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

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Finding the equation of motion

I am currently working on a problem where a particle of mass $m$ can move along the x-axis with no friction. The particle is moving in a gravitational field and the potential energy is given by: ...
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90 views

Why is Earth's gravitational pull only at its center?

Why is Earth's gravitational pull only at its center? Does acceleration due to gravity remain constant wherever I go in and on the Earth?
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1answer
28 views

Velocity of mass colliding with another mass under the influence of gravity

If two spherical objects of mass $m$ and mass $4m$ are in outer space with no other forces other than the gravitational attraction between them and they're separated by distance $d$, what velocity ...
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15 views

Superposition of accelerations in multibody problem

I am currently trying to design a game that implements Newtonian gravity, and am trying to code something that draws the trajectory of a small mass being acted upon by the gravity of much larger ...
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30 views

Infinite force between two point charges as $r$ approaches 0 [duplicate]

According to coulombs law the Force experienced by two point charges increases with the inverse square of their separation. This would imply that at distances approaching 0, the Force approaches ...
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74 views

Variation on the “Hole through the Earth” problem

In the news recently was the announcement that the answer to the classic Newtonian mechanics question of the time it takes for a body to fall all the way through the Earth was corrected to account for ...
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67 views

The correct integral for Newton's shell theorem

I am trying to prove Newton's Shell Theorem, and the natural integral I think of to use does not seem to give the right answer, so I am trying to find my mistake. For simplicity, I will work in one ...
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2answers
90 views

How is the uniform gravitational field approximation $F_g\approx mg$ near Earth's surface derived from Newton's law $F_g=GMm/r^2$ of gravitation?

I am really bothered about how we can derive the equation of projectile motion. Suppose a point mass will move in the gravitational field of the Earth according to the equation $$\ddot R ...
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37 views

How to increase flow rate? [closed]

I am coming up with ideas of how to increase grain (corn, soybeans etc,) flow in a tube. My first idea is to have spiral ribs inside of the tube to create a vortex effect that will allow the grain to ...
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1answer
66 views

Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
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1answer
46 views

What are the tidal effects of Io on Jupiter?

I recall reading an essay by Asimov (I think) around 1980 stating that the tides are a function of a power of the diameter of the primary, so (surprisingly) small close moons of Jupiter raise large ...
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1answer
79 views

Understanding Millikan's oil-drop experiment

This is quoted from A.P. French's Newtonian Mechanicsabout Millikan's oil-drop experiment: The droplets randomly produced in a mist of oil vapor are of various sizes. The ones that Millikan found ...
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30 views

Why isn't $g$ larger on the equator? [duplicate]

I understand that at the equator, you will have maximum centripetal force acting on you, whereas if you're standing directly on the pole you will have none. But because centripetal is a resultant ...
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2answers
49 views

Period of a simple pendulum accounting for friction

The period of a simple pendulum is $$T=2\pi\sqrt{\ell/g},$$ but no where in there do I see that it accounts for friction. Does it somehow account for friction, and if not, how could you do that?
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2answers
718 views

Why aren't satellites increasing speed because of gravitational acceleration?

Satellites orbiting the earth are experiencing almost as strong gravitation as we do, but they don't hit the earth because of their velocity outwards and the earth's curvature. But if they're ...
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0answers
54 views

measuring distances

We measure distances using half of the time of flight of light, 'a la Einstein'. What is the geometrical shape of the surface that is the locus of the points that are at a definite distance of an ...
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45 views

Free fall for a longer time

When I'm in free fall, I'm weightlessness for only about 1-2 seconds. Is there any way I can feel weightlessness for a longer period of time?
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1answer
31 views

Why does the medium affect the Coulomb's constant but not the gravitational constant?

Why does the medium affect the Coulomb's constant but not the gravitational constant? My friend said maybe the particles of the medium affect the electric field. But the net charge in the medium is 0 ...
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2answers
195 views

How do we age if we tunneled to Earth's core?

Scenario Suppose there exists an advanced technology that can hypothetically transport living humans to study the center of the Earth, as they goes deeper underground most of the Earth's mass would ...
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3answers
54 views

I were to travel to the other side of the world then is this logic possible? If no, why?

I go straight up and stay stationary at a particular point (at a point above action of gravity) in the sky. The earth will rotate and I decide to drop down when my destination has come exactly below ...
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35 views

Force of gravity at quantum level is indetermined?

Newton's law of Universal Gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional ...
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4answers
78 views

Sun and planets orbit each other

Do not the planets and the Sun revolve in orbits around each other and the shape of the orbit depends on where the center of gravity of the system is? The greater the mass of the Sun, the closer the ...
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1answer
43 views

Two Bodies Orbiting Around Each Other and Kepler’s Laws?

If two bodies are orbiting around a central center of gravity, how does Kepler’s first law (the one regarding the ellipse) apply?
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87 views

Comparing the orbit radius of two spherical objects [duplicate]

Assume the mass of star 2 is 4 times the mass of star 1. Compare the radius of the orbit of star 1 to that of star 2. Possible answers: R1:R2=1:4 R1:R2=1:2 R1:R2=2:1 R1:R2=4:1 R1:R2=16:1 ...
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Does the gravitational force of one object interfere with that of another?

Assume we have two iron spheres, Sphere A and Sphere B, with identical masses floating in the vacuum of interstellar space separated by some distance from each other. The gravitational force of each ...
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1answer
89 views

Largest size of a low gravity, Earth-like planet with Volcanoes and Earthquakes?

Provided that the Solar System consists only of Sol, a planet, and the planet's moon.... How large can my planet be so that it has low enough gravity that teenage human girls trained for jumping, are ...
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26 views

Can the gravitational constant be directly measured?

