What is Newtonian gravity: Definition and 60 Discussions
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The publication of the theory has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.
In today's language, the law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is proportional to the product of the two masses, and inversely proportional to the square of the distance between them.The equation for universal gravitation thus takes the form:
F
=
G
m
1
m
2
r
2
,
{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},}
where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
The first test of Newton's theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has the product of two charges in place of the product of the masses, and the Coulomb constant in place of the gravitational constant.
Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme accuracy, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at small distances (such as Mercury's orbit around the Sun).
I want to find a dimensionless value that differentiates between concentrated mass systems such as the solar system and dispersed mass systems such as a galaxy. I assume spherical and radial symmetry, consider both the cases for point masses or smooth mass distributions.
The only value I can...
Assume that, in a binary system, one (and only one) of the two stars has a non-zero quadrupole moment. Then the other star feels the usual gravity force $F_g$ plus an additional force $F_q$ coming from the quadrupole potential. On the other hand, the first star feels only the usual gravity force...
Hello, I am attempting to work through problem 12.6 in MTW which involves formulating Newtonian Gravity using Curvature as opposed to the standard formulation. This is a precursor before standard GR. In it he states that the curvature tensor in this formulation is as follows...
I’m analysing the gravitational relationships between different mass astronomical bodies and am getting sick of having to individually google and document these.
Are there data sets out there that list pairs/sets of objects which includes their mass and distance from each other?
Including...
...y and Coulomb's law diverge as ##r\rightarrow##0? I mean, if a point light source emits light omnidirectionally, the intensity converges at the source, right?
THIS is how I should've worded my previous post!
Listen to the following arguments:
Earth's orbit isn't perfect ellipse because classically there is the gravitational field of moon and possibly of Mars and Venus which affect it
According to general relativity isn't perfect ellipse because there is the curvature of space time which doesn't...
It's a well known fact that acceleration due to gravity is independent of the mass of the accelerating body, and only depends on the mass of the body it is accelerating towards and the distance from it.
One can prove this mathematically very easily.
F=GMm/r^2 (equation 1)
but also F=ma...
[Mentor Note: thread split off from a different thread]
https://www.physicsforums.com/threads/heavier-objects-fall-faster.1002022/
Since seeing this thread yesterday, I have been trying to derive the time equation for the collision of two masses due to Newtonian gravity. Unfortunately, this...
Hello there.My question is:can Newtonian gravity be generalised to include not only bodies with mass but energy also?Thank you.Can my thread be moved to classical physics?
Before I attempt to delve into the math of tensors and curved spacetime, I'm hoping to get a more general intuitive grasp of things. As such, I'm parsing through a lot of lower level articles on these topics, and several that I've come across have argued that Newtonian gravity can be thought of...
I am a student of physics at a local Junior College in Mendham NJ and am planning on transferring to a 4 year program at the University of Alabama in a year. Iam having a bit of a difficult time understanding general relativity. Why does a photon bend twice as much under a gravitational field...
Code: https://pastebin.com/5LajNBpj
So I was messing with VPython, trying to create an Earth-Moon System. I got the actual gravity to work, and can create some nice ellipical orbits. However I run into trouble trying to make the actual (almost) circular orbit of the moon.
I know that the...
Homework Statement
A binary stellar system is made of one star with ##M_1=15{M}_\odot## and a second star with ##M_2=10{M}_\odot## revolving around circular orbits at a relative distance of ##d=0.001pc##. At some point ##M_1## explodes in a supernovae leaving a neutron star of mass...
So, I have heard that the deflection of starlight using Newtonian gravity is only half of the deflection predicted by Einstein. NE1 know where I can find an example of the former calculation? thanks
One particular form of the equivalence principle states that
The laws of physics for freely falling particles in a gravitational field are locally indistinguishable from those in a uniformly accelerating frame in Minkowski spacetime
My question is, does one arrive at this conclusion from a...
