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

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Projectiles and escape velocity [closed]

Q: The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of $45^\circ$ with vertical, the escape velocity will be? ...
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2answers
396 views

Gravitational potential outside Lagrangian points or Lagrange points

The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly: If I ...
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1answer
142 views

Gravitational field v.s. Physical variable?

I went to a talk on Newtonian mechanics some time earlier and the speaker said, and I quote, Newton's equations of motion admit a larger symmetry group than the Galilean group alone. Therefore, ...
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1answer
105 views

What Speed Would an object need to leave the earth at to reach L1? [closed]

Let's say the Earth is an airless sphere. What speed would an object weighing 1 kg need to leave the surface at in order to get to and be motionless at L1, where the Moon's gravity becomes stronger ...
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Is Feynman's explanation of how the moon stays in orbit wrong?

Yesterday, I understood what it means to say that the moon is constantly falling (from a lecture by Richard Feynman). In the picture below there is the moon in green which is orbiting the earth in ...
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4answers
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Why do objects accelerate as they fall?

Most importantly, what must change in order for the falling object to change its speed? Is it the distance to the centre of the planet? If you pull the earth away from the object as the object falls, ...
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1answer
103 views

Simulating an orbit, primary is not at focus

I've been toying around with some -very- simple orbital simulators, mostly using preexisting physics libraries (I took a layman's stab at doing it with vectors too). The thing that is confusing me is ...
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2answers
198 views

So gravity turns things round

It makes sense, since gravity tends to push the surface of a body towards it's center. Unless I'm mistaken, everything with mass has it's own gravity, every atom and for instance, our own bodies ...
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158 views

Kinetic energy with no velocity

When a body is displaced against the gravitational field of force it gains potential energy. When we drop the body it begins to move downward with a certain amount of acceleration, and the potential ...
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4k views

Force inversely proportional to the squared distance

Newton's law of universal gravitation: "Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to ...
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1answer
199 views

How is gravitational force is compared to flow of water?

I listened to a lecture. The professor said that the gravitational field around the particle (spherical in shape) can be compared to a pond having a constant height and depth and water is constantly ...
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3answers
706 views

How do you explain Kepler's third law in general terms without complex math?

I understand the first law-elliptical orbits, and the second-equal area in same time, but I need help with the third one. Note that I am not in an AP course or taking calculus at the moment so simple ...
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5answers
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Einstein gravity versus Newton's gravity

What's the basic difference between the gravity as seen by Einstein, and that by Newton?
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2answers
147 views

Is quantum mechanics similar newtons laws of gravity? In a way [duplicate]

Is quantum mechanics similar to Newtonian gravity in respect that it explains how something works but not why it works? Or does Quantum mechanics explain why it works? (I haven't actually studied QM) ...
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2answers
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Where are we : On level ground or on a ramp - moving in a train?

Let's say we are traveling in a train. The path has two parts: one at ground-level and the other moving up on the ramp. The ramp has an inclination of $\arctan\frac{a}{g}$ with the horizontal, where ...
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1answer
559 views

Gravitationally bound systems in an expanding universe

This isn't yet a complete question; rather, I'm looking for a qual-level question and answer describing a gravitationally bound system in an expanding universe. Since it's qual level, this needs a ...
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0answers
89 views

Formulation of the Three-Body Newtonian problem

I am trying to understand three body problem in Newtonian space. I want to make formulation of differential equations for known initial conditions for the case with: Identical three masses ...
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2answers
202 views

Infinitely many planets on a line, with Newtonian gravity

(I apologize if this question is too theoretical for this site.) This is related to the answer here, although I came up with it independently of that. $\:$ Suppose we have a unit mass planet at each ...
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1answer
969 views

Slinky base does not immediately fall due to gravity

Why does the base of this slinky not fall immediately to gravity? My guess is tension in the springs is a force > mass*gravity but even then it is dumbfounding.
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1answer
367 views

Weightlessness for astronauts

Well, this question has been puzzling me for kinda long time, many people believe that orbiting astronauts feel weightless because they are "beyond the pull of Earth's gravity"...How far from the ...
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2answers
307 views

Newton's Law of Graviation: Why $G$ and not e.g. $\dfrac{1}{4\pi G_0}$?

I've been wondering, in Coulomb's Law, $k_e = \dfrac{1}{4\pi\epsilon_0}$. Therefore, why do we use $G$ in Newton's Law of Gravitation? What if the constant is more like Coulomb's Law, e.g. $G = ...
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5answers
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How to get the angle needed for a projectile to pass through a given point for trajectory plotting [closed]

I am trying to find the angle needed for a projectile to pass-through a given point. Here is what I do know: Starting Point $(x_0,y_0)$ Velocity Pass-through point $(x_1, y_1)$ I also need to ...
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1answer
147 views

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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3answers
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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
117 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
3k views

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
726 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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2answers
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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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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
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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
126 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
763 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
193 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
209 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
130 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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1answer
378 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
384 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
164 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
310 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
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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
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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
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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
204 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
172 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
103 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
380 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
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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
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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 ...