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62 views

Why do we not have devices like inductors or capacitors to hold gravitational field? [closed]

I know that a capacitor can store electric field and an inductor can store magnetic field. So is there a way that gravitational field field can be stored in any such device. Also we do not have a law ...
7
votes
4answers
2k views

Can Newton’s law of gravitation be derived from Coulomb’s law? [duplicate]

I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another ...
1
vote
1answer
153 views

Newton's “Shell theorem” in higher dimensions

In Newtons's shell theorem, the net gravitational force is zero inside a hollow sphere, if the gravitational force is proporional to $1/r^2$. In 2D, the net force is zero inside if the force is ...
0
votes
1answer
110 views

The Gauss's law for gravitational field and the unit system

Here $g$ is the gravitational field, $G$ is the gravitational constant, and $M$ is the total mass in the volume $V$. I wonder if this formula holds for any unit system. That is, does the coefficient $...
2
votes
2answers
56 views

References on how dimensionality relates to inverse square laws

https://en.wikipedia.org/wiki/Spacetime#Privileged_character_of_3.2B1_spacetime Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions? Why are so many ...
1
vote
2answers
287 views

Gravitational potential inside a long but finite cylinder

Suppose a cylinder of length $\ell$, radius $R$ with a bore hole through its long axis of radius $r$. How can the gravitational potential (not the gravitational field) inside the cylinder be derived. ...
2
votes
2answers
342 views

Gauss's Law for Gravity to find the Gravitational field of a finite rod

To find the gravitational field at Point P in the figure: One solution is to draw the field of a mass $$\mathrm{d}\vec{g} =\frac{G\,\mathrm{d}m}{r^2}$$ and integrate over $\mathrm{d}m$, adding ...
-1
votes
2answers
277 views

What conservation law is implied by the symmetry between Newton's law of gravitation and Coulomb's law?

My question relates to Noether's theorem, which I've recently been reading about, and I couldn't find any good answers on the internet relating a conservation law to the symmetry between Newton's law ...
2
votes
0answers
62 views

Is the gravitational field $\mathbf{g}(x)=-G\int_{\Bbb R^3}\rho(y)\frac{x-y}{|x-y|^3}\,\mathrm{d}y$ continuously differentiable?

I apologize for mathematician-style question, but I was wondering if for continuous mass density $\rho:\Bbb R^3\to\Bbb R$ with compact support, the gravitational field $$\mathbf{g}(x)=-G\int_{\Bbb R^3}...
3
votes
4answers
490 views

Help understanding the divergence theorem as it relates to Gauss' Law

I don't see why Gauss' Law holds for volumes that contain no source or sink. I am trying to understand Gauss' Law as a general effect of any vector field, so I would appreciate if any answers do not ...
0
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2answers
118 views

Calculus problem, fluid dynamics with Gauss's form of gravity

Is this derivation correct? $$\frac{\partial\rho}{\partial t}=-\nabla\cdot(\rho \overline{u})\qquad (1)$$ $$\nabla\cdot \overline{g}=4\pi G \rho \qquad (2)$$ If we differentiate with respect to $t$ ...
0
votes
1answer
283 views

Gauss' law of gravitation for a spherically symmetrical shell

I have been trying to figure out how Gauss' law of gravitation implies that the gravitational field within a spherically symmetrical shell is zero. I have spent a very long time thinking about this ...
0
votes
1answer
1k views

Deriving the gravitational field strength within a solid uniform sphere

I am struggling to derive the gravitational field strength within a solid sphere. I am considering a point a position vector $\textbf{r}$, and a small mass element of the sphere within, at a position ...
0
votes
1answer
1k views

Divergence of gravitational field

Intuitively, why is the divergence of the gravitational field zero outside a planet but non-zero inside it? Outside it feels 'obvious' but when I actually think about it I don't really get it.
0
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3answers
82 views

Go deep to get light(er)? [duplicate]

I happened to look upon a section of Yakov Perelman's Physics for Entertainment, part I, the author was discussing the relation with distance from centre of earth, and the attraction. When $d>r_{...
-2
votes
3answers
141 views

Why does the differential form of Gauss' law gives $div\vec g=-4\pi G \rho=0$ outside the earth, when in fact it isn't zero?