I have a (somewhat) strange energy equation which has the following form:
KE = A + B W + C \exp(-D W),
where A,B,D are known constant, C is an unknown constant to be determined and kinetic and potential energy are given by KE and W respectively with W\equiv W(r) i.e. is a function of...
Currently reading the following document which is a bit of a brain overload at the minute!
Im considering Equation (4.61). It is the general relativistic correction due to the Schwarzschild field for a near Earth satellite when the parameters \beta, \;\gamma \equiv 1. However, as you will...
In coordinates given by x^\mu = (ct,x,y,z) the line element is given
(ds)^2 = g_{00} (cdt)^2 + 2g_{oi}(cdt\;dx^i) + g_{ij}dx^idx^j,
where the g_{\mu\nu} are the components of the metric tensor and latin indices run from 1-3. In the first post-Newtonian approximation the space time metric is...
Homework Statement
Consider the Earth's orbit around the sun orbit as circular. Suppose the sun slowly loses mass from mass M1 to mass M2. Suppose that the initial orbit is R1 and the final orbit is R2. Express R2 in terms of the other parameters.
2. The attempt at a solution
The problem I'm...
In his little book for the layman, Seven Brief Lessons on Physics author Carlo Rovelli states:
What is it about SR which is incompatible with gravity-as-a-force?
Homework Statement
The space shuttle is in a 300 km-high circular orbit. It needs to reach a 520 km - high circular orbit to catch the Hubble Space Telescope for repairs. The shuttle's mass is 6.5 E4 kg. Mass of the Earth = 5.98 E24 kg. Radius of Earth = 6.37 E6 m.
How much energy is required...
I recently put together a simple 2D gravity simulator and I'd like to get some feedback or suggestions you may have for future updates. I'm planning to make a 3D version and improve the animation (framerate, realism, etc).
This first simulation includes the Sun, Mercury, Venus, Earth, and Mars...
I understand that General Relativity can make a difference between a spinning and non spinning mass thus can make better prediction for planetary orbits for example. The effect is frame dragging.
However if we simulate a Newtonian gravitation and instead of representing a planet as a sphere...
In Schutz says When we have weak gravitaional fields then the line element *ds* is
$$
ds^{2}=-(1+2\phi)dt^{2}+(1-2\phi)(dx^{2}+dy^{2}+dz^{2})
$$
so the metric is
$$
{g_{\alpha\beta}} =\eta_{\alpha\beta}+h_{\alpha\beta}= \left( \begin{array}{cccc}
-(1+2\phi) & 0 & 0 & 0\\
0 & (1-2\phi) & 0 &...
The Galilean equivalence principle (or weak equivalence principle) is the statement of the universality of free-fall under gravity. For example, according to Wikipedia, it can be stated as follows
My question regards the limitation of the principle to point masses. Does universality of...
I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##.
Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give...
Sorry for the amateurish setup that follows. Here's my thought experiment. Consider a 2-dimensional universe on the Cartesian plane. Earth is located at point (0,0). There is a binary system {A,B} oscillating around (1,1). To simplify, assume that the oscillation is 1-dimensional and occurs on...
I asked recently on another thread about relativity and its affect on gravitation. I have been informed that gravity is due to how energy bends spacetime, not the Newtonian idea of mass or even the special "relativistic mass."
However this leaves me wondering why general relativity does not...
Hello,
So i know that the gravitational acceleration experienced by a body is -GM/||d||^2 * dhat, where dhat is the current displacement unit vector, which has a magnitude of 1. the magnitude of a vector is equal to to the square root of the sum of its squared components. This will be a 2d...
Homework Statement
A 1.0kg object is released form rest 500km above the earth. What is its impact speed as it hits the ground? Ignore air resistance.
Homework Equations
##U_g = \frac{GmM_e}{r}##
##K = \frac{1}{2}mv^2##
## \Delta U = - \Delta K##
The Attempt at a Solution
Using energy...
Just a small newbie question. If Newtonian gravity is outdated and therefore inaccurate, why is it still taught?
