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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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$N$-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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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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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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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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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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Why do two masses orbiting around their CM emit gravitational radiation?

Two (extended, non-point-like) masses orbiting around their CM are emitting gravitational waves. However, these masses are both in free fall and follow a geodesic path through space-time. Now ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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How strong can tidal forces get?

I am imagining a planet the size of Earth being in close proximity to something of high mass such as a gas giant or a star, but ultimately I'd be more interested in how to figure this out myself. So (...
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How to calculate launch angle for tangentially launched satellites?

What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, ...
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Only gravitation and Newton's $2^{\mathrm{nd}}$ law needed to derive Kepler's laws?

It is known that Kepler's laws of planetary motion can be derived from Newton's laws of motion and his law of universal gravitation. However, are all of Newton's laws of motion necessary? According ...
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Where are the L3, L4, and L5 points of a hyperbolic orbit?

Do the L3, L4, L5 points exist in hyperbolic orbits? If yes, then where do they lie?
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Reference Frame conceptual confusion

I am getting confused as to why a ball still feels gravity when inside a moving car. The point of a reference frame is to reinterpret all the forces acting on a particle in one frame only. Hence all ...
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Gravitational potential of an infinite plane

In this link http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 , Feynman first computes the gravitational field generated by an infinite plane of constant density, and then he computes the ...
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How to derive the gravitational potential on an infinitely thin disc of finite radius?

I am stuck on a problem that requires me to calculate the gravitational potential on an infinitely thin disc of finite radius $R$ with mass $M$. This infinitely thin disc models a galaxy. Once I have ...
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Estimating the Pressure of Earth's Center

The pressure of a medium of density $\rho$ and in a graviational field with strength $g$ at a depth of $z+dz$ is equal to the pressure at $z$ plus the pressure caused by the weight of a slab of volume ...
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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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Mass distributions within two bodies such that the orbit is no longer Keplerian?

The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits. Consider that the bodies have finite size with respect ...
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Restricted 3-body problem - Rotating coordinate system

I'm trying to follow the formulation of the restricted 3-body problem in Taff's "Celestial Mechanics" book as I'm writing an essay on Lagrange points and am confused by the transformation into the ...
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How severe would the consequences be if the earth's moon were wrenched from orbit?

The old TV series Space 1999 from the early 1970s seems to have resurfaced on Youtube reminding me of something I watched as a child. It is one of those obviously ridiculous SciFi series (from the ...
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Gravity train and fastest path

As a fun exercise to kill some time, I have been thinking in the gravity train. For a point mass falling through a tunnel dug from pole to pole in an spherically symmetric planet of radius $R$, the ...
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Calculating gravitational effect of a suspended mass on an object within an atmosphere

How could one calculate the mass / density / dimensions of a suspended mass to lift an object off the earths surface at sea level with gravity alone? e.g. ...
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Connection between Kepler Problem and Harmonic Oscillator

Background. Take the Kepler Lagrangian as $L^K = \frac{1}{2}\dot{q}_i\dot{q}_i + \frac{k}{q}$, and the Lagrangian for the isotropic harmonic oscillator as $L^H = \frac{1}{2}\dot{q}_i\dot{q}_i - \...
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Exponents in physical laws

There are two very important laws in physics, namely the Newton's law of universal gravitation and the Coulomb's law, both of which contain a $r^{-2}$. I am curious about the exponent $2$ here. There ...
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Doubts about the effective potential in Newtonian gravity

I'm studying for a physics exam in a CS degree and the professor introduced the effective potential related to gravitation. Given $\vec v_r$ the component of the velocity of a planet that is parallel ...
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If there were positive and negative masses similar to positive and negative charges, would there be some kind of gravitational magnetic force?

Coulomb's law is very similar to Newon's law of gravitation. But as we go deeper into electromagnetic phenomena we see that it is very complex compared to newtonian gravitation. For example if the ...
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How do we measure the masses of far away galaxies?

One piece of evidence that is supposed to show that dark matter exists is the rotation curve diagram. Apparently Fritz Zwicky used the Viral Theorem to make a prediction which does not fit with the ...
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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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Power Generation Via 2 connected objects below distinct orbits

As an example: Large weight A sits just below Earth's orbit Large weight B sits just below Moon's orbit A, B are connected by sufficiently strong material (may not exist, and if so how much ...
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Ignoring orders of magnitude in a problem

I am so lost in this solution to a physics problem. In the problem I find the gravitational force on the Moon due to Earth and the gravitational force on the Moon due to the Sun They are about $1....
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Can you do an n-body simulation in terms of energy and momentum?

An N-body simulation typically works directly in terms of the gravitational forces and accelerations. If you can solve the equations exactly, this is fine, but there are many instances where this is ...
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Center of gravity of a hollow tank

I have to find the center of Gravity of a hollow oblong tank with 1 side missing. For installing lifting lugs x 4 on top which must align with the intersection point. (the tank will be lifted off the ...
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the torsion balance of the Cavendish experiment

I need to perform the Cavendish experiment and build a torsion balance but I can't find metallic spheres with enought mass so I was thinking about using a pair of dumbbells instead. My question is if ...