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

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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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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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42 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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76 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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491 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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39 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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200 views

What is the simplest way to perform a Cavendish experiment?

The Cavendish experiment is cool, but seems complicated to experimentally perform. What is a simple way to recreate the experiment?
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86 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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208 views

Deceleration rate of objects of different mass but the same otherwise

Using a tennis ball as an example object, if one ball weighs 1 ounce and the other is 2 ounces, and both are struck at 100 mph on the same trajectory, would there be any difference in the deceleration ...
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1answer
261 views

Tension in string and gravitational force on bob relative strength

When calculating time period of simple pendulum (an approximation of SHM at small amplitudes) we take gravitational force greater than tension in string and resolve gravitational force in two ...
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1answer
109 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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23 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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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
102 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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21 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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1answer
184 views

Is gravitation really a conservative force?

A spinning gyroscope has a rigidity in space. That means it maintains its axis in relation to space – and not to the surface of the earth: Imagine a spinning gyroscope that is freely mounted in ...
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2answers
101 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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63 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
304 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
22 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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30 views

Condition on $U_{eff}$ for a mass to get trapped in orbit around a heavier mass

this question is now solved, and I have already edited the wikipedia page The wikipedia page on Effective Gravitational Potential states that $$U_{eff} \leq E$$ is a condition for a free mass getting ...
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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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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
50 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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64 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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4answers
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Gravity - What happens when two objects of unequal masses fall freely towards the ground? (Revisited)

The common perception regarding what happens when two objects of equal sizes but unequal mass are allowed to fall freely towards the ground is that - both the objects make contact with the ground at ...
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2answers
110 views

Expression for Atmospheric Pressure with Altitude, including Tidal Forces

Is this simple to obtain? I've tried to modify the constant-gravity model to use the $GM/r^2$ form instead, but my result was shown to be wrong with some testing. Constant Gravity Model You can ...
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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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What is the particle distribution in Saturn's Ring System?

In watching the scientifically scream-inducing film 'Interstellar', there was a shot of the spacecraft moving through the Rings of Saturn. In this shot, and in every graphical representation of the ...
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6answers
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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
28 views

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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143 views

Calculate orbit height from tangential velocity

Is it possible to calculate the altitude of a satellite orbiting a planet, just from the planet's mass and the satellite's velocity, assuming that the satellite is in a perfect circular orbit? If so, ...
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113 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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225 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 ...
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4answers
91 views

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
39 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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Is it possible to prove that planets should be approximately spherical using the calculus of variations?

Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical? Lets assume that a planet is 'born' when lots of ...
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0answers
37 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" ...
11
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1answer
591 views

Apollo and orbital mechanics: orbital decay if the Trans Earth Injection (TEI) burn had failed

I'm reading Jim Lovell (Apollo 8 and 13) and Jeffrey Kluger's book Apollo 13, which is a fantastic read about a long past era I only have kindergarten memories of. On page 54 there is a paragraph that ...
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1answer
75 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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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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6answers
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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 ...
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10answers
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Why do space crafts take off with rockets instead of just ascending like an aircraft until they reach space?

I guess it's not a very educated question, but I never quite understood why spacecrafts have to shoot up and can't just reach space by simply continuing an upwards ascent like an airplane.
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2answers
49 views

The mass/energy of an $H$-atom and the gravitational force between it and another particle of mass $m$

The gravitational force between an $H$-atom and another particle of mass $m$ will be given by Newton's law: $$F=\frac{GMm}{r^2}$$ The question is, what is $M$ here? I thought the answer would be ...
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128 views

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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6answers
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If the gravity at the center of the Earth is zero, why are heavy elements like iron there?

If gravity is zero at the center of the earth, why is there a core of heavy elements, such as iron? Alternate question for the opposite hypothesis: If gravity is greatest at the center of the ...
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1answer
83 views

What is the Jacobian matrix of Newton's law of gravity? [closed]

I am trying to come up with the gradient of a vector (Jacobian matrix) for Newton's Law of Gravity. In other words, the differential gravitational field in 3-dimension. Here's the initial Law. ...