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

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Are elliptical orbits really elliptical?

I have wondered for a long time how elliptical orbits can work. It seems awkward for a freely-moving object to come very close to a source of gravity and then return to the exact point where it ...
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4answers
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Forces on a ball thrown upwards

When a ball is thrown up in upward direction, it is said that force is in downward direction. Why we don't we consider the force given to the ball to throw up in the upward direction? Is there is no ...
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1answer
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Gravity and angular momentum

When a mass moves towards a bigger mass at a constant velocity, they will be attracted to each other such that the smaller mass will revolve around the bigger mass with the same speed as before. ...
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0answers
59 views

Why does a velocity that gives gravity's centripetal acceleration make you stay in orbit?

Explanations of basic orbital mechanics that I can find all go, $$\frac{v_{satellite}^2}{r} = a_c = \frac{F_{gravity}}{M_{planet}} = \frac{(\frac{G M_a M_s}{r^2})}{M_{planet}}$$ , and so you get a ...
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1answer
342 views

Solving the Three-body problem numerically

I want to create a program in $Mathematica$ that solves numerically the Three-body problem by Euler-Lagrange's equations. I was searching some methods to sucessfully do it. So I found a way to solve ...
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2answers
97 views

If maximum speed limit $c$ is made infinite, will general theory of relativity become equivalent to Newton's gravitational theory?

We know that special relativity tends to become equivalent to classical theory of relativity as the speed limit of nature becomes infinite. If this happens, clock will tick at the same rate ...
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1answer
110 views

Balanced and Unbalanced Forces Help

I am a newbie pondering in Physics concepts. I just had a question about Newtonian physics. The reason why "everyday" objects come to a rest is because there are unbalanced forces working against ...
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1answer
46 views

Derivation Poisson's gravity equation by divergence theorem [closed]

I'm trying deduce the poisson's equation $\nabla^2\Phi (x)=-4\pi G\sigma(x)$ by divergence theorem Let $D:x^2+y^2+z^2\leq 1$ and $\sigma:D\to \mathbb{R}$ be the mass density function of $D$ (suppose ...
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1answer
100 views

Why Poisson's equation is important?

The Poisson equation can be deduced by Newton's mechanics: $$\Delta \Phi =-4\pi G\sigma$$ Einstein tried to give a "Poisson's equation" that works with his theory. This equation seems to be ...
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4answers
105 views

Orbits for dummies [duplicate]

In a certain universe a perfectly spherical, uniformly dense planet is found to be in a stable orbit around a stable star. The rest of the universe is empty space with no silly stuff like dark matter. ...
3
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3answers
368 views

Why the $r$ is cubed in the vector notation for of Newton's Law of Universal Gravitation? [duplicate]

I'm learning about astrodynamics on my own and I was wondering why the $r$ is cubed in the vector notation for of Newton's Law of Universal Gravitation: $$\vec{F}_g=\frac{Gm_1m_2}{|\vec{r}|^3}\vec{r}$...
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2answers
853 views

Why is there no permittivity-type constant for gravitation?

When I look at electric or magnetic fields, each of them has a constant that defines how a field affects or is affected by a medium. For example, electric fields in vacuum have a permittivity constant ...
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2answers
49 views

Why doesn't the gravitational force have a permittivity in its formula? [duplicate]

We know that the electrostatic force between two charges depends on the medium between the charges and its permittivity. Why, then, doesn't the gravitational force depend on the medium?
2
votes
3answers
712 views

Can Newton's Law of gravity be deduced using dimensional analysis?

I tried using dimensional analysis to deduce Newton's law of gravity but I wasn't able to do so as one of the equations were $0=-2$ which is a contradiction. But I thought that we can't do that ...
2
votes
7answers
13k views

Trouble understanding the concept of true and apparent weight

I need help understanding the concept of true weight vs apparent weight. I understand this much: if someone is standing in an elevator on a scale, the further up they go the less the reading on the ...
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4answers
4k views

If water is essentially incompressible, why are there tides?

