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

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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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1answer
17 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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4answers
916 views

Does gravity slow down a horizontally thrown baseball?

I have a simple question: Does gravity slow down a horizontally thrown baseball? Assuming when a baseball is thrown it has a vertical velocity as well, does it slow does the ball? Any help is much ...
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1answer
73 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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6answers
1k views

Is gravitational force affected by intervening medium?

If we leave a iron ball and feather into the water, feather returns to the surface and floats or moves into the water slowly. On the other hand, iron ball (of certain mass greater than mass of ...
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5answers
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Why is potential energy negative when orbiting in a gravitational field?

I had to do a problem, and part of it was to find the mechanical energy of satellite orbiting around mars, and I had all of the information I needed. I thought the total mechanical energy would be the ...
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0answers
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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0answers
76 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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2answers
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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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2answers
100 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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2answers
64 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
73 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
59 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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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
73 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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57 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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2answers
203 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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2answers
56 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
34 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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3answers
60 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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3answers
2k views

Derivation of Kepler's laws

How can analytically be derived the Kepler's laws? I found some extremely synthetic equations which from the Newton's laws (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's ...
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0answers
37 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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1answer
2k views

Proving Kepler's 1st Law without differential equations

Is there a way to show that motion of Earth around the Sun is elliptical (Kepler's 1st law) from Newton's laws without resorting to the use of differential equations of motion?
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4answers
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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
100 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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1answer
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Kepler problem in time: how do two gravitationally attracted particles move?

Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ ...
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51 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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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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551 views

How does the gravity of a massive non-spherical object act on things around it?

Firstly, not sure if this question ought to be in the space SE site. Please let me know if it should. (Posted in both for now) Secondly, I don't know a whole lot about physics (I'm just inquisitive). ...
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2answers
52 views

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
102 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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1answer
152 views

Clearing up confusion about orbital mechanics

When I see an orbital mechanics problem, I recall the following things from my "toolbox": Angular momentum is conserved for a body orbiting a planet, since the torque due to gravity is 0. Kinetic ...
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1answer
27 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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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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3answers
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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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4answers
129 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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1answer
31 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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2answers
110 views

Newton's Principia: Astronomical prerequisites?

I am planning to read the Principia but I currently have no knowledge about Astronomy. What astronomy prerequisites do I need to understand the Principia? I would prefer older books (or "treatises"), ...
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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
330 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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2answers
31 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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5answers
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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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1answer
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Tidal tails of galaxies after collision

When there is a collision of 2 disc shaped galaxies, there is a tail formation created from both the galaxies. I read here that this was due to tidal forces, but I couldn't figure out how this ...
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1answer
53 views

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
77 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 ...
4
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1answer
2k views

Is acceleration due to gravity constant?

I was taught in school that acceleration due to gravity is constant. But recently, when I checked Physics textbook, I noted that $$F = \dfrac{G \cdot m_1 \cdot m_2}{r^2} $$ So, as the body falls ...
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6answers
2k views

The square in the Newton's law of universal gravitation is really a square?

When I was in the university (in the late 90s, circa 1995) I was told there had been research investigating the $2$ (the square of distance) in the Newton's law of universal gravitation. ...
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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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2answers
118 views

Why is the potential energy for a body raised up by a height negative?

I tried deriving the potential energy of a body when raised at a height $h$ above the earths surface, using the formula: $$PE = -W_\text{conservative}$$ where $W_\text{conservative}$ is the work ...
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3answers
244 views

Two bodies of equal mass thrown from a height-Practical physics question

I have a doubt about this question: Two bodies of masses $M$ and $m$ are allowed to fall from the same height. If the air resistance be the same for each of the bodies, will the two bodies reach ...