If I dig straight down, will I come out in China?

[ultrafilter]

Using spherical coordinates for your location on the planet, if you’re at (r, [symbol]q[/symbol], [symbol]f[/symbol]), then the antipode should be (r, [symbol]q[/symbol] + [symbol]p[/symbol], -[symbol]f[/symbol]). Of course, this does assume that the earth is a perfect sphere…

[Earthling]

If I dig a hole through the earth from here, where do I wind up?

FInd ou the E-Z Way.

Regarding the “I’ll come out in China” notion, apparently it isn’t restricted to the U.S. from Everest, the companion book to the IMAX movie:

The Icefall crevasses are so deep that when Sherpas look into their blue-black depths they often joke that they’re “looking into America.” Falling into one is referred to as “getting a visa to the U.S.”
Broughtton Coburn, Everest, National Geographic Society, p. 137

Whether the Sherpas came up with this idea independently or due to the influence of Western climbers, I can’t say.

[robby]

*Originally posted by Chronos *
At the top of a tower of that height, gravity would be about .85 g, as you note. But nobody’s ever been to the top of such a tower. The only way anyone’s ever gotten to the altitude of the Space Shuttle is in orbit, and in a very real sense, gravity is zero in orbit.

Chronos, I can’t believe that you, of all people, would make such a statement! :eek: While the apparent weight of objects in orbit is of course very near zero, the commonly held belief that the force of gravity is also zero for such an object should be stamped out! IMHO, it is just about impossible for students to understand orbital motion until they understand that: (1) a centripetal force is necessary to keep an object in orbit, and (2) the force of gravity is that centripetal force. As I often pointed out to my students when I taught physics, if the force of gravity was zero for an object in orbit, it would fly off at a tangent in a straight line.

[bibliophage]

According to the model used by the CRC Handbook, the force of gravity increases from 9.81 ms[sup]-2[/sup] at the surface to 9.83 at the top of the mantle (21 km down) to 10.69 at the top of the outer core (2886 km down). It then decreases to 4.27 at the top of the inner core (5156 km down) and to zero at the center (6371 km down).

[amarone]

*Originally posted by ElvisL1ves *
**
Do any of the global Dopers have similar expressions? Do Aussies dig “straight down to England”, for instance? **

No idea, but they do the other way round - in England they talk about digging straight down and coming up in Australia. That’s a whole lot more accurate than USA -> China.

[dtilque]

*Originally posted by amarone *
No idea, but they do the other way round - in England they talk about digging straight down and coming up in Australia. That’s a whole lot more accurate than USA -> China.

Yes, much more accurate, but still somewhat off. The area antipodal to the British Isles is south of New Zealand. In fact, there’s an island near that area called Antipodes Island, but it is actually antipodal to somewhere in the English Channel off Normandy.

Like the British Isles, Australia is not antipodal to any land, unless you count Heard Island which is opposite Canada. As someone else pointed out, Bermuda is antipodal to just offshore from Perth. A couple of the Azores are opposite to the Bass Straight, just north of Tasmania.

[Cubsfan]

*Originally posted by robby *
**

Chronos, I can’t believe that you, of all people, would make such a statement! :eek: While the apparent weight of objects in orbit is of course very near zero, the commonly held belief that the force of gravity is also zero for such an object should be stamped out! IMHO, it is just about impossible for students to understand orbital motion until they understand that: (1) a centripetal force is necessary to keep an object in orbit, and (2) the force of gravity is that centripetal force. As I often pointed out to my students when I taught physics, if the force of gravity was zero for an object in orbit, it would fly off at a tangent in a straight line. **

The normal acceleration of an object in orbit is equal to the tangential velocity^2 divided by the distance from the center of the little object to the center of the earth. For an object to remain in orbit the tangential velocity must be just enough to create a normal acceleration that is equal to but opposite the normal acceleration created by gravity. Any more and it flies away to a further orbit, any less and it will crash to earth. That is why it seems like a person is weightless in orbit because the force of gravity and the normal accel due to tangential velocity cancel each other out. Therefore the total force is equal to zero and you float.

Correct me if I am wrong here.

[CookingWithGas]

There was an article in the Washington Post a couple of years ago by a guy who wanted to visit the spot exactly opposite Washington, D.C., on the globe. He found out it was a spot in the Indian Ocean off the coast of Australia. So he found the nearest island, more of a big rock really, and visited that.

BTW he didn’t dig to it.