In Pole 10 Pole, an early science fiction story by George Griffith. three explorers attempt to travel by capsule through a naturally formed (and, of course, fictional) tunnel directly from the south pole to the north pole . According to the story, as the capsule approaches Earth’s center, the gravitational force on the explorers becomes alarmingly.
SOLUTION: Newton’s shell theorem gives us three Key Ideas here:
1. When the capsule is at a radius r from Earth’s center. the portion of Earth that lies outside a sphere of radius r does produce a net gravitational force on the capsule.
2. The portion that lies inside that sphere does produce a net gravitational force on the capsule.
3. We can treat the mass M;n, of that inside portion of Earth as being the mass of a particle located at Earth’s center.
This equation tells us that the force magnitude F depends linearly on the capsule’s distance r from Earth’s center. Thus. as r decreases. F also decreases (opposite of Griffith’s description). until it is zero at Earth’s center. At least Griffith got zero at the center correct.