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

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Newtonian Gravity on a Riemannian $3$-Manifold

To solve the Poisson equation for the Newton Potential, say $\phi$, one can use the divergence theorem, such that $$\int_U \nabla^2 \phi \sqrt{g}~ dV= \int_{\partial U} <\nabla \phi,n> ...
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Gravitational Potential of a Sphere vs Gravitational Binding Energy of a Sphere

My question is about two equations regarding uniform spheres that I've run into: $V=\frac{GM}{r}$ ... and ... $U = \frac{3}{5}\frac{GM^2}{r^2}$ $V$ is unknown to me, and is described (in Solved ...
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1answer
120 views

Distance traveled in a simple two body problem [duplicate]

I'm trying to program an $N$-body simulation and I'd like to be able to test it with a known solution to a simple, two-body problem. I've looked at multiple sources, but I just don't know how to apply ...
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3answers
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Similarity between the Coulomb force and Newton's gravitational force

Coulomb force and gravitational force has the same governing equation. So they should be same in nature. A moving electric charge creates magnetic field, so a moving mass should create some force ...
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2answers
902 views

How can a satellite's speed decrease without its orbital angular momentum changing?

I have no idea what the answer is. I'm supposed to answer it within 3-4 sentences.
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How does Earth carry Moon with it, if it can not force Moon to touch it by gravitational force?

Earth's gravitational force is acting on its Moon in such a way that it forces the Moon to rotate round its orbit by centripetal force and carries it while rotating round the Sun by gravitational ...
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3answers
132 views

Stresses in asteroid during close flyby

The acceleration of an asteroid (such as 2012DA14) as it approaches earth is proportional to the reciprocal of distance $r$ from earth center, squared. the derivative of the acceleration, or jerk, is ...
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4answers
654 views

What's the exact gravitational force between spherically symmetric masses?

Consider spherical symmetric$^1$ masses of radii $R_1$ and $R_2$, with spherical symmetric density distributions $\rho_1(r_1)$ and $\rho_2(r_2)$, and with a distance between the centers of the spheres ...
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2answers
135 views

Shoot object into the Sun using minimal energy

Say I want to shoot a cannonball into the Sun with minimal energy (minimal initial velocity relative to Earth). In which direction do I shoot it? Let's neglect Earth's gravity, if that would make ...
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4answers
813 views

Staying in orbit - but doesn't any perturbation start a positive feedback?

I am not a physicist; I am a software engineer. While trying to fall asleep recently, I started thinking about the following. There are many explanations online of how any object stays in orbit. The ...
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2answers
212 views

How is space ship's acceleration perceived if the acceleration is perpendicular to the velocity?

Spacecraft in orbit around the Earth are constantly accelerated by the gravitational field of Earth. That's why the spacecraft ($m \ll M$) is in an (elliptical) orbit around the centre of gravity of ...
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2answers
251 views

Escape Velocity question

I would like some help in understanding the derivation of the formula for escape velocity. Why does $t$ approach infinity? And why is $v(t)$ approaching zero? I know that $r(t)$ is infinite because ...
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1answer
138 views

Weightlessness on Earth

Would the following work? Imagine one would 1) create a straight 4000 km long tube (at ground level), following the curvature of the Earth, wide enough to hold a pod the size of an aircraft cabin; ...
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5answers
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When driving uphill why can't I reach a velocity that I would have been able to maintain if I started with it?

Consider these two situations when driving on a long straight road uphill: Starting at a high velocity $v_h$, which the car is able to maintain. Starting at a lower velocity $v_l$, and then trying ...
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2answers
460 views

Gravity and free fall

In Wikipedia it's stated that "[..] gravity, is the natural phenomenon by which physical bodies appear to attract each other with a force proportional to their masses". Then I found many examples ...
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3answers
427 views

If you could reverse gravity, what velocity would you achieve on leaving Earth?

