Understanding Gravitational Force: Exploring its Effects on Objects with Mass

[firewall]

What is gravational force? Is that every object with certain number of mass will have gravational force?

 

[whozum]

Any object with mass will experience a gravitational force from any other object with mass. It doesn't matter how much mass either object has.

Gravitation is an inherent attraction between objects with mass, supposedly due to some space-time curving neat stuff that someone more qualified will elaborate for you.

 

[Jameson]

I think gravity is one of many things that we have been able to describe but not fully understand. Why does gravity exist? What really causes it? There is the basic Newton equation to calculate it, but for me there is still so much mystery to it.

 

[Thinktank]

Just wondering...our planet Earth has gravity and every objects on Earth fall towards the Earth. So, it that possible we will know more gravity if we can study or explore the center of the earth?

 

[yourdadonapogostick]

the Newtonian equation is $$F=-G\frac{m_1m_2}{r^2}$$ where G is the gravitational constant and r is the distance between objects. if you want to get g, then the equation is $$g=-G\frac{m}{r^2}$$ where m is the mass of the object and r is it's radius. i see no advantage in going to the center of the Earth when it comes to studying gravity.

edit: crap, this forum doesn't appear to have the same LaTeX system as http://scienceforums.net

 

[fliptomato]

Thinktank--not only does our Earth cause a gravitational field, but every mountain, rock, piece of dirt, molecule, and massive particle making up our Earth does as well. So not only does every object on Earth fall towards Earth, the rest of the Earth is falling (albeit very slightly) towards every object (in the universe, not just Earth).

We know from observation that the gravitational force is attractive and acts radially from a source. That is to say that the gravitational force of the Earth pulls apples down towards the center of the Earth, not side-ways or pushing away.

We also know from observation that the gravitational field from a spherically symmetric object (such as our Earth and things like bowling balls and oranges) is also spherically symmetric. That is to say that it should look the same if we rotate the object. Why is this? Well, imagine you had a perfectly spherically symmetric object. If you rotated the object in any way, it would look exactly the same. Ineed, we would expect the physics of the object to be exactly the same. Thus, the gravitational pull of the object should itself be spherically symmetric.

What happens at the center of the ball bearing? If you "look" in any direction from the center of the ball bearing, the mass distribution is exactly the same. (By the spherical symmetry of the object.) That is, if I look in anyone direction, I see so-and-so length of material of so-and-so density, and if I look in any other direction, I see the same thing. Thus, we expect the physics to be the same in every direction (if it weren't, what could have caused one direction to behave differently from another?). Thus, at the center of the Earth, what do you think the gravitaitonal field will look like?

-Flip

 

[rbj]

i see no advantage in going to the center of the Earth when it comes to studying gravity.

you might be able to easily light your cigi's there. no need to bring your butane lighter.

maybe we wouldn't need rides in the "vomit comet" to test out weightlessness if we could go to the center of the earth.

edit: crap, this forum doesn't appear to have the same LaTeX system as http://scienceforums.net

it's different than wikipedia, too.

r b-j

 

[yourdadonapogostick]

maybe we wouldn't need rides in the "vomit comet" to test out weightlessness if we could go to the center of the earth.

wieghtlessness at the center of the earth? i don't think so. it obeys the INVERSE square law. that means, the shorter the distance, the less force. as the distance approaches zero, the force approaches infinity. $$\lim_{r\to0}\mathbb{F}_{grav}=\infty$$

 

[krab]

Approaches infinity only for a point mass. IOW, you need infinite density to get an infinite force. As you approach the centre of the earth, your weight decreases to zero, in a sense because all the other mass above you is pulling the other way, cancelling the force that's pulling you down.

 

[yourdadonapogostick]

yea, it would be zero. if you place yourself in the center, you would need to find the net force. you split the Earth into an infinite number of spheres that are tangental to the center and have a radius of .25 the radius of the earth. net force would be zero. i wasn't thinking about it that way. way different answers, wow.

edit:i should have known that, too. i once calculated the force of a ring of black holes and found that there is a place in the exact center of the ring where there is no force.

 

[Dr.Brain]

Gravitational Force is the result of the Gravitational Field and is not the inverse. Any object with mass will hinder spacetime around it with its Gravitational Field and when another object enters or is kept in this field , it experiences a push toward sthe first object an dthis push is called the Gravitational Force and is a result of the field.

BJ

 

[rbj]

wieghtlessness at the center of the earth? i don't think so. it obeys the INVERSE square law.

not inside the planet. you need to apply Gauss's Law and, assuming a constant density of mass, the strength of the gravitational field is directly proportional to r, the distance to the center.

anyway, it seems like someone else set you straight.

r b-j

 

[Thinktank]

Thanks for sharing. I also wondering is it possible to create an object with gravity? If we can create an object with huge gravity, does it mean we can create a black hole?

 

[wisredz]

theoretically, yes. For example if you could make the radius of the Earth close to 3 inches. You would have a black hole. Keep in mind that you should not change the mass. Practically we can't make a black hole.(as far as I know)

By the way, everything that is done by human has a mass, and therefore has a gravitation field... So your first question is kinda weird...

 

[yourdadonapogostick]

i wasn't aware that Guass's Law applied to gravity as well. what is it for the gravitational force?

 

[Thinktank]

Mmm..let me rewrite my first question...is this possible to create an object with a huge gravitation field

 

[yourdadonapogostick]

yea, dump a bunch of stuff on it.

