Questions tagged [newtonian-gravity]

This tag is for questions regarding the Newtonian model of gravity in which the force between two objects is given by $~GMm/r^2~.$ It is a natural phenomenon by which all things with mass or energy – including planets, stars, galaxies, and even light – attract one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides.

The Newtonian model of gravity in which the force $(F)$ between two objects of mass $M$ and $m$ situated at a distance $r$ is given by $F=\frac{GMm}{r^2}$, where $G$ is the Gravitational constant and its value is $G=6.674×10^{−11}$ m$^3$⋅kg$^{−1}$⋅s$^{−2}$ (in SI units).
Newtonian concepts also include the gravitational field, the gravitational potential energy, and the gravitational potential.

It is to be noted that gravity has an infinite range, although its effects become weaker as objects get further away.

The gravitational field is the gravitational force divided by mass. The gravitational potential energy is the integral of the gravitational force. The gravitational potential is given by the gravitational potential energy divided by the mass.

Newtonian gravity can also be formulated in terms of Poisson's equation $\nabla^2\Phi=4\pi G\rho$.

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Are the basins of attraction of two static gravitational sources two half-planes?

Consider the following setup: Two massive bodies of mass $M$ are fixed at the positions $\vec{A}=(d, 0)$ and $\vec{B}=(-d, 0)$. Now imagine a test particle $p$ with initial position $\vec{r}_0=(x_0,y_0)$ and initial velocity $\vec{v}_0=(0,0)$. Its…
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Does gravity turn itself off when it has nothing to work with?

The formula tells us that the force of gravity is equal to the mass of Object 1 multiplied by the mass of Object 2 multiplied by the Gravitational Constant and then divided by the distance between the objects, squared. It is implied, I think, that…
Ricky
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How would a large a mass be stable at the Earth Sun L4 or L5 point?

I've heard about the Trojan asteroids and there is the famous idea of putting a space colony at one of these points, but the explanations I see for how something is stable at those points it they are 'insignificant mass.' What does that mean? …
Scott
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Can we use normal gel pens to write in zero gravity?

Some say that astronauts use special space pens which uses pressurized nitrogen to write at space (zero gravity) and the normal gel pens does not write at space as there is no gravity for the gel to flow. But, some others say that due to surface…
Kawin M
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About Newton's Shell Theorem

Newton proved in Principia that the total gravity that a sphere exerts over a material point is the same as if all the mass of the sphere were concentrated on its center. I wonder if it's possible to prove that a sphere / spherical shell is the only…
Ricbit
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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_{S}}} $ where $P$ : Roche Limit $r_M$ : radius of…
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Using centre of mass in gravitational field calculation

When calculating the gravitational field of a continuous mass, like a rod, at some point outside it, why can't we just use the centre of mass of the rod and then directly plug in the distance between the point and the centre of mass in the…
user34304
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Is the formula of gravitational field $\vec{I} = \lim_{m\to0}\frac{\vec{F}}{m}$?

Which formula for gravitational field is correct $\vec{I} = \lim_{m\to0}\frac{\vec{F}}{m}$ or $\vec{I} =\frac{\vec{F}}{m}$ . My teacher told me that the former is correct because for an infinitesimally small mass we can neglect its effect of…
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Must the minimum of the gravitational potential generated by a given charge density occur at its center of mass?

An idle wondering that falls out of some comments trying to clarify this question: Suppose that you have some isolated mass distribution $\rho(\mathbf r)$, in principle with a smooth volumetric distribution, and that you're interested in the bottom…
Emilio Pisanty
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Pluto's gravitational pull on a person on the Earth's surface?

My physics teacher stated that Pluto has a gravitational pull on objects on Earth, namely humans. Is this true? What is the free-fall acceleration of Pluto with respect to being on the Earth's surface (i.e. the Earth's free-fall acceleration is…
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What did Feynman mean by "gravity itself is a pseudo force"?

Feynman writes: One very important feature of pseudo forces is that they are always proportional to the masses; the same is true of gravity. The possibility exists, therefore that gravity itself is a pseudo force. ... It might seem all right to…
user36790
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How to calculate gravitational force

Suppose the centre of mass of 2 bodies coincide , then how will we calculate the gravitational force between the 2 bodies ??
XZark
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How can we get this formula for Gravitational potential?

I just read the wikipedia page http://en.wikipedia.org/wiki/Gravitational_potential But I don't understand how to get this formula: $$\rho(\mathbf{x}) = \frac{1}{4\pi G}\Delta V(\mathbf{x})$$ Can anyone tell me why?
NGY
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Would Newton's Law of Universal Gravitation be accurate in voids?

Newton's Law of Universal Gravitation is used to approximately model gravitational forces close to Earth. I'm curious as to if there is a weaker-gravity limit to the law's applicability, such as in a void in the Universe. Assuming voids have less of…
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Gravitational force due to a ring but not at it's center!

While I was reading a proof on Newton's Shell Theorem, an idea struck my mind. It was that if there is a 2-D ring of mass $M$ and radius $R$ with constant linear mass density and we keep a point mass $m$ anywhere inside the ring other than it's…
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