So recently we were taught in school that tides are formed because the moon 'cancels out' some of the earth's gravity, and so the water rises because of the weaker force. But if water is not ...
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1answer
35 views

What is the gravitational/electric/inverse-square field inside a cylinder?

I've read from the shell theorem that an inverse-square potential has zero field inside a spherical shell. What about the field inside a cylinder? Are objects inside a long cylinder attracted to the ...
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0answers
61 views

Are tides just very very very weak spaghettification?

I was wondering as to why there are two tidal bulges instead of just one on Earth, and then I saw this diagram: The oval shape that the Earth's water is transformed into in this image reminded me of ...
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3answers
405 views

Terminal velocity after vertical launch

If an object is launched directly up at its terminal velocity, will it have enough time/energy to reach its terminal velocity again before it hits the ground, or will drag prevent this? In this case, ...
2
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2answers
86 views

Question about inertial mass and gravitational mass

I know that inertial mass $m_i$ is the quantity that appears in Newton's second law: $F=m_ia$ and that gravitational mass $m_{g_1}$ is the quantity that appears in Newton's gravitational law: $F_g=Gm_{...
6
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2answers
170 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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2answers
67 views

Which timestep should I use for a $N$-body simulation of the Solar system?

I am trying to implement a $N$-body simulation of the Solar system and I am stuck on the issue of the simulation timestep size. At first I would like to use a simple Euler stepping scheme. Knowing ...
3
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2answers
148 views

How are the theoretical properties of a gravity train linked to orbital properties?

Whilst perusing a question on WorldBuilding, a link was given to an article about Gravity Trains. Some of the answers on the question, and the Wikipedia article, state a travel time of 42 minutes ...
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1answer
40 views

Unification of Newtonian gravity and electrostatic force [closed]

Can we not unify Newtonian gravity & electrostatic force? All properties are almost same. We can imagine the atoms of the Earth's core to become dipoles when a body is freely-falling. Thus, due to ...
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2answers
71 views

Proportional acceleration due to changing density of the Earth

My question has to to do with a recent video Minutephysics posted about the time it takes for a person to fall through the earth, found here http://www.youtube.com/watch?v=urQCmMiHKQk At around 4:05,...
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2answers
216 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, planet)...
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2answers
2k 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 ...
5
votes
3answers
694 views

Rocket launch from a mountain

If we were to build a high speed rail up the side of a mountain like in some Science Fiction movies, what is the velocity needed at the point of leaving the mountain excluding angular momentum from ...
3
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3answers
278 views

Why does earth have a minimum orbital period?

Using the equation for Kepler's constant for Earth $K$: $$K = \frac{GM}{4\pi^2}$$ $$K = 1.01 \times 10^{13} \;\rm m^3/s^2$$ Finding time ($r = 6.4 \times 10^{6} \;\rm m$ (radius of Earth)): $$K = \...
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4answers
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Why do some location on Earth have only one tidal maximum per day instead of two?

Most places in the ocean have two high tides and two low tides per "day" (~25 hours). But I remember reading that some locations only have one of each per day. This answer has some great explanations ...
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2answers
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Reference frame, gravitation and kinetic energy

English is not my primary language. I apologize (and would like corrections) if the terms I use are not the right ones. In a geocentric reference frame, the moon rotates around the Earth. So its ...
131
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7answers
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Does Earth really have two high-tide bulges on opposite sides?

The bit that makes sense – tidal forces My physics teacher explained that most tidal effect is caused by the Moon rotating around the Earth, and some also by the Sun. They said that in the Earth and ...
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1answer
107 views

Potential of an axisymmetric disc with constant rotation velocity

I am having trouble understanding why the form of the 3D potential for a disc with a constant rotation velocity for circular orbits of stars within the disc \begin{equation} v(R) = v_0, \tag{1} \end{...
6
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4answers
603 views

Can the gravitational constant $G$ be calculated theoretically?