The value of the gravitational constant $G$ is $6.67384\times 10^-11 {\rm m}^3{\rm kg}^{-1}{\rm s}^{-2}$. This value is used in the formula to calculate the attractive force between two objects with ...
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65 views

How do these factors affect the free fall of objects?

Take an example of two balls of different masses being dropped from about 250 meters from the ground. How do the following factors affect free fall: Air resistance. Absence of air resistance. ...
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1answer
24 views

Could you give boundary conditions to the gravitational potential given the density distribution?

We´re doing a project that's all about solving differential equations with separation of variables. We´re trying to find the gravitational potential given the density distribution (that has azimuthal ...
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4answers
108 views

What exactly is the mass of a body? What determines it?

The term "mass" is very common. But what does it depend on? How is it known?
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25 views

Perturbations of planetary Orbits

I have, for years, been an Astronomy and physics nerd. For the first while, I was a total astronomy nerd. Then I slowly transitioned into physics and have been, for less than a year, a physics nerd. ...
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86 views

Would a planet in a binary star system follow Kepler's Laws?

I'm thinking it would not. I am thinking Kepler's Laws were a simplification that were possible with a simple two body (sun, planet) but would not apply for something more complex (sun1, sun2, ...
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2answers
64 views

$N>2$ gravitating masses can never reach equilibrium [closed]

If you have $N>2$ point masses, each attracted to each other by the force of gravity, how could you go about showing that they will never reach equilibrium?
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2answers
25 views

Does the microgravity environment in highly elliptical orbits differ from circular orbits?

I think everyone understands the microgravity environment broadcast from the ISS. But the ISS stays in a fairly circular orbit, the acceleration of gravity should be fairly uniform, the altitude and ...
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In circular motion, with a constant distance, why does the mass of the orbitting object have no effect on its revolution at all?

Using Newton's universal equation and some circular motion equation, the orbiting object's mass cancels out. But can someone please explain why this is without using pure algebra?
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Why doesn't an airplane simply go up in the air and stay there?

To get where a plane wants to go for example if I wanted to go from California to Japan, why can't an airplane simply stay up in the sky and let the earth rotate underneath it? Is it the ...
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3answers
70 views

How high could i jump if I weighed only half as much? [closed]

E.g. I weigh 150 lbs I had a thrust device that lifted 75 pounds. How high could I jump? What if that thrust lifted 2/3 of my weight (100 lbs)? Obviously, I cant fly, but I guarantee if I weighed ...
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2answers
314 views

Before Einstein came up with General Relativity, were there serious reasons to doubt Newton's theory?

Before Einstein came up with General Relativity, was there any serious reason to doubt Newton's theory (and its various developments)? I only know about the discrepancy in Mercury's orbit, which may ...
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What is the particle distribution in Saturn's Ring System?

In watching the scientifically scream-inducing film/movie 'Interstellar', there was a shot of the spacecraft moving through the Rings of Saturn. In this shot, and in every graphical representation of ...
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2answers
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Centre of Mass and tangential velocity star and planet

We have two objects - one massive star, and one planet which has a considerably smaller, but non-negligible mass, in a circular orbit about a common centre of mass. Using equation $F$=$GMm$/$r^2$ ...
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4answers
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Gravitational force of a ring [closed]

Given a ring with mass $m_1$, radius $R$ and a point mass $m_2$ with distance $x$ regarding the center of the ring. How can I calculate the gravitational force of this ring ? At first glance I'd say ...
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What is total force in this context?

One site said the total forces is the sum of the vectors. My homework question is "A skydiver of mass 90 kg is falling with a terminal speed of 60 ms-1. What does that mean? What is the total force ...
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1answer
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What's my $dM$? Gravitational Potential inside a circle of mass

I'm trying to find the gravitational potential for an arbitrary point within a ring of uniform mass density. The point is constrained to be in the same plane as the ring. So we start with: ...
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1answer
41 views

How to find an equation for $x$ in terms of $t$ for a particle falling under gravity with resistance given by $mkv^2$? [closed]

Okay so I have determine the velocity $v$ and displacement $x$ as functions of $t$ for a particle falling under gravity with resistance given by $mkv^2$. I have set up the equation of motion divided ...
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39 views

Explaining why planets are round [duplicate]

is it possible to prove that planets (and/or stars) are always round (elliptical if you consider the spin)? Is there a set of equation that demonstrate that fluids (after all, molten rocks "floating" ...
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2answers
185 views

Kepler's Laws to Determine Radius of Circular Orbit

"In nonrelativistic limit of general relativity there is a correction to the Newtonian gravitational potential energy $−h/r^3$ with $h = αL^2/(mc)^2$, where $c$ is the speed of light, $α = GMm$ ...
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2answers
74 views

How to solve the inverse square law equation of motion

From $$m\boldsymbol{\ddot{r}}=\boldsymbol{\hat{r}} f(r)$$ I can get $$r''-r \theta '^2=-\frac{k}{m r^2}$$ $$2 r' \theta '+r \theta ''=0$$ Now it seems that all the books tells me the method to solve ...
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Collision of two satellites

In a theoretical situation in which two identical satellites travelling around the Earth in opposite directions collided head on so that there velocities relative to the earth both became 0, would ...
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1answer
84 views

Calculating the first cosmic velocity / velocity for a circular orbit

Today in class we calculated first cosmic velocity using this equation $$G\frac{mM}{(R+h)^2}=\frac{mV^2}{R+h},$$ where $m$ = mass of the body, $M$ = mass of the Earth, $R$ = radius of the Earth, $h$ = ...
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Could we send a man safely to the Moon in a rocket without knowledge of general relativity?

I'm wondering if it's possible to send a man to the Moon using equations consistent with Newtonian gravity and without the elaborate tools of Einstein gravity. Are the predictions made by Newtonian ...