Surely the fact that Einstein's gravity is right takes priority over the fact that Newton's method is easier.
Am I being ridiculous?
Mahmoud.
Can we just combine special relativity and Newtonian gravity? If cannot, why is it intuitively not possible? If can, why is the intuition behind it? Because if can, there seems to be a need for a mediator of force for gravity which can only travel at light speed.
Hi all:
In my free time, I've been playing with creating a code to help do toy simulations of gravity in my personal code of choice, FORTRAN. The first step was to get Newtonian gravity up and running and this has been pretty successful so far and I've been able to implement about 4 different...
This is part of a personal project... I've recently become addicted to modeling various physical systems from scratch, such that I find explicit solutions of position as a function of time, and graph em.
But I've hit a glass ceiling trying to find an analytic solution to the 1-dimensional...
For example at very low speed (v<<c), in Special Relativity, we can approximate relativistic motion to Classical Newtonian motion.
But in General Relativity, what situation can make there an approximation to Newtonian Gravity
( just like v<<c ) ?
Thanks.
Hey guys,
in classical mechanics Newton's law of universal gravitationa force says that the force between two bodies is equal to the product of their masses divided by the square root of the distance between them. So far, so good. In SR, lengths depend on the frame that we are in, and so the...
Hi everyone!
I've been thinking about a certain problem for a while now. And that is a Lagrangian formulation of Newtonian gravity. I know there is a Lagrangian formulation for general relativity. But I was hoping to find a Lagrangian for Newtonian gravity instead (for some continuous mass...
Homework Statement
A spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50 km. The on board thrusters fire, decreasing the speed of the spacecraft by 20 m/s, What is the speed (in km/h) in which the spacecraft crashes into the moon...
Hi guys! It is well known that the usual force based formulation of Newtonian gravity can be recast in a purely geometric form much like general relativity. This was originally done by Cartan and his theory is known as Newton-Cartan theory. Now I've tried to read up on rigorous formulations of...
In General relativity: an introduction for physicists, the authors derive Newtonian gravity from the EFE, but then they also give a short statement that inserting in the cosmological constant derives down to:
\vec{g}=-\nabla\Phi=-\frac{GM}{r^{2}}\hat{\vec{r}}+\frac{\Lambda...
Homework Statement
In deep space, three spherical masses are held in fixed positions (by rods light compared to the masses) at three corners of a square of side length sqrt(18) m as shown. The masses of the three spheres are m1 = m3 = 1.76×10^9 kg, and m2 = 2.75×10^9 kg. A relatively small...
Has anyone here looked at this paper?
Testing Newtonian gravity with distant globular clusters: NGC1851 and NGC1904
R. Scarpa, G. Marconi, G. Carraro, R. Falomo, S. Villanova
http://arxiv.org/pdf/1008.3526v1
(Submitted on 20 Aug 2010)
Globular clusters are useful to test the validity...
Hello. I've recently been working on the mathematics of atmospheric/stellar density, but I've run into an apparent paradox with the assumptions I have been using. I hope this is the right forum for this question.
At the moment, I'm working on the equations for the atmospheric pressure/density...
I've been told for many years now that the speed of Newtonian gravity is infinite. However, I've never received an explanation (or derivation) as to why this is that completely satisfies me. Even the explanations in textbooks (e.g Hartle) seem lackluster to me. So let's see...
The field...
Understanding the short-distance behaviour of gravity is crucial for constructing a quantum theory of gravity. The Newtonian inverse square law approximation has been tested in laboratory down to millimeter scales, but I'm not aware of any laboratory scale experiments testing general...
What exactly was wrong with Newtons gravity. I understan that GR says that gravity is the curveture of space and time. However if Newton was wrong wouldn't that mean that F= GMm/d^2 is actualy wrong?
I'd appreciate any explanations and maybe an available source that discusses how and why time is relatively more curved than space. Is there is particular source for time curvature in the stress/energy/momentum tensor?? Thank you.