How Does Earth's Gravity Accumulate?

[Mutsi]

Hello,

I am no Physicist nor studying anything near this field (I study Game Development).
Though I am greatly interested in Physics and try to learn as much as I can in my free time. To bad that there are only 24 hours in a day.

Anyway learning that everything with mass has gravity I came up with the following question and could not find the answer.

Everything with mass has gravity (according to general relativity) but how is this added. For instance: Earth is gigantic and thus we are drawn towards it. But if you would breakup Earth you would get little pieces of sand dust dirt water etc. All separate with very little mass. I asume that all these elements are added in Earth's gravitational force. But how about a human for instance. We stand on Earth as a single grain of sand lays on it. Are we then to added along with Earth's gravity?

I hope you can supply me with a satisfying answer.

Greetings,
Mitchel Disveld

 

[Bloodthunder]

You could. It wouldn't matter. the mass of the Earth is 5.9742 × 10^24 kg. Even taking the total mass of all humans on Earth (people to be ~6 billion, each person ~80 kg), we still only have ~5 x 10^11 kg.

We stand on Earth as a single grain of sand lays on it.

Well, the grain of sand will be attracted to you too, in whichever direction you are. However, the gravitational attraction you have to the sand is very small...

 

[Mutsi]

Bloodthunder you state that we are added to Earth's mass and still we have gravitational attraction on the grain of sand. Would that not make us a separate gravitational force then the grain of sand? Or is it so that all mases have a "private" gravitational force on all other masses and a "public" gravitational force which is all the "private gravitational forces" added to that "public" one?

 

[Bloodthunder]

Oops, sorry for the misunderstanding.

What I mean to say is, we can take the entire Earth, and everything on/in it, as a whole, to see how it is acting on this grain of sand.
Or we can take every particle on Earth individually and add them all up, taking into consideration the magnitude and direction of the attraction.

Both will add up to the same answer.

 

[Mutsi]

Thank you Bloodthunder. Now one question remains for me. Is it so that when matter is close enough to each other their gravitational forces are added?

 

[Skaperen]

Suppose you have a car which, even though its gearing is set in neutral, has just too much inertia and resistance for you to push it to make it roll. So you ask a couple friends to help you push it. With three of you pushing it, the car now rolls. Change the scenario to pulling the car instead of pushing it (maybe with attached ropes). So how is this pushing or pulling summed up? Is that something you understand or need to ask?

Gravity is just its own case of pulling. It's just very weak and requires a lot of grains of sand to pull you at the acceleration that Earth would.

 

[Skaperen]

Thank you Bloodthunder. Now one question remains for me. Is it so that when matter is close enough to each other their gravitational forces are added?

They are added, but in the sense that each is pulling the other. Two (nearly) equal masses would both be seen to accelerate toward each other. When you fall toward the Earth, the Earth is causing you to accelerate towards it, and at the same time you are causing the Earth to accelerate towards you. It's just that the latter acceleration is so extremely small and insignificant that we just ignore it. But when one of the masses is a significant fraction of the other, it can no longer be ignored.

 

[Mutsi]

Thank you Skaperen.
That clarifies it for me!

the Earth is causing you to accelerate towards it, and at the same time you are causing the Earth to accelerate towards you.

Can I conclude from the above quote that that also works with the third law of Newton (every action has an opposite and equal reaction) ? Cause I always wondered if that applied to gravity.

 

[Bloodthunder]

Yes. Equal in magnitude, with the 2 masses going opposite in direction.

 

[QuantumPion]

As can be derived using Gauss's law, a spherical object attracts external objects as though all of its mass were concentrated at its center. As long as you are standing on the surface of the Earth (i.e. external to the surface), then you are two separate objects attracted to each other.

 

[Cleonis]

Or is it so that all mases have a "private" gravitational force on all other masses and a "public" gravitational force which is all the "private gravitational forces" added to that "public" one?

Yes.
The gravitational pull we feel arises from the individual gravitational pulls of the particles that make up a particular lump of mass.

For every particle that makes up the Earth there is an individual tug on every other particle. Perhaps your thinking was more towards an idea that you need, say, a certain "critical mass" in order to have any gravity at all, with planets above that "critical mass", but grains of sand below it.
Well, there is no lower limit. Of course, with the gravity of individual particles being so weak it's only in the case of celestial bodies that it all adds up to something significant. But any mass, no matter how small, has a corresponding gravity.During 1797/1798 Henry Cavendish conducted the research that has become known as http://en.wikipedia.org/wiki/Cavendish_experiment"

In the setup Cavendish used a lead sphere with a mass of 158 kilogram as a primary source of gravity. (Actually, he used two of them, as the mechanics of his setup was a torsion balance.)

 

[Jake4]

I think a better way to think about it is that objects don't "have" gravity, objects are simply effected by other objects' gravity.I mean it in the sense that asking a person's personal gravitational effect is irrelevant without speaking about objects it has an effect on.

 

[pallidin]

Funny this should be brought-up.

The mass of the earth, and hence it's gravity, is constantly changing.
Though mostly on the "increase" side of the equation.

Our Earth's gravity pulls nearby space "gas", space "dust", etc... and incorporates that into a total of Earth's mass.
Then we have meteorites and such becoming part of earth.

On the other hand, we launch spacecraft to areas outside Earth's gravitational influence which thus reduces Earth's mass.

Importantly, nearly all of the above has a meaningless measurable difference on Earth's mass, except for collecting space gas/dust which, over vast time, can measurably increase total mass.