Questions tagged [newtonian-gravity]

The Newtonian model of gravity in which the force between two objects is given by GMm/r^2.

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Boundary conditions in Poisson's equation for gravity

Say we want to calculate the gravitational potential everywhere around(outside) a solid, circular, right cylinder. We want to use Poisson's equation for gravity for that (Laplace(U) = -4*pi*density ...
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409 views

Does gravity affect water permeability?

Suppose I have an approximately rectangular prism composed entirely of folded paper. If I place 600lbs on top of these rectangular sheets of paper, the paper should compress. How does this affect ...
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141 views

$N$-body gravity simulator: why does energy conservation break down when introducing an adaptive timestep?

I am playing with an N-body gravity simulator using the velocity-verlet algorithm. In the actual simulation I normalize everything so that it is nicely behaved numerically, but I'll express things in ...
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2answers
170 views

How do you derive a quantum field theory from a spacetime metric?

What are the first steps in converting a metric into a quantum field theory? I know roughly what to do once I have a pair of non-commuting operators, but how do I get to that point? Specifically, I'd ...
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59 views

The (Newton-Laplace-Ivory-Arnold) shell theorem in general relativity

It is well-known that Birkhoff's theorem and the classification of LTB spacetimes proves one version of Newton's shell theorem in the context of GR. Another statement in Newtonian gravity, often ...
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1answer
104 views

Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
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1answer
103 views

Is there a prediction when our solar system would fall apart?

Within a few billion years our Sun would become a red giant and destroying Mercury and Venus and perhaps even the Earth. But nevertheless our solar system will still have some planets like Jupiter and ...
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75 views

What Is the Roche Limit Factor for a Tension-Free Solid Rubble Pile?

I have reached a confusion when searching for derivations of the Roche Limit, which differ in value and explanation. All equations are given of the form: $ P = r_{M} \sqrt[3]{f\frac{\rho_{M}}{\rho_{...
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1answer
335 views

How to measure gravitational acceleration in airplane?

I want to see (actually: show to my kids) evidence of the $1/r^2$-decay of gravitational acceleration by measurement, in a way as simple as possible. So I was thinking of measuring gravitational ...
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1answer
227 views

Why is Newtonian cosmology correct for curved space?

The Newtonian model of an expanding Universe gives Friedmann's equation exactly for non-zero spatial curvature $k$ (see http://hyperphysics.phy-astr.gsu.edu/hbase/astro/expuni.html). Instead of using ...
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113 views

How do measurements of $G$ account for variations in the local gravitational field?

One of the notable discrepancies of modern physics is the current disagreement of measurements of the gravitational constant $G$, well beyond reported uncertainties (and agreeing only to about 1 part ...
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Partition function of an asteroid gas (gravity)

Consider the classical problem (Newtonian gravity) of a large number of $N$ identical non-interacting asteroids orbiting around a big planet. I wanted to see if the problem was solvable. I wrote my ...
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1answer
56 views

What would the ideal amount of gravity be for an Olympic sprinter?

The goal here is to get the sprinter running as fast as possible. How much of an effect would more or less gravity have on the top speed of an Olympic sprinter, say... Usain Bolt? 6 ft 5 in (1.95m) ...
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224 views

Orbital period and nodal precession & apsidal precession

In classical orbital mechanics as per Newton/Kepler, the time taken to complete one orbit around a body of mass $M_e$ is: $$ T = 2 \pi \cdot \sqrt { \frac {a^3} {G \cdot M_e} } $$ But also, for ...
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75 views

Minimal value of angular momentum in a close binary

I just noticed something interesting with the angular momentum of a close stellar binary. This question is somewhat related to another question of mine, but the question here is clearly different : ...
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1answer
162 views

Gravity assist, Coordinate system transformation

I am currently learning about the physics and the mathmatics behind gravity assist. I have a question regarding the coordinate transformation between the planet frame and the sun frame. I want to ...
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1answer
295 views

Different versions of Einstein's equivalence principle

As I understand it, there are two versions of Einstein's equivalence principle. The first states that "Locally, a frame in free-fall in a gravitational field is equivalent to an inertial frame in ...
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477 views

How can escape velocity be independent of the direction of projection of a body?

I read that the escape velocity of a body is independent of the direction of projection. For example, I could throw a ball at $11.2$ km/s velocity horizontally, and it would still leave earth. I am ...
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429 views

Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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247 views

From Newton to Kepler without infinitesimals

I've read some interesting calculus-free proofs of at least parts of the derivation of Kepler's Laws from Newton's gravitational force. One is of course Feyman's "Lost Lecture" (which was already ...
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Would a very long massive rod exhibit a large deviation from Newtonian gravity (specifically a deficit angle rather than 1/r force)?

In General Relativity the metric corresponding to an infinitely long massive rod is flat but with a deficit angle. It exhibits a very large deviation from Newtonian gravity in all regions of space in ...
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128 views

Can one verify the Earth tide in his yard?

The ocean tide you can see on the coast. But the Earth tide beneath our feet is hardly perceivable. Is there any way to verify it in one's yard?
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154 views

If the field concept was invented by Faraday, then how did Newton interpret the $g$?

This is Newton's law of universal gravitation. $F=G\frac{m_1.m_2}{r^2}$ Gravitational field $g$ is derived from this formula $g=G\frac{m_1}{r^2}$ This is named gravitational "field" strength. If ...
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What is the gravity on a “partial” ringworld?

This was inspired by https://worldbuilding.stackexchange.com/questions/149706/life-on-the-broken-ring-an-issue-of-size. Let's say I have a part of a Ringworld (see link for specifications). ...
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Most precise way to measure $g$ at home?

