comes from Dennis who asks how long would it take for people to notice their weight gain if the mean radius of the world increased by 1 cm every second assuming the average composition of rock were maintained let's imagine the whole earth from crust to core starts expanding uniformly beneath our human structures which don't expand to avoid another drain the ocean scenario we'll assume the ocean expands too when the earth started expanding you'd feel a slight jolt and then you'd be moving steadily Upward at 1 cm/ second and wouldn't feel any kind of ongoing acceleration for the rest of the day you wouldn't notice much of anything after the first day the Earth would have expanded by 864 M gravity would take a long time to increase noticeably if you weighed 70 kg when the expansion started you'd weigh 70. 1 at the end of the first day with the ground expanding beneath them how fast would our roads and bridges fail well not as quickly as you might think here's a puzzle I heard once imagine you tied a rope tightly around the earth so it was hugging the surface all the way around now imagine you wanted to raise the rope 1 M off the ground how much extra length would you need to add to the Rope miles hundreds of miles the answer is about 6 M circumference is proportional to radius so if you increase the radius by 1 unit you increase the circumference by 2 pi units after 1 day the 40,000 km circumference of the earth would increase by 2 pi * 864 M or 5. 4 km which is about 0.
01% and that'd be handled easily by virtually all structures concrete expans and contracts by more than that every day one of the first real effects you'd notice would be that GPS satellites would stop working correctly the satellites would stay in roughly the same orbits but the incredibly precise timing and synchronization between ground stations and satellites would be ruined within hours most other clocks would keep working fine however if you have a very precise pendulum clock you might notice something odd by the end of the day it would be 3 seconds ahead of where it should be after a month the Earth would have expanded by 26 km an increase of 0. 4% surface gravity would also only have gone up 0. 4% even though the Earth's mass would have increased by 1.
2% surface gravity is proportional to radius which is because as the planet grows it gets more massive but you also get further away from the middle you wouldn't notice this difference in weight even using a scale human body weights vary by much more than 0.
