How Does Mass Influence Gravity?

[PWiz]

What is the definition of 'to fall' ?

To move along a geodesic path is spacetime.

 

[jerromyjon]

OK, hang on a minute, I had thought from this thread that the force of gravity is influenced by the mass of the two objects and their distance apart. Vacuums and magnetic fields are not relevant if I have understood correctly.

You are fine.

Furthermore, how can a Cannon Ball and a Feather possibly 'fall to Earth' or anywhere else if they are in a vacuum ?

This shows very little understanding.

 

[GlobalHealer69]

But the feather and cannon ball are just within a vacuum, no mention of gravitational forces from elsewhere. May I suggest the question be rephrased with regard to where these objects in question are in relation to time and space and not merely somewhere in a vacuum 'falling to Earth'.

 

[robbertypob]

The feather and cannonball are in a vacuum chamber on Earth. So Earth's gravity is the only force working on them. The vacuum removes the 'distraction' of air resistance for this purpose.

 

[jerromyjon]

Simple; neither the Cannon Ball nor the Feather have their own Magnetic field.

I assure you they do, but this is irrelevant to gravity.

You are obviously not familiar with this forum, or how threads function. Start a new thread with your question, stated as clearly as you can, and what you don't understand about it, and you will be guided to an understanding.

 

[GlobalHealer69]

That part isn't quite "figured out" yet. Gravity between 2 atoms is virtually undetectable and gets into very complicated models of quantum physics.

So if we consider masses such as planets as atoms on a larger scale.....?
How can we be sure about gravity at all ?

 

[GlobalHealer69]

What is Gravity ?

Does mass dictate the strength of gravity or attraction and repulsion ? If so, what about size and density of a collapsed star compared to say a similar body twice it's size or more but lighter in weight ?

[Mentor's note: Post edited by moderator]

 

[PWiz]

What is Gravity ?

It is intrinsic spacetime curvature. You have to construct the stress-energy tensor for an object first, and then set up the required partial differential equations after taking into consideration the charge, angular momentum and other characteristics of the object and use the EFE:
$R_{μν} - \frac{1}{2} g_{μν} R = 8πG T_{μν}$ (setting c=1 and ignoring the cosmological constant [a vacuum solution])
Where $T_{μν}$ is the covariant version of the stress-energy tensor, $R_{μν}$ is the Ricci curvature tensor (the contraction of the Riemann curvature tensor), $g_{μν}$ is the metric tensor and $R$ is the trace of the Ricci tensor.
The Riemann curvature tensor (which is what really measures the intrinsic curvature of the manifold) is dependent on the Christoffel symbols, and the Christoffel symbols are in turn depend on the metric tensor in a complicated way. The eventual goal is to find an expression for the metric tensor using the stress-energy tensor. In some cases, an exact solution is obtained. In other cases, numerical analysis must be used. Once you have the metric tensor, you can perform all sorts of calculations, and get the "rectified" version of the behavior of objects in the presence of other massive objects.
I recommend that you start a new thread on this if you want a more detailed answer.

 

[rumborak]

So if we consider masses such as planets as atoms on a larger scale.....?
How can we be sure about gravity at all ?

Exactly how you know there's light because of the sun, but it takes a special apparatus to show the existence of photons.
Just because something is hard to measure doesn't mean it no longer exists.I must say this thread has gone quite off the deep end. It mixes the most basic of basic questions about gravity with stuff like Riemann tensors. I can guarantee that everybody is essentially lost at this point.

 

[jerromyjon]

with stuff like Riemann tensors. I can guarantee that everybody is essentially lost at this point.

Nah, I don't understand the math exactly, but I'm not lost either. Going from Newtonian to Einsteinian physics takes a big leap in mathematics but a very small change in forces. Instead of gravity being a force that attracts mass, it is a force that warps space, which causes mass to "roll downhill" through space.

 

[Drakkith]

Something is confusing me...

1. If I drop a cannonball and a feather in a vacuum they will fall to Earth at the same rate. The mass and size of the objects do not appear to be affecting the 'strength' of the gravitational force acting upon it.

2. The Earth's gravity is stronger than the Moon's, because the Earth is more massive.

How can both these statements be true? I must be missing something. It looks like mass doesn't matter in the first statement but in the second statement it does?!

Please help!

If you're still wondering, it may help to see some numbers.
See my post here, especially the last few paragraphs: https://www.physicsforums.com/threads/object-falls.815279/page-2#post-5144985

 

[rumborak]

Let's get back to the basics here.

Acceleration (the $a$ in $F=ma$) IS the rate of falling.

The rest of your post notwithstanding, am I the only person who finds this wording ambiguous? To me, "rate of falling" could mean either speed or acceleration.

 

[Bandersnatch]

The rest of your post notwithstanding, am I the only person who finds this wording ambiguous? To me, "rate of falling" could mean either speed or acceleration.

Yes, I understand your objection. However, I chose 'rate' consciously, sacrificing precision for clarity. It was tailored for the OP, who appeared to have a fundamental issue with wedding acceleration from the equation with the concept of falling. It didn't matter for me to say what exactly is acceleration, and I didn't want to spend time and attention of this specific reader in order to explain the difference between acceleration, velocity, and position, their relation, and which one is normally called motion etc. As such, 'rate of falling' is broad enough to encompass motion in general, and not technical enough to exclude one aspect or another.
The issue at hand was the equality of gravitational and inertial mass, so I focused on that.

Perhaps that was a pedagogical mistake on my part, but it seems to have worked for its intended purpose.

 

[Darryl]

Yes I see what you mean!

Gravity is really interesting to me. It just seems to behave in a bizarre way (i.e. the force is actually stronger on the cannonball than the feather), although of course it makes sense when you look at the equations. Do we understand how gravity works at a molecular level? What specifically is happening to attract the two masses towards each other?

I think you could say that the force of Gravity is the same on each 'unit' of mass, equally (be it protons or whatever) and it does not matter if those units of mass are connected together or separate, or if there are more or less of them.
So the force at any point is the same (regardless of what is in that point of space), so a bowling ball could be there, or a feather or nothing. Even air is bound by it's force.

But it is very weak (compared to the other forces). The force of gravity is not 'stronger' on a more massive object, there just is more stuff to interact with it.