Would a gyroscope have solved the longitude problem?

Question

So I was thinking about the longitude problem, which was the problem of determining the longitude at sea. It caused great problems in sea navigation. See: https://en.wikipedia.org/wiki/Longitude#Determination

Ultimately it was solved by proper clocks I believe. And I wondered if it could also be solved by a continuously running gyroscope that was started (and resetted) at ports where the longitude was known. Would this have solved the problem? Could it even practically be done? Maybe you could've used mirrors to measure small angles like in the cavendish experiment. It would need to be regularly sped up but maybe you could've used something like a weight-falling device.

Answer 1

I think so. One procedure would be as follows. First calibrate the gyroscope: at a known longitude, face due North with the gyroscope frame fixed in front of you and, after starting the gyroscope's rotation, measure the angle of the rotor within its frame when the sun or a reference star is at its zenith. Repeat this for several days in a row at the same location, measuring the angle of the rotor within its frame whenever the sun or star is at its zenith, in order to determine the effect of torque or frictional loss of degrees per day (i.e. how many rotational degrees are lost on average when the earth rotates once). Having calibrated the gyroscope in this way, you can now move eastward or westward over the globe from the initial location and measure the angle of the rotor just as you did during calibration, whenever the sun or star is at its zenith. If you have moved eastward by 3 degrees, the rotor should have rotated counterclockwise within its frame by three degrees as compared to its expected location after correcting for torque/frictional loss; and if you have moved westward by 3 degrees, the rotor should have rotated clockwise within its frame by three degrees as compared to its expected location after correcting for torque/frictional loss.

Answer 2

With simplifications, to help visualize:

On the equator of a non-rotating globe at 0° of longitude, set a gyro spinning with its axis horizontal, and aligned east-west. If the gyro is free from drift, and has frictionless gimbals, as we transport it along the equator, its angle from local vertical is a direct readout of longitude.

But if the globe spins, as does our Earth, even if the gyro remained at its initial location, its axis would make full rotations (in a vertical plane) with a period of one sidereal (or inertial) day.

Even with a perfect gyro, we would still need a very accurate clock to find longitude from it.

Answer 3

They could already measure the ship's absolute orientation by looking at the fixed stars, so I don't think a gyroscope would have helped. The difficulty is that you cycle through a set of absolute orientations over the course of a day, and that set is a function of latitude but not longitude (it corresponds to one of the parallels). Longitude only affects the phase, and to detect a shift in the phase you need a reference signal that doesn't shift, which is what an accurate clock is.

The position of the sun relative to the fixed stars can be used as a clock in principle, and a gyroscope could be calibrated to a star at night and then compared to the sun during the day. But I suppose it would be easier and more accurate to use the moon, which doesn't require the gyroscope. They actually did use the moon for a while.