I've tried measuring acceleration due to gravity, using a photogate with free falling picket fence. I've also tried photogate with picket fence on a low-friction cart and inclined plane. So far, ...
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2answers
78 views

How to calculate gravity inside of a circle of mass?

I've been reading about the Shell Theorem and how the gravitational force inside of a sphere is equal to zero. I was wondering if the same was true for a circle, but couldn't find any definitive ...
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1answer
70 views

How is Gravity created in opposite to centrifugal force?

Wikipedia points out that Gravity is: most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity not as a force, but as a ...
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Experimental limits on non-Newtonian gravitational force at length scales larger than 1 meter?

This answer from 2012 shows some information on an exponential term characterized by relative strength and range parameters $\alpha$ and $\lambda$, One potential tested here is here $$V(r)=-G\...
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Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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2answers
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Velocity of earth due to the rotational motion of the earth moon system about the center of mass

I calculated the location of the centre of mass of Earth-Moon system using $$\frac{\sum m_ix_i}{M} = \frac{mx}{M}$$ where m is the the mass of the Moon $= 7.35\times10^{22} kg$, x is the distance ...
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1answer
63 views

What does it mean for a graviton to have mass?

On wikipedia we can read: Astronomical observations of the kinematics of galaxies, especially the galaxy rotation problem and modified Newtonian dynamics, might point toward gravitons having non-...
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97 views

Geometric Explanation for the Equality of Active and Passive Gravitational Masses

In Newtonian gravity, as such, there are three masses: the active gravitational mass (the mass that generates the gravitational field), the passive gravitational mass (the mass that responds to the ...
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101 views

What would gravity be like on the surface of a right rectangular prism?

Let's assume there is a right rectangular prism floating about in space, what would the gravity be like across its 6 flat surfaces? Let's assume that this right rectangular prism has a constant ...
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1answer
85 views

How far apart are two initially $1000m$ separated bodies that fall to earth from infinity, when the closest body reaches earth?

Imagine two bodies (very, very small compared to the size of the earth), 1(km) separated from each other (in the direction of the earth) at infinity. After they reach earth after an infinite long trip ...
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1answer
89 views

Determine initial velocity of an object which was thrown (WITH air resistance)

I have the following problem: I want to determine the initial velocity of an object which is for example dropped from a moving plane. I know the position, from where the object is dropped and I know ...
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150 views

Why are all galaxies roughly the same size?

what determines the stable mass of galaxies, stars, star clusters or even galaxy clusters? Is there some obvious way to determine the classes of stable mass clusters from the initial conditions of the ...
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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}...
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centrifugal acceleration and circular velocity in curved space time

I'm studying a problem on rotation systems in general relativity. I would like to know how do these two well know newtonian formulas: $$a_{c}(r)=\dfrac{V_{c}^{2}(r)}{r},\\-\:\dfrac{\partial\Phi(r)}{\...
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144 views

Maxwell-like equations from Newton's law of universal gravitation and special relativity

It is known that Maxwell's equations can be derived from Coulomb's Law and Special Relativity. Since Coulomb's Law is so similar to Newton's law of universal gravitation, is it also possible to derive ...
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55 views

Eight-shaped orbit determination

I was playing a game on my smartphone whose goal is to draw certain orbit in presence of certain central gravitational potential. I noticed that when there are two center of force is possible to have ...
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1answer
141 views

Motion described by $a=\frac{k}{x^2}$

Say a particle in one dimension experiences acceleration inversely proportional to the square of displacement. What is its displacement as a function of time? $$ a=\frac{d^2x}{dt^2}=\frac{k}{x^2} \\ \...
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398 views

Proof of unsolvability of $n$-body problem for $n\geqslant 3$ in general

We know there are general solutions for 1-body problem and 2-body problem and also we know in some "special cases" there are some possible solutions for $n$-body problem for $n \geqslant 3$ and there ...
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115 views

Gravity's potential energy is it measurable?

In vacuum all object fall with no resistance and the object keeps on accelerating without stopping at a particular velocity. If i manage to make the fall to take place for 20 sec, then will the object ...
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364 views

Binding energy of a galaxy?

I'm a novice in physics and new to the forms, so please forgive me if this is a dumb question or if this is in the wrong section to be posted, but how would one find the gravitational binding energy ...
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1answer
67 views

Satellite and gravitational acceleration

According to $0.5gt^2$ object will fall 5m in first second. Earth curve is 5m for 8km So if we can project object at 8000 m/s speed object will never fall into ground. Above scenario is correct for ...
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Can we calculate the gravitation radiation using the similar method in electrodynamics?

Let's just forget GR for the moment. Newton's theory of gravity and Maxwell's theory of electrodynamics are very similar,i.e both Columb type interaction, can we just use the method develop there to ...
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40 views

Initial conditions for a massive objects to follow a path

Suppose I have a path, such as the one traced out by $r^2 = \cos(2\theta)$, and $n$ objects with mass $m$ at equidistant points on this path. What velocities should each object initially have in order ...
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359 views

Misbehaving singular isothermal sphere potential

The singular isothermal sphere (SIS) is a useful simple model often used in astrophysics. It has density profile: $$\rho(r) = \frac{\rho_0 r_0^2}{r^2}$$ This is well known to have some quirks (...
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1answer
72 views

Eccentricity of planetary orbits: What information is contained?

I'm having a little trouble understanding what makes a planetary orbit explicitly elliptical. Is it simply that the initial velocity was different from the circular orbit case for a given starting ...
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1answer
89 views

How did the Moon survive next to the Earth since earth and Moon came into existence?

What mechanism(s) prevented the gravitational effect of the earth on the moon from shattering the moon when it was closer to the earth than the Roche Limit some 4.5 billion years ago?