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My superhero generates a force field which lets him and his equipment sustain the extreme conditions found inside the Earth. He decides to travel from the Geographic North Pole to the Geographic South Pole by taking the shortest path, i.e., digging in a straight line inside the Earth core.

My question is how can he ensure that he follows follow a straight line to reach the South Pole?

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    $\begingroup$ So...your superhero wants to make a volcano at the north and south pole? $\endgroup$ – Michael Kutz Sep 9 '18 at 13:18
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Your hero can simply use a plumb bob.

plumb bob

Until the modern age, plumb-bobs were used on most tall structures to provide vertical datum lines for the building measurements. A section of the scaffolding would hold a plumb line, which was centered over a datum mark on the floor. As the building proceeded upward, the plumb line would also be taken higher, still centered on the datum.

During the descent to the center and during the climb on the other side, thanks to the shell theorem your hero won't have to care about the mass of Earth above him. The plumb bob will always point to the center of mass of the part of the planet beneath their feet.

Once they reach the center, they simply have to turn it around.

To know when the center has been reached, it is sufficient to hang a mass to a spring of known elastic constant. Since the weight of the mass will decrease until reaching zero at the center, the deformation of the mass is a good indication of the reached depth.

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    $\begingroup$ Also, for several reasons, Plumb Bob is a good name for this hero. + $\endgroup$ – Willk Sep 9 '18 at 18:21
  • $\begingroup$ Fun point: within a homogeneous sphere the gravity felt will decrease linearly with the radius to the centre point, so calculating depth is even easier! Navigating the central region where Plum Bob’s own motions are the largest force acting on his instruments will require a bit of dead reckoning though. $\endgroup$ – Joe Bloggs Sep 10 '18 at 15:02
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Which North and South Pole? There is a geographic and a magnetic one. it even moves...

I'd say it depends on his powers. If he's in a protected bubble only, I'd say he'll be shifted around by the currents of the core, so he can't. If he can keep the whole tunnel fixed, it should just be to follow straight in relation to the earlier parts of the hole. Assuming he know the direction to start off in.

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    $\begingroup$ Just to add to the confusion, there is more than one north pole. There's the Geographic, the magnetic, north geomagnetic pole, the pole of inaccessibility (furthest point from land) and of course, North Pole, Alaska, which doesn't count as a pole. $\endgroup$ – gwally Sep 9 '18 at 17:13
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Assuming that the earth is spherical enough that it is actually possible to have a straight line from the poles going right through the core, keeping a straight line could be easy.

Put up a strong light source (possibly laser) at the mouth of your hole, such that it cast a light beam to the center of your hole, then start digging such that the beam dot remains at the center of the tunnel.

You can also put intermediate relays in the tunnel to keep the light beam strong and visible.

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  • $\begingroup$ NASA uses lasers to measure the distance to the moon. Relays aren't needed. I'd by more worried about the effects of tunneling through the spinning core that keeps us safe from SMEs. $\endgroup$ – Michael Kutz Sep 9 '18 at 13:55
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    $\begingroup$ The OP specified that the superhero has a forcefield that protects himself and his equipment, not that the forcefield can maintain a tunnel thousands of kilometres long. As soon as the (somehow) digging superhero moves past a point it will fill up behind him - initially with water (he started at the north pole, which is water under the ice cap, then with rock, then with molten rock etc $\endgroup$ – KerrAvon2055 Sep 9 '18 at 13:56
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    $\begingroup$ @KerrAvon2055 Hmm... Didn't actually thought of that. Hope the superhero doesn't get us killed. $\endgroup$ – V.Aggarwal Sep 9 '18 at 14:10

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