Say we want to calculate the gravitational force at a point outside a mass and consider the differential form of Gauss' law: $$\text{div }\vec g=-4\pi G \rho$$ where $\vec g$ is the acceleration at ...
-1
votes
2answers
284 views

Can one use Gauss' law to calculate the gravitational field around an arbitrary (continuous) mass ditribution?

Consider an arbitrary mass distribution. Can we use Gauss' law to calculate the gravitational field around the mass? Or can we apply Gauss' law only in cases where in Gauss' law we can take $\vec g$ ...
3
votes
0answers
47 views

Inverse square laws & dimensionality [duplicate]

I have been thinking about the famous Inverse square-laws and how they came out to be that way. Gauss's law elegantly describes the square law for electricity to spherical distribution. Now I am ...
5
votes
2answers
468 views

Gravitational field within hollow cylinder

Gauss says that there should be no field within a hollow shell, spherical or cylindrical. But when I integrate the contributions to gravitational potential from a cylindrical shell to an off-axis ...
1
vote
3answers
334 views

How would Newtonian gravity work in a 1-dimensional universe?

I have come across the idea of gravity in different dimensional space. From the standard formula for gravity $F=\frac{GMm}{r^2}$ I have found that the $1/r^2$ term is a result of a three dimensional ...
0
votes
1answer
310 views

Is the curl of the gravitational field required to fully describe Newtonian gravity?

We are familiar with Newton's law of gravitation: $$\textbf{F} = \frac{-GMm}{r^2} \hat{\textbf{r}},\tag{1}$$ which leads to a gravitational field strength relation: $$\textbf{g} = \frac{-GM}{r^2} \...
2
votes
2answers
295 views

The inverse square law [duplicate]

Why the nature has chosen the inverse square law. For instance, the gravitational force as well as the Coulomb force is inversely proportional to the square of distances. Why not these forces are ...
0
votes
1answer
106 views

Gauss's law: divergence and mass density

I'm watching Leonard Susskind's lectures on relativity (http://www.youtube.com/watch?v=s8UrYIZhm60&feature=youtu.be&t=31m08s), and he just introduced Gauss's law on gravity, that is: $$\vec\...
-1
votes
1answer
53 views

Is there a connection between Newton's law of universal gravitation and the area of a sphere? [duplicate]

According to Newton, the force between two objects of masses $m$ and $M$ is $$ F = \frac{GmM}{r^2}, $$ where $r$ is the distance between the two objects. Basically, if distance between the object ...
8
votes
5answers
6k views

Period of oscillation through a hole in the earth

Special mention to the QI episode that kicked this off: Anyway, the host points out that a tunnel that connects a pair of points on the earth's surface can be thought of as a gravity train - where ...
3
votes
3answers
464 views

Does Gravity Depend on Spatial Dimension?

Consider a line containing two point masses, $m$ and $M$. The line is a $1D$ space. What's the gravitational force between the two masses? Newton's formula for the gravitational force $F$ between ...
0
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2answers
1k views

Derivation of Inverse Square Law

Is there a mathematical derivation of the inverse square law that doesn't depend on geometry or empirical data fitting?
8
votes
2answers
277 views

Calculating the potential on a surface from the potential on another surface

The question is short: If a charge (or mass) distribution $\rho$ is enclosed by surface $S_1$, I can calculate the electrostatic (or gravitational) potential on that surface by integrating $\rho(r') \ ...
-1
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1answer
24 views

Density is zero in circular potential

Is it true that the density is zero in a circular potential $$\Phi = \frac{-GM}{r}?$$ Using the Laplacian, it yields a value of zero for $\rho$.
0
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0answers
129 views

Where is centre of gravity on a Dyson Sphere? [duplicate]

Suppose there is a Dyson sphere earth thick, on the inner surface would the gravity be pointing outwards of centre of sphere with same strength as Earth's gravity?
3
votes
1answer
671 views

How does the distribution of mass affect gravitational attraction?

