T.its seems simple enough. Your weight comes from the earth’s gravity pushing you down. Earth’s gravity comes from its mass. Less mass should mean less gravity. Remove mass from the Earth and you will lose weight.
You decide to give it a try.
Removing a lot of mass from the Earth will take a lot of energy, so you will start by taking the entire planet’s oil reserves.
You turn oil into fuel and use it to launch several hundred billion tons of rocks into orbit. This shaves an average of 0.2 mm of rock from the earth’s surface. You jump on the scale.
Ok, it didn’t work. But this makes sense; a few hundred billion tons are a tiny fraction of the earth’s mass.
Burning the other fossil fuels of the Earth helps a little, especially coal, which there is quite a lot of it, and allows you to remove almost a millimeter of the earth’s surface. * Step back on the scales.
You need more energy.
Cover the entire planet with highly efficient solar panels and spend a year absorbing all the sunlight hitting the Earth and using it to power your rock throwers. Humanity lives in the shade under your panels. People are probably pretty mad at you at this point.
One year of sunlight would give you enough energy to remove nearly 100 trillion tons of rock, several inches of the planet’s surface. Unfortunately, that’s not enough.
Clearly, this incremental approach doesn’t work.
You need more power. Instead of only capturing the small fraction of the solar energy that hits the Earth, you decide to capture all of its energy by building an energy harvesting fence around it – a Dyson sphere. Once you have harnessed the full power of the sun, you have enough energy to start ripping off the earth’s surface much more quickly.
The rocks of the Earth get warmer as you go deeper. After removing a few hundred meters of the crust, people begin to notice that the ground is warming. When you remove a kilometer of rock, the surface reaches 40 degrees Celsius. It might be nice on your feet when you get out of bed on a cold morning, but it will make life quite uncomfortable. Also, since you removed the tops of all the various hotspots, all the volcanoes in the world would erupt.
You control the ladder.
You use your Dyson sphere to remove more rock. You have now removed a 5 kilometer layer, which takes about 20 minutes. (For good measure, spend a few more minutes clearing the oceans.) Earth is no longer remotely habitable. Thanks to the magma exposed beneath the Yellowstone super volcano, northwestern Wyoming is a lava lake. The ground in most places is warm enough to boil water and make fires.
Try the scale again.
Okay, you just have to remove more rock, maybe with some kind of solar peeler.
It cuts away 20 kilometers of crust, which exposes the Earth’s mantle over much of the former seabed.
Nobody ever said losing weight was easy. She takes off for another 20 kilometers, removing layers of molten mantle and pockets of deep crust.
Go on. After four hours of working with your planet peeler, you have removed 60 kilometers of mostly molten rock. When you step on the scale, you finally see a change.
You are a pound heavier.
How can it be?
If the Earth had a uniform density, removing the layers would make you lighter. But our planet becomes denser as you go deeper and the density nullifies the loss of mass. The planet is getting a little lighter as you remove the surface, but you are also getting closer to that dense core. The net effect is that the removal of the outer layer of the Earth makes its gravity surface harder.
Gravity continues to increase as you go deeper. It levels off only after you’ve shaved about 3,000 kilometers, reducing the Earth’s diameter by half and expelling two-thirds of its mass. (It takes about a week for your sun-powered planet skin.) Your weight peaks at around 207 pounds, after which it begins to drop as you begin to remove the denser outer core.
After removing 3,450 kilometers of rock, your weight returns to what it was when you started. After 3,750 miles of rock, you finally reach your goal of losing 20 pounds. At this point, you’ve removed 85 percent of the land mass. But you have lost weight!
This plan has some flaws. It destroys the Earth, yes, but it is also unnecessarily inefficient. There is a much easier way to reduce the Earth’s gravitational pull on you without changing your mass or leaving the surface.
A spherical shell of matter exerts no gravitational force on the objects within it, which means that if you go underground, the rock layers above you stop contributing to your weight. From a gravitational point of view, it is as if it vanishes. You didn’t actually need to remove the mass from the Earth, you just needed to go under it. You could have avoided all that work with a relatively simple tunnel.
Have you at least avoided exercise? Well, more or less. Your project ended up requiring you to do a lot of work. Removal of the earth’s surface took 5 x 1028 calories of energy, which are more calories than would be burned if the entire human population started doing intense workouts 24 hours a day from now until the sun runs out and its residue cools to room temperature.
If your goal was to avoid work, you couldn’t have failed more badly.
Randall Munroe is the author of # 1 New York Times best seller What happens if? And Explainer of things, the science question and answer blog What If, and the popular webcomic xkcd. A former NASA robot, he left the agency in 2006 to draw comics on the Internet full-time. He lives in Massachusetts.
Taken from What happens if? 2 by Randall Munroe. Copyright © 2022 by Randall Munroe. Retrieved with permission from Riverhead, a brand and a division of Penguin Random House LLC, New York. All rights reserved. No part of this excerpt may be reproduced or reprinted without the written permission of the publisher.
* People might complain, but on the plus side, that millimeter probably includes all the grime and grime on the floor. Maybe you can turn it around as a free cleaning.