 

[Danger]

Mmm..let me rewrite my first question...is this possible to create an object with a huge gravitation field

If you mean some kind of artificially high field without an increase in mass, no. Even a black hole still has only the total gravitational field of the original collapsed object, but it's extremely concentrated. If you could compress the Earth to black hole status, it would still keep the moon in orbit, but wouldn't start sucking Jupiter toward it.

 

[yourdadonapogostick]

the Earth DOES suck Jupiter toward it. :Þ

 

[whozum]

Gauss' Law for gravity is almost identical to the law for electrics. Its just a flux integral. You can find more info in it http://physics.smsu.edu/faculty/broerman/fall03/phy203/gauss1.htm .

 

[yourdadonapogostick]

thanx for the link

 

[Thinktank]

Sorry about i have so many questions...i want to know more about physics..however, i don't have a chance for the education...hope you guys can answer my silly questions...

Question: The gravational force base on mass of the obect. If both Earth and Jupiter become black holes, will the (jupiter) black hole suck the Earth (black hole)? Or both forces will pull each other and expand the space between them?

 

[yourdadonapogostick]

they will affect each other the same way they do now

 

[rbj]

i wasn't aware that Guass's Law applied to gravity as well. what is it for the gravitational force?

it's just like Gauss's Law for electrostatics when you make the corresponding substitutions. mathematically, Gauss's Law applies for any inverse-square field.

$$\oint_A \mathbf{E} \cdot d\mathbf{A} = 4 \pi G M$$

where $\mathbf{E}$ is the gravitostatic field and $M$ is the mass contained in the surface integral. the force on a small test mass $m$ in that field would be

$$\mathbf{F} = m \mathbf{E}$$

wikipedia has a link http://en.wikipedia.org/wiki/Gauss's_Law .

the reason the field get lower (proportional to $r$ ) when you're inside the planet is that the amount of stuff contained in the surface integral (the smaller sphere) is smaller.

r b-j

 

[Danger]

the Earth DOES suck Jupiter toward it. :<THORN>

No, it doesn't. They maintain a balanced relationship, along with all other objects. If the Earth's gravity was intense enough to pull Jupiter out of orbit, the moon, Mars, and Venus would already be in our laps.

 

[pallidin]

I would like to address the question with my limited physics knowledge(not to mention limited English grammar)

Anyway, I heard that you CAN increase the mass of an object by accelerating it.

Is that true?

 

[DaveC426913]

If both Earth and Jupiter become black holes, will the (jupiter) black hole suck the Earth (black hole)? Or both forces will pull each other and expand the space between them?

If Jupiter and Earth both turned into black holes - but did not increase their mass, then there would be no difference in how they interacted with each other.

Gravity is contingent on only two factors: the mass of the object and the distance to it. Black holes do not change this. The thing that makes black holes unique is that, with that same mass, they are much, much smaller. And that means you can get much, much closer. The closest you can get to the centre of the Earth is 6000km; the closest you can get to the centre of a black hole of that size is a few hundred metres. At that range, the gravitational force is way, WAY stronger (it increases 4x for every half distance).

 

[rbj]

I would like to address the question with my limited physics knowledge(not to mention limited English grammar)

Anyway, I heard that you CAN increase the mass of an object by accelerating it.

Is that true?

i suppose so. i think what you are asking about are the effects of special relativity. time, length (along the direction of motion), and mass all change as an object is accelerated to a velocity that is very fast (in the same order of magnitude as the speed of light). specifically, for mass,

$$m = \frac{m_0}{\sqrt{1 - v^2/c^2}}$$

where m is the mass that a "stationary" observe measures of an object that is moving past him or her at a velocity of $v$ and $m_0$ is the "rest mass" or the mass an observer who is moving along with the object observes.

r b-j

 

[pallidin]

i suppose so. i think what you are asking about are the effects of special relativity. time, length (along the direction of motion), and mass all change as an object is accelerated to a velocity that is very fast (in the same order of magnitude as the speed of light). specifically, for mass,

$$m = \frac{m_0}{\sqrt{1 - v^2/c^2}}$$

where m is the mass that a "stationary" observe measures of an object that is moving past him or her at a velocity of $v$ and $m_0$ is the "rest mass" or the mass an observer who is moving along with the object observes.

r b-j

Ok, so is the mass increase dependent on a specific range of accelerative velocity? Or, is the mass increase an inherent nature of acceleration, regardless of how small the acceleration?

 

[pervect]

"Relativistic mass" does increase with velocity, but invariant mass does not increase with velocity. See the sci.physics.faq

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Furthermore, the gravitational field of a moving object is MOST DEFINITELY NOT the gravitational field of a stationary object with a mass equal to the relativisitc mass of the moving object. The gravitational field of a moving mass is non-isotropic, for one thing. For another point, objects defintely do not become black holes if they move too fast.

An issue that makes it hard to talk rigorously about "the gravitational field of a moving mass" is that the idea of gravity as a force starts to fail when objects move at relativistic velocities. This demands a treatment of gravity as curved space-time rather than as a force, which requires a significant amount of math to explain properly.

 

[BoTemp]

Ok, so is the mass increase dependent on a specific range of accelerative velocity? Or, is the mass increase an inherent nature of acceleration, regardless of how small the acceleration?

For velocities much smaller than c, mass can be treated independently from velocity, since the denominator is approximately
1, but strictly speaking, any object has mass determined by the formula above,
no matter what velocity it has.

Special relativity tends to deal in inertial (non-accelerating) reference frames,
so I'm not sure if that formula holds for a mass of non-constant velocity.
Any SR experts want to help me out? I'm a bit curious myself.