If you could reverse gravity, to make it repulsive instead of attractive, what velocity would you achieve on leaving Earth? A simple question really, but I have completely forgot how to calculate ...
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1answer
177 views

Lagrange L4 L5 points and perifocal plane

I have 2 satellites at the L4 and L5 points and these are watching an object. Each satellite provides the angle to the object from its own position from a line parallel to the $\text{x-axis}$ of ...
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3answers
364 views

What was wrong with action a distance?

It is usually said that the idea of fields was introduced (electric and magnetic fields) in electricity and magnetism after Coulomb's law to cure the conceptual problems of action at a distance. ...
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1answer
141 views

The Value of Newton's Gravitational Constant $G$ within an Atom

Can the value of Newton's Gravitational Constant $G$ be measured within a stably bound atom? PLEASE NOTE: Since scattering experiments do not involve stably bound systems, their results are not ...
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4answers
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Paradox- Object thrown parallel to the ground will never fall down

Suppose an object is thrown parallel to the ground. The gravity acts downward (ie. perpendicular to the direction of motion of the object). The work done by gravity on that object will be given by : ...
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2answers
10k views

Newtonian gravity vs. general relativity: exactly how wrong is Newton?

Is there a simple function I can use to describe the difference between simple Newtonian dynamics and the actual observed motion? Or maybe some ratios for common examples of, say, the motion of stars ...
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1answer
2k views

Energy in orbit of satellites around the earth lost?

If the total mechanical energy in a satellite's orbit (assuming circular) is greater when it is closer to the earth, and hence smaller when it is farther from the earth, then we can say that as the ...
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2answers
210 views

Two moons of Earth?

Hypothetically, suppose there is a situation where the Earth's moon gets neatly sliced into two equal hemispheres, and the force responsible for this slicing also creates a distance between the two ...
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1answer
179 views

Idealized trajectory from sloped surface

I am a GIS programmer implementing a visualization. I am modeling the idealized trajectory of a particle ejected from a volcanic vent using: $$\text{distance} = \frac{(v^2 \times ...
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1answer
108 views

Gravity question [duplicate]

Possible Duplicate: Don’t heavier objects actually fall faster because they exert their own gravity? When true: The force pulling the "heavy" object down is greater BUT it also takes more ...
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6answers
462 views

Relation between field strength and potential?

In terms of gravity and electric fields, I'm not sure what the difference is between field strength and potential is and how they are related? Both using maths and not.
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3answers
3k views

Gravity in other dimensions than 3 and stable orbits

I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity ...
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1answer
989 views

If 2 charges have the same sign, the coulomb force is positive but repulsive, while with 2 masses the gravitational force is positive but attractive

If you have two point objects both the same positive charge and both of the same mass at a distance $r$ from each other. The force between them due to gravity is $F_g=\frac{Gmm}{r^2}$ and $F_g$ is ...
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4answers
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What is the difference between center of mass and center of gravity?

What is the difference between center of mass and center of gravity? These terms seem to be used interchangeably. Is there a difference between them for non-moving object on Earth, or moving objects ...
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1answer
156 views

Effect on mass of Earth if it stops revolving around Sun

If the object in motion gains mass, will it affect the change in mass of Earth if it stops revolving around Sun, since mass is responsible for gravity how will be the gravitational force change?
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1answer
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How can the Moon have such a strong effect on the ocean?

The gravitational acceleration on Earth is approximately $ 10 \mathrm{m}/\mathrm{s}^2 $. Compared to this, the tidal effect of the Moon's gravity gives a local variation in the acceleration of ...
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3answers
483 views

Is the gravitational potential of a planet in orbit always equal to minus the squared velocity?

Say a planet (mass $m$) is orbiting a star (mass $M$) in a perfect circle, so it is in circular motion. $F=ma$ and the gravitational force between two masses $F=\frac{GMm}{r^2}$ so ...
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1answer
99 views

Forces: Worth worrying anything?

