Question from a child that I was unable to answer

[Derek Smith]

I was explaining gravity, or rather its effects, to a 12-year-old. No problems up until question time.

If things 'weigh' less the further they are from the centre of gravity, will an elongated object, such as a 1,000 mile pin, weigh less if stood on end rather than placed horizontally on the ground. After all, almost all of the pin stood on end would be further from the centre of gravity.

I didn't answer, other than to say it was a good question, as there would have been a follow up of the dreaded: Why?

[Hugo a Gogo]

because gravity depends inversely on the square of the distance, it's further away, it weighs less

remember you are starting not at 0 for ground level, but at 4000 miles from the centre of the earth, and the centre of the 1000 mile pin is only 500 miles further away

[Foliage]

Yes, because it does. Also try not to confuse, weight and mass.

[V40Vinnie]

Weight is Mass X 9.8 or something like that on earth

[55palfers]

This pin. How many angels were dancing on its head?

[CrutyRammers]

The closest end would have more force acting on it than the furthest. But unless the difference in force was enough to pull it apart, the pin would be accelerated as a single object and hence all effectively weigh the same at both ends....I thunk.

[Fastchas]

CrutyRammers said:

The closest end would have more force acting on it than the furthest. But unless the difference in force was enough to pull it apart, the pin would be accelerated as a single object and hence all effectively weigh the same at both ends....I thunk.

I concur.

[MiggyA]

CrutyRammers said:

The closest end would have more force acting on it than the furthest. But unless the difference in force was enough to pull it apart, the pin would be accelerated as a single object and hence all effectively weigh the same at both ends....I thunk.

Your first sentence is correct but the second one isn't really. Maybe put it this way: think about a pile of bricks rather than a single object. Pile them up high and hopefully it's clear that the ones at the top weigh less than the ones at the bottom, even though they're all pushing down through each other? Would adding mortar to bind them together change that? Of course not. Same situation with the atoms making up this theoretical pin. It doesn't have to be pulled apart for the thing to weigh less when stood on end.

[SpeckledJim]

The upright pin would weigh less. The centre of gravity of the pin has been moved 500 miles further from earth, so the gravitational force between earth and the pin is diminished.


Compounding this (but a separate phenomenon) is, assuming you haven't stood the pin upright on the north or south pole, the fact that the top of the pin is effectively being 'flung' toward space by the rotation of the earth. So lessening its weight further.

[Davel]

I'm so glad I'm thick...

[dxg]

But is the conveyer belt that this pin is resting on running towards or away from earth?

(More seriously, isn't gravity one of the few remaining forces that we just don't understand? We can measure and model it, but do we know what actually causes it?).

[Eric Mc]

If you have a long elongated object with one end pointing at the earth and the other end pointing away, it indeed will experience a different gravitational pull between the end towards the earth compared to the end away from the earth. This is known as the gravitational gradient and can be made use of to stabilise objects in earth orbit, such as artificial satellites.

It is also this gradient that gives rise to the tides and, in an extreme case, such as near a black hole, will stretch an object into a long line of molecules.

[Cotty]

Makes me think of the space elevator, like the pin but on a much bigger scale
https://en.wikipedia.org/wiki/Space_elevator

[Hugo a Gogo]

that's different, using geostationary orbit to balance it, not really to do with reduced gravity

[SpeckledJim]

Hugo a Gogo said:

that's different, using geostationary orbit to balance it, not really to do with reduced gravity

It's a similar principle though. If the vertical pin's length was over double that of it's geostationary orbit height, then it would be so 'weightless' at ground level that you would have to tether it to the ground to stop it taking-off.

That's not something that would happen to the same pin lying horizontally on the ground.

So it demonstrates the principle that 'heavy stuff' weighs more/less depending on its position relative to earth.

[paul789]

It's a great question for a 12 year old.

Incidentally, my oldest asked a similar (but superior) question when she was 11 and a half. We were on holiday in Elevenerife at the time.

[Eric Mc]

Bank in 1966, one of the Gemini space flights (Gemini 11) tried an experiment with its Agena target vehicle. They attached a tether and then allowed the two craft to drift apart to see if they would establish a stable relationship due to the gravity gradient.
It kind of worked but they hadn't taken into account the elasticity of the connecting tether - which cause the two craft to oscillate in and out a bit.
The two astronauts on board the Gemini were not terribly happy with the way the two combined craft seemed to be developing a mind of their own.

[Derek Smith]

I now feel better about not being able to give an answer off the cuff as no one else has been convincing.

I was pleased with the question as it showed I'd been listened to. Shouldn't the answer be obvious, though?

My physics teacher taught that that there are three ways to transfer heat, conduction, convection and radiation. I asked which one is in use when I blow on a cup of tea to cool it.

He told me to work it out myself, then go back to him with the answer.

[Eric Mc]

What hasn't been explained?

If a long object is in orbit around a planetary body and one end is pointed directly at the centre of the planetary body with the other end pointed directly away, the long object will experience a stronger gravitational pull at the end nearest the planetary body and a proportionally weaker pull at the end furthest away from the planetary body.

The difference between the strength of the gravitational pull between either ends is what I described above as "the gravitational gradient".

[SpeckledJim]

Derek Smith said:

I now feel better about not being able to give an answer off the cuff as no one else has been convincing.

That's a bit brusque, Derek. The answer has been clearly stated several times.

The crux of the question is in the term 'centre of gravity'. That is the place where an object's gravitational force is centred.

The strength of gravity is a function of the mass of the objects, and the distance between their centres of gravity.

When you stand the pin up, you move its centre of gravity away from Earth's centre of gravity. In doing so the gravitational force between the objects reduces.

Just as the gravitational force between earth and the moon is stronger that between the earth and any more distant moon-sized bodies.