We know all that the gravitational constant is $$G=6.67428±0.00067\times 10^{-11}\mathrm{m^{3} \:kg^{-1} s^{-2}}.$$ But can we calculate it theoretically?
1
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1answer
90 views

Period of a pendulum [closed]

In the book 'Calculus the Early Transcendetals' at page 776 (7th edition) they give that the period of a pendulum with length $\text{L}$ that makes a maximum angle $\theta_0$ with the vertical is: $$\...
0
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1answer
73 views

As planets orbit around the Sun, does the force of gravity due to the Sun remain constant?

I know that the force of gravity is: $$F = GMm/R^2$$ Where $G$ is gravitational constant, $M$ is mass of sun, $m$ is mass of the orbiting planet and $R$ is the distance between the center of their ...
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4answers
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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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0answers
60 views

Does a ball bearing cause bigger tides than the moon?

As per the answer to this question it is suggested the relative tidal pull of objects of equal angular area is equal to their relative density. Which lead me to the click-baity question: Does a ball ...
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2answers
50 views

Would an astronaut floating in space at zero speed get drawn to the Earth?

The question came to mind after watching this video: http://www.youtube.com/watch?v=MTY1Kje0yLg If the Earth and Moon can bend space-time, and if the Earth's gravity is strong enough to reach the ...
3
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1answer
76 views

Why didn't I beat the avalanche?

Yesterday, while skiing out of bounds on the south west canyons of Mt. Hood, I experienced a small and extremely mild quake. This, combined with the melting conditions caused an extremely small ...
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2answers
48 views

Calculate gravity between two points

I am trying to build a simulation of gravity in LibGDX using Bullet physics. To simplify it, I just want to apply a force on some body towered a (0,0,0) point. I got my body mass and it's location ...
0
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0answers
614 views

Gravity change as a function of time only [duplicate]

Is it possible to find how gravity changes with time? That is, height is not part of the equation. For example, $g$ can be expressed as a function of height that does not involve time with this ...
13
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2answers
833 views

How can we recover the Newtonian gravitational potential from the metric of general relativity?

The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration: $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\...
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votes
2answers
77 views

Use equations to create a realistic problem [closed]

Given the following equations: $100$ m = $0$ m + ($50 \cos\theta$ m/s)$t_1$ $0$ m = $0$ m + ($50 \sin\theta$ m/s)$t_1$ - $\frac{1}{2}(9.80$ m/s2$) t_1^2$ I am supposed to make up/create a real-life ...
5
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2answers
838 views

$1/r^2$ gravitational force of triangles in 2D

Suppose I have two triangles relatively close together (so they probably shouldn't really be treated as point masses). I want to calculate the gravitational force (and potentially torque?) generated ...
5
votes
1answer
97 views

Trying to understand Newtonian limit of GR

First ever post - please be kind. I'm trying to understand how General Relativity becomes equivalent to Newton's laws of motion, plus Newton's law of gravitational attraction in the limiting case of ...
3
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1answer
35 views

Orbital parameters of more than two bodies

I am not even entirely sure that the question makes sense except in certain simple cases, but let me explain what I am trying to do, but with the question first. The question is essentially: Given n ...
0
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1answer
61 views

Gravity Sun Earth Moon [duplicate]

The gravitational pull the Sun has on the Moon is roughly two times greater than the pull the Earth has on the Moon. If this is the case, why does the Sun's gravity not pull the Moon away from the ...
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0answers
39 views

Centre of gravity of system [closed]

We have a uniform rectangular tray of dimensions 40x60, with weight 3. We place the coordinate axes in such a way that the bottom-left corner of tray is at the origin and the tray sides are parallel ...
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0answers
26 views

falling in a gravitional field [duplicate]

It is often stated that masses fall at the same rate towards the Earth at the same rate (barring things like friction), and this seems to be quoted as the Equivalence Principle. Is this statement ...