For example, if a planet is considered as a point mass, then an object inside the planets' gravitational field experiences an equal attraction from all of the planets' mass. However if the planet is ...
1
vote
1answer
242 views

Floating in a Dyson Sphere

Consider your typical Dyson Sphere scenario. You are standing on the inner side of the sphere. You look up and see the shining sun far away. My question (or thought experiment rather) is: ...
2
votes
1answer
516 views

What is the significance of the Inverse-square law? [duplicate]

Considering its occurrences in various fields like Electrostatics, Gravitation, Acoustics etc. how does the law bind these topics together?
1
vote
1answer
86 views

Is there an underlying reason why some forces are inversely proportional to the square of the distance? [duplicate]

This is the first time I'm studying those subjects (I'm still in high school) and my teacher couldn't give me an answer. I'm referring specially to Newton's law of gravitation and Coulomb's law of ...
1
vote
1answer
2k views

Gauss law in gravitation

Is it possible to use Gauss's law of electromagnetism, (The net electric flux through any closed surface is equal to $1⁄\epsilon$ times the net electric charge enclosed within that surface.) to ...
1
vote
1answer
352 views

Couple of questions about Gravitational field of an infinite plane

Is it possible to find the gravitationaal field without using infinite integrals or Gauss's law? I would like to know if so because I haven't learnt doing infinite integrals or using Gauss's law yet. ...
0
votes
1answer
415 views

Why Poisson's equation is important?

The Poisson equation can be deduced by Newton's mechanics: $$\Delta \Phi =-4\pi G\sigma$$ Einstein tried to give a "Poisson's equation" that works with his theory. This equation seems to be ...
1
vote
0answers
450 views

Proof of the Gauss's law for gravity without divergence [duplicate]

The proof of the Gauss's law for gravity provided by Wikipedia takes use of the divergence theorem. Is it possible to arrive at the integral form of the Gauss's law in a way which doesn't require ...
1
vote
1answer
262 views

Derivation Poisson's gravity equation by divergence theorem [closed]

I'm trying deduce the poisson's equation $\nabla^2\Phi (x)=-4\pi G\sigma(x)$ by divergence theorem Let $D:x^2+y^2+z^2\leq 1$ and $\sigma:D\to \mathbb{R}$ be the mass density function of $D$ (suppose ...
1
vote
0answers
67 views

In Newton's gravity, is the inverse square law related to the fact that our Universe has (apparently) 3 dimensions? [duplicate]

I read, long ago, a book, whose title I can't remember but I think the author was Carl Sagan. In the book was saying that gravity follows the inverse square law because of our Universe was 3 ...
1
vote
1answer
269 views

Why can center of mass be used in calculating gravity?

Why can gravitational forces be based on the center of mass. Due to the fact that gravity is related to the square of the distance should not the gravitational sum of every particle exceed the force ...
2
votes
1answer
848 views

Newton's shell theorem in 2d [closed]

I was wondering how to prove the analog of Newton's shell theorem for 2 dimensions, in which gravity obeys an inverse-linear law. Meaning: that an anywhere inside a circle, the gravitational field ...
0
votes
1answer
513 views

What would happen if the Earth were hollow? [duplicate]

This is a question of my exam. What would a person experienced if he were put in any point inside the Earth that is hollow (all its mass is concentrated in the surface). Finding the gravitational ...
1
vote
2answers
6k views

Is there a mathematical proof show that $F=G\frac{m_1m_2}{r²}$? [duplicate]

Is there a mathematical proof about The general law of attraction between two point masses $m_1$ and $m_2$ which represented as: $$F=G\frac{m_1m_2}{r²} ,$$where $r$ is the distance between the ...
0
votes
2answers
1k views

Gauss law for gravitational field

Gauss's law is fundamental law of electrostatics. But Can we apply Gauss's law for Gravitational field also?
0
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0answers
75 views

Sphere of electric charge revisited

I am thinking about a sphere of homogeneous charge distribution (see Electric field due to a solid sphere of charge, for example). Here we use a Gaussian surface (blue area) to find the electric ...
4
votes
2answers
5k views

Why inverse square not inverse cube law? [duplicate]

So as I understand, the inverse-square law which shows up in a variety of physical laws (Newton's universal law of gravitation, Coulomb's law, etc.) is a mathematical consequence of point-like ...
0
votes
1answer
160 views

What's the geometry of a gravitational field at the flat end of a cylinder?

Gauss's law is fairly straightforward in explaining the gravitational field strength around the curved sides of a cylinder - but what is the geometry of the field at the flat end? For example, does ...
1
vote
1answer
989 views

Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
12
votes
2answers
5k views

Gravitational field intensity inside a hollow sphere

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero....