# How noticeable is the gravitational pull of a mountain range?

A massive object like a planet exerts a great gravitational pull on nearby objects. This will cause them to accelerate towards the center of the planet with the same acceleration regardless of their mass, if we disregard other forces such as air resistance.

How does objects "connect"?

Mountain ranges are of great mass, and I assume they exert a gravitational pull of some degree. If you could theoretically "lift" this mountain range of the face of the planet by as little as 1 meter, would objects then get attracted to it enough for us to physically feel it? If not, would it help to place this mountain in space so that the pull of the earth wouldn't counteract the mountain effect?

• The ffect will be negligible, the mass of the earth is far too great. However in empty space it'll have a better influence on you, but you'll feel light as a feather. – Lelouch Jul 10 '16 at 13:14
• Measuring a mountain's gravity in the 19th century en.wikipedia.org/wiki/Schiehallion_experiment. (Or at least trying to). – user108787 Jul 10 '16 at 13:56

The effect is noticeable even here on Earth, and in fact it has been used to measure the mean density of the Earth in experiments such as the Schiehallion experiment.

The principle is simple: take a pendulum. If there is no large-mass object nearby (such as a mountain), it will hang straight downward, pointing to the center of the planet. But if there is a large-mass object nearby it will pull the pendulum out of true.

In fact, with a sensitive enough instrument, it is possible to measure the gravitational pull of much smaller objects. In 1798 Henry Cavendish used a torsion balance to measured the gravitational attraction between balls of lead.

In space, the effect would of course be much greater because the predominant gravitational field of Earth wouldn't be there.

Update: clarification

I was quite sloppy with my last sentence, as CuriousOne correctly pointed out. Here's what I meant:

If you were able to detach the whole mountain from the surface of the planet and take it far from the planet itself, as it seems you are suggesting when you talk about "lifting" the mountain, the effect -the deflection of the pendulum- would indeed be greater. In fact, the gravitational pull exerted by the planet is proportional to $r^{-2}$, where $r$ is the distance from the planet's center. Since the deflection of the pendulum is (see here)

$$\theta = \arctan \left(\frac {F_M} {F_E}\right)$$

where $F_M$ is the force exerted by the mountain and ${F_E}$ the force exerted by the Earth, you can see that in this case the deflection would be greater.

If you took the mountain an infinite distance away from the planet (into deep space), the deflection would be entirely due to the mountain and you would of course have $\theta = \pi/2$ (the pendulum would point towards the mountain's center of gravity).

• I was about to give you a +1, until I saw the last sentence, which is utterly nonsensical. Of course the bulk effect of the rest of the planet is still there in space. The gravitational acceleration in low earth orbit is only a few percent smaller than at the surface, we can simply go into a circular or elliptic free fall around the planet without being stopped by the atmosphere or... worst case scenario, the surface. That doesn't make the relative force of a mountain any larger or easier to detect. It's actually harder because one has to be, at least, 180km away from the mountain. – CuriousOne Jul 10 '16 at 21:27
• @CuriousOne I think there has been a misunderstanding. I meant that it would be easier to measure the gravitational force exerted by the mountain if it was detached from the planet's surface and taken far from the planet itself. The gravitational pull of the planet would then be lower (being $F\sim r^{-2}$ and the deflection of the pendulum would be greater. Maybe I should explain this better, though. – valerio Jul 10 '16 at 22:29
• OK, that makes a lot more sense, even though it doesn't answer the OP's question, I believe. His scenario of "lifting the mountain" is based on a misunderstanding of what is going on. I would suggest to modify the last sentence to make it clearer. I will give you that +1, anyway. :-) – CuriousOne Jul 10 '16 at 22:33
• @CuriousOne I am editing the answer right now. I was in fact trying to address the part in which the OP talks about "lifting" the mountain, but it is not really clear what he means there... – valerio Jul 10 '16 at 22:35