Plumb bob question

[bilcoy]

I was reading in my geology book (Earth: An Introduction To Physical Geography, 7th ed. by Tarbuck and Lutgens, 2002, p.560) that "during the first survey of India, an error in measurement occurred because the plumb bob on an instrument was deflected by the massive Himalayas." There is more detail on this, but this statement on deflection is allowed to stand.
Am I crazy, because this just seems wrong to me? I understand that a plumb bob always points to the earth's or any body's center of gravity, no matter the shape or lack of uniformity in density of the body or where the plumb bob is situated. I do understand the "outside" influences, like the changing position of the moon, could compromise the pb's results, but not features of the body itself, which are part of the net mass.
Am I wrong about this?

[Studiot]

I understand that a plumb bob always points to the earth's or any body's center of gravity, no matter the shape or lack of uniformity in density of the body or where the plumb bob is situated.

Not really.

The plumb bob is affected by both the attraction of local masses and the rotation of the earth. The latter effect is embodied in Focaults Pendulum experiment.


Welcome to PF, are you studying Physics or Geology?

[bilcoy]

Well, the influence of rotation is not the issue. As I said, it's the MOUNTAIN! Can the mountain be part of the net effect and also have special local influence?

[Cleonis]

I was reading in my geology book (Earth: An Introduction To Physical Geography, 7th ed. by Tarbuck and Lutgens, 2002, p.560) that "during the first survey of India, an error in measurement occurred because the plumb bob on an instrument was deflected by the massive Himalayas." There is more detail on this, but this statement on deflection is allowed to stand.
Am I crazy, because this just seems wrong to me? I understand that a plumb bob always points to the earth's or any body's center of gravity, no matter the shape or lack of uniformity in density of the body or where the plumb bob is situated. I do understand the "outside" influences, like the changing position of the moon, could compromise the pb's results, but not features of the body itself, which are part of the net mass.
Am I wrong about this?


I'm assuming for now that among the data collected by the surveyors was altitude data.

I'm assuming for now that the surveyors work out altitude data as follows: they start in a coastal area, referencing local altitude to sea level. Then they work in inland direction, working out everywhere (from the measurments) whether the next data point is at a higher altitude than the previous one, or lower, or equal. So at every data point they need to establish the local vertical, and then you measure the angle between that local vertical and the line to the next data point.

That procedure is perfectly reliable on a planet that is a perfect reference ellipsoid (with perfectly uniform density). On such a perfect planet the direction of the local vertical is perfectly predictable: perpendicular to the reference ellipsoid. That allows you to process surveying data: It will allow you to figure out which parts of the inland are above or below sea level.

I gather from your question that in the neighbourhood of the Himalaya the local direction of gravity (hence the local vertical) is significantly deviated from being perpendicular to the reference ellipsoid.

[bilcoy]

"That procedure is perfectly reliable on a planet that is a perfect reference ellipsoid (with perfectly uniform density). On such a perfect planet the direction of the local vertical is perfectly predictable: perpendicular to the reference ellipsoid. That allows you to process surveying data: It will allow you to figure out which parts of the inland are above or below sea level.

I gather from your question that in the neighbourhood of the Himalaya the local direction of gravity (hence the local vertical) is significantly deviated from being perpendicular to the reference ellipsoid."

Thanks. I appreciate your explanation which I think fits with what the authors of the text book were saying, but to me it is counter intuitive to think that there could be such thing as a "local" deviation from vertical at all, when the the mountains are part of the net-mass center of gravity to begin with. I was hoping that some principle (I can't do the math) would explain that the center of gravity, as a point in space, alone controls the plumb bob.

[Cleonis]

to me it is counter intuitive to think that there could be such thing as a "local" deviation from vertical at all, when the the mountains are part of the net-mass center of gravity to begin with.


I wonder...

You see, if you would be considering the gravitational force from the Earth exerted on the Moon, keeping the Moon in its Earth orbit, then the exact position of the Himalaya with respect to the Moon is a negligable factor; the gravitational force exerted on the Moon points to the Earth's center of mass; for the Moon the Himalaya are just a contribution to the overall Earth mass.

I wonder, maybe you are extending that notion to Earth based measurements (which is unjustified), making you believe that wherever you are on the surface of the Earth, gravity ought to act towards the Earth's center of mass.

[Studiot]

Hello Cleonis,

With regard to your comments about the local vertical to the Geoid.
The equipment used in the Great Survey (of India) used spirit levels to establish local horizontal in much the same way as modern theodolites.
Similarly the local vertical was then mechanically established within the instrument as a function of its operation.
Plumb bobs were used to locate the instrument above a reference point - they did not have the modern optical plummets used today.

So the error would have been in plan position, not vertical alignment.

[Doc Al]

Am I crazy, because this just seems wrong to me? I understand that a plumb bob always points to the earth's or any body's center of gravity, no matter the shape or lack of uniformity in density of the body or where the plumb bob is situated.
That's not true. You are thinking that the plumb bob will always point towards the center of mass of the entire earth including the mountain, but no. Ignoring the earth's rotation, the plumb bob always aligns with the local gravitational field. If you are close to the mountain, then the local gravitational field will be deflected towards the mountain.

[bilcoy]

That's not true. You are thinking that the plumb bob will always point towards the center of mass of the entire earth including the mountain, but no.

Yes, OK. I see that my assumption was wrong. It just occurred to me that a dumbbell shaped mass would have a net center of gravity, but a plumb bob constructed on either end would point the center of nearest "bell".
Thanks to all that responded.

[Studiot]

It would still have been more useful to know what your point of interest is. Replies might have been more forthcoming.

Are you aware there is also an Earth Sciences section here?