Strange Journey

This will seem strange, like something out of The Rime of the Ancient Mariner.

For the past few weeks I’ve been adapting my orbital simulation model to calculate the tidal forces at the surface of the Earth due to Sun and Moon gravitation, as well as the rotation of the Earth. One effect of the rotation of the Earth is that there is a centrifugal force, CF, acting outwards from the Earth’s axis everywhere on its surface. In the northern hemisphere, the sum of this centrifugal force and the Earth’s gravitational force, GF, produces a small resultant force, RF, in a southerly direction in the plane of the Earth’s surface. And this small force, constantly acting on a body on the surface of the Earth, would act to gradually accelerate it southwards across the surface of the Earth.

That we don’t see things moving southwards the whole time in the northern hemisphere is probably because most things are restrained by strong forces of friction, because the Earth is not a perfectly smooth sphere. But what if there were no frictional resistance? What would we see happening? If we started our journey in the middle of England, where would we end up?

In my model I simulated this journey with a ball-bearing which was dropped onto the surface of the Earth, and allowed to just keep on frictionlessly bouncing on its surface. My journey started just outside the village of Hurley, northeast of Birmingham, at 52.567ºN, -1.632ºW. As expected, the bouncing ball-bearing gradually began to accelerate southwards.

Fairly soon, it had travelled all the way south over England and out into the English Channel (completely frozen over for this experiment).  As it did so, it began to swing surprisingly westwards, moving in an arc first over Brittany in France, and then towards Galicia in Spain. The blue track in my simulation map (right) shows the curving path. This is the effect of the coriolis force, which acts in the northern hemisphere to turn southward-moving  bodies to the right.

By the time we passed over Galicia, in NW Spain, the effect of the coriolis forces acting along the way had shifted the direction of travel strongly towards the south-west.

And thence we continued, out over the flat frozen Atlantic ocean, passing just west of Madeira.

On and on we travelled, until finally we made landfall west of Cayenne, French Guiana, in South America. By now we were almost travelling westwards.

We continued over the state of Amazonas in Brazil, and finally departed South America on the coast of Peru, a little south of Lima, and headed out over the frozen plains of the South Pacific.

And now that we were in the southern hemisphere, both centrifugal and coriolis forces began to operate in the opposite sense that they had in the northern hemisphere, and we began to slow, and to turn southward.

Finally, at -52.564ºS, -117.732ºW, while heading directly south, we came to a stop, far out in the South Pacific ocean. But this was no place to get off. We had started at 52.567ºN, and now we’d stopped at almost exactly the same southern latitude. And it became clear that the trajectory of the ball-bearing was just like the swing of a pendulum – and now that we had come to a stop in the southern hemisphere, we would next head northward back to the northern hemisphere.

And this is exactly what happened. We began to move northwards. But instead of retracing our journey eastward, we continued moving westward.

Moving northwest over the Pacific, we passed over the atoll of Maupiha’a, in French Polynesia, which was completely deserted aside from a single house.

And we passed between the deserted atolls of Taka and Utrik in the Marshall Islands.

And when we’d finally completed the crossing of the Pacific, it was a tremendous surprise to pass right over the middle of Tokyo, Japan.

And thereafter we passed right over Japan and out across the sea of Japan, making landfall on the Asian continent just east of Vladivostok.

By now we were beginning to slow and swing northwards. For a while it looked like we would come to a halt somewhere in the wilds of Mongolia, and be arrested by Chinese police.  But instead we just managed to limp across the Amur river, which divides Russia from China, and landed on the northern Russian side, at 52.559ºN, 126.167ºE, a mere 150 m from the frozen river, to be arrested there by waiting surly Russian police instead.

The journey had begun on Julian date 2457687.60 ,and ended on Julian date 2457689.24056975. So it had taken exactly 1.64056975 days, or 39.373674 hours. During that time we had travelled from 52.56ºN to 52.56ºS, and back again. And we had traversed 232.2 degrees of longitude. When I checked our speed as we passed over Taka atoll, I found we were doing 400 m/s, or 895 mph.

And all this without any expenditure of fuel energy whatsoever, by simply reducing frictional resistance to zero, and allowing tiny centrifugal and coriolis forces to do the work of accelerating and decelerating bodies. We didn’t even use sails.

If it could have been arranged that the point of departure was also the final destination (and maybe it could be), it would have been possible to consider a low energy (and carbon-neutral!) north-south transit system along these lines, with trains arriving and departing at exact times, and returning a day or two later. The trains would probably need an auxiliary engine of some sort – a 125 cc Lambretta engine would probably suffice.

And that was the strange journey I took today.

I told you it was going to be strange.

I hope it made a tiny bit of sense.

…

Here’s the track through the southern hemisphere:

And here’s the departure from England, and the arrival on the banks of the Amur river.