I am a general physics student, I had a question in my text-book and according to it two students having gravitational attraction between them = ($6.67\cdot10^-8\ \mathrm{Nm}^2/\mathrm{kg}^2$) is not ...
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1answer
606 views

Gravity force strength in 1D, 2D, 3D and higher spatial dimensions

Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions. Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ...
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2answers
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Will two trains running along the equator in opposite direction experience same wear out?

Two identical trains, at the equator start travelling round the world in opposite directions. They start together, run at the same speed and are on different tracks. Which train will wear out its ...
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1answer
508 views

Classical 3-body problem

There is a formulation of the classical 3-body Newtonian problem reducing this problem to 6 equations (e.g. http://www.3bproblem.blogspot.com). I would like to know where can I find a discussion or ...
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2answers
788 views

How does one measure Earth's speed of revolution around the sun?

I know that there are several formulae that one can plug numbers into to arrive an estimate of Earth's speed around the sun (Kepler's third law for instance), but I'm wondering how these things are ...
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3answers
290 views

Dynamics of a Rocket

I am interested in modelling the trajectory of a rocket from the Earth to the Moon by solving a differential equation numerically. Below are some key facts and assumptions I am using. I want to make ...
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2answers
255 views

What is the mass distribution within the sun?

Jupiter is roughly 1/1000 the total mass of the sun. To get some idea of what effect Jupiter's gravity may have on the sun I'd like to know the approximate mass distribution of the sun. (i.e) the ...
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0answers
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Integration question from book “e: The Story of a Number” by Eli Maor [closed]

In the book 'e: The Story of a Number', a derivation of a parachutist problem is given on pg. 109-110. A parachutist jumps from a plane and at $t=0$ opens his chute. At what speed will he reach the ...
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1answer
412 views

What is the physical meaning of a flux of gravitational field in classics?

I've stumbled upon an answer to a question about square power in Newton's law of gravity. After reading it I got a question whether the flux of gravitational field has actually any physical meaning. ...
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5answers
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Intuitive explanation of the inverse square power $\frac{1}{r^2}$ in Newton's law of gravity

Is there an intuitive explanation why it is plausible that the gravitational force which acts between two point masses is proportional to the inverse square of the distance $r$ between the masses (and ...
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4answers
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Why are so many forces explainable using inverse squares when space is three dimensional?

It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three ...
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3answers
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Escape velocity from Earth

We know the escape velocity from the Earth is 11.2km/s. Isn't it the velocity required to escape from earth if we go normal to the surface of earth? i.e while we derive the formula for the escape ...
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1answer
1k views

Why is a cycloid path the fastest way to roll a ball downward? [duplicate]

Possible Duplicate: Path to obtain the shortest traveling time I've been told that if one would want to make a ramp to get a ball from point A to a lower point B (at a certain horizontal ...
5
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1answer
275 views

Potential Energy tends to infinity on the N-Body Problem

I need help to solve this problem related with the N-Body problem, i dont understand quite well what I need to define or to express in order to solve it. We assume a particular solution to the N-Body ...
4
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2answers
867 views

Efficiently calculating the gravitational force from spherical shell

I am reading Kolenkow and Kleppner's Classical Mechanics and they have tried to calculate the gravitational force between a uniform thin spherical shell of mass $M$ and a particle of mass $m$ located ...
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1answer
117 views

Gravity near surface of a large body

The question I want to ask is what point is there in using $$ F = G {m_1 m_2 \over r^2} $$ when we don't talk about point masses, but one of the masses is a sphere of radius ...
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5answers
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Is there a small enough planet or asteroid you can orbit by jumping?

I just had this idea of orbiting a planet just by jumping and then flying upon it on its orbit kind of like superman. So, Would it be theoretically possible or is there a chance of that small body to ...
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4answers
5k views

Acceleration of two falling objects with identical form and air drag but different masses

I have a theoretical question that has been bugging me and my peers for weeks now - and we have yet to settle on a concrete answer. Imagine two balloons, one is filled with air, one with concrete. ...