If you burrow into a shrinking planet and get close to its center why would your weight decrease?

Answer 1

Gravity attracts every dot of mass to every other dot of mass. Your body is attracted to every dot of mass in the earth. What happens if you burrow into the earth, so that some of the mass is in a shell 'outside' you ... farther from the center of the earth than you are ? It would be very complicated to try and prove it here. Trust me. So I'll just tell you ... When you're inside a solid sphere, so that there's a shell that's completely 'outside' of your depth, gravity acts as if the whole shell doesn't exist ! You're then attracted by the mass 'inside' the depth where you are ... which is less than the whole sphere, and has less mass. That's why as you go deeper into the earth, or any solid sphere or any planet, you progressively weigh less. I think it's true that wells and research shafts have been drilled deep enough into the earth's crust that this effect has actually been measured down in a deep hole.

Answer 2

As you move toward the center of a shrinking planet, the mass surrounding you decreases, resulting in a decrease in gravitational pull. This decrease in gravitational force makes you feel lighter, even though your mass remains the same.