Plumb Bob Problem at 34.5° North Latitude

[merksican]

A plumb bob does not hang exactly along a line directed to the center of the Earth's rotation. How much does the plumb bob deviate from a radial line at 34.5° north latitude? Assume that the Earth is spherical.

I have no idea where to go or what to do.

Thanks

 

[Delphi51]

Something to do with precession?

 

[nlightner]

for bringing this interesting problem to my attention. I would approach this problem by first understanding the concept of plumb bobs and their use in determining vertical lines. A plumb bob is a weight attached to a string, and it is used to determine a vertical line by hanging it from a fixed point. In theory, the plumb bob should hang exactly along a line directed to the center of the Earth's rotation, which is known as the radial line.

However, due to the Earth's rotation and its shape, the plumb bob will deviate from the radial line at 34.5° north latitude. This is because the Earth is not a perfect sphere, but rather an oblate spheroid with a slightly flattened shape at the poles. Additionally, the Earth's rotation causes a centrifugal force that pushes objects away from the axis of rotation.

To calculate the amount of deviation of the plumb bob from the radial line at 34.5° north latitude, we can use the formula for the deflection of the vertical. This formula takes into account the latitude, the Earth's rotation rate, and the shape of the Earth's surface.

After plugging in the values for 34.5° north latitude and assuming the Earth is a perfect sphere, we can calculate that the plumb bob will deviate from the radial line by approximately 0.37 degrees, or about 0.0065 radians.

It is important to note that this deviation is relatively small and may not be noticeable in everyday situations. However, it is crucial to consider these factors when conducting precise measurements or experiments that require accurate vertical lines.

In conclusion, the plumb bob problem at 34.5° north latitude is a result of the Earth's rotation and its oblate spheroid shape. By understanding these factors and using the appropriate formula, we can calculate the amount of deviation and account for it in our scientific work.