So, I’ve got my shovel and I’ve packed extra sandwiches. I’m going to start digging this afternoon. My plan is to go straight through, directly through the Earth’s core. (OK, so I’m geographically off. Nevermind. This ain’t a geography question.) For safety reasons, I also plan on lining the hole with special tubing, so as to save myself from the harmful effects of heat and crushing pressures. Safety first, after all.
So I figure that the first half of the trip will involve me climbing down the hole. The second half I will be climbing up the hole. This leads me to believe that at some point near the middle, I’ll be climbing neither up nor down, but instead I’ll be weightless.
Is that true? Will the Sun and Moon have an appreciable effect on my fun yet inefficient weight loss plan? How about if I used my special disintigration gun to eliminate them?
You haven’t got time for this BS get back to digging. I am arranging to meet you at Town Hall station with an official welcoming party on August 19th about 7.30 PM OUR TIME so don’t forget to set your watch.
Yes, that is true. All the mass of the earth will be evenly distributed around you, so it all cancels out. As you go deeper into the earth you will feel lighter and lighter, as all the mass outside the sphere at your level cancels out. So if you are only 1000 miles from the center of the earth it would be like being on the outside of a planet just 1000 miles in radius (ignoring that the earth isn’t constant density).
As to the sun and moon, I don’t think their effect would be noticable, what with all the digging going on.
You be orbiting around the Sun at the same speed and distance as the Earth orbits around it, so the gravitational pull of the Sun would be effectively cancelled by your orbital velocity.
But where are you going to put all that hot metal that you dig out of the hole? And how do you lift it to the surface all those thousands of miles?
I, for one applaud your forethought. Most folks dig to China. Do they think about the language barrier? No. Do they stop and think about whether the beer is any good? No. They just dig on blithely, on their way to China.
Australia, now, that’s the ticket. Folks there speak your language, and have those great big cans of beer! Now that’s the ticket!
Yes, which is why you feel lighter and lighter. Because the gravity pulling you “up” (back toward home) gets stronger while the gravity pulling you “down” (toward the free beer) gets weaker, until in the middle, they cancel out exactly (again, neglecting density considerations) and you feel completely weightless. By the way, once you’re done digging, just dive back into the hole, head first, with your arms stretched out superman-style, and you’ll fly all the way through (neglecting air resistance and other frictions). Just make sure you grab the sides of the hole when you get back here, otherwise you’ll slide all the way back to Australia again.
Not at all cool!
You forgot your asbestos fire suit and you will be burned to a crisp cinder before you reach the centerline.
Say “Hello” to Old Nick! (IF you get the chance.)
It might be cool to do it the way prisoners do it when they plan a big jail break. Fill your pockets, then climb out and dump them in the rec yard. Oh, and carry a shiv for the correct atmosphere.
I think the question had to with the statement that if you were 1,000 mi from the center, the gravity would be exactly equivalent to being on the surface of a 1,000 mi diameter sphere.
That one had me going too, but I don’t rembember enough math to do a formal proof. I think you would have to integrate the gravity vector from you to all points.
But a diagram convinced me it’s possible. If you are 1,000 from the center, you have 3,000 mi directly over your head and 5,000 mi directly under your feet, netting out to 2,000 mi under your feet, the same as on a 1,000 mi sphere.
There mass of the earth further away from the center than you (assume a spherical earth) is distributed so that it all cancels out. From a gravitational standpoint, it is if all that mass doesn’t exist. Picture it like an onion, as you dig deeper you are removing layers of the onion. By the time you get to the center, there is no onion. Only beer.
Right. Assuming the Earth’s mass distribution is spherically symmetric (reasonable enough for this), then the gravitational pull you’ll feel at a point inside the Earth is a function of the amount of mass below you, and not above you. The net gravitational force from all the mass above you comes out to zero.
Calculus is one way to show it, but here’s a page that makes a simpler geometric argument. (Near the bottom, “Field Inside a Spherical Shell”.)
