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 When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.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:









{\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Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications.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).

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  1. I

    Dimensionless value to differentiate between concentrated and dispersed

    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...
  2. A

    I Star with quadrupole in a binary system violates Newton's 3rd Law?

    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...
  3. J

    MTW Exercise 12.6: Formulating Newtonian Gravity Using Curvature

    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...
  4. ForTheLoveOfPhysics

    B Data needed - Related bodies and their stats

    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...
  5. N

    B Why does ##F## often appear as inverse square laws such as Newtonian gravity?

    ...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!
  6. Delta2

    I Earth's orbit not perfect ellipse

    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...
  7. Lunct

    B Gravitational Force acting on a massless body

    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...
  8. alan123hk

    Testing Newtonian Gravity: Collision of Two Masses

    [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...
  9. T

    I Is it possible to extend Newtonian gravity to include energy as well as mass?

    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?
  10. G

    I Can Newtonian Gravity be Thought of as a Theory of Curved Time?

    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...
  11. A

    Derive Newtonian gravity from symmetry?

    Is it possible to derive laws of Newtonian gravity from some symmetries?
  12. M

    I General Relativity and light deflection

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  13. Quantum Physics

    I Newtonian Gravity Vs. Quantum Gravity

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  14. CrosisBH

    (VPython) Can someone help me with my orbit simulator?

    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...
  15. A

    Binary Stellar System: 15M⊙ & 10M⊙ Revisited

    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...
  16. H

    I Deflection of Starlight by Newtonian Gravity - Example Calculation

    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
  17. F

    I Inertial & non-inertial frames & the principle of equivalence

    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...
  18. M

    Newtonian energy integral and suitable boundary conditions

    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...
  19. M

    A Brain Overload: Comparing Proper Time, Ephemeris Time & Coordinate Time

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  20. M

    A How to obtain components of the metric tensor?

    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...
  21. Rwindsor1

    Change in the Earth's orbit radius from changing mass of the Sun

    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...
  22. Peter Martin

    I Special Relativity vs Newtonian Gravity: Understanding Their Compatibility

    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?
  23. S

    Problem using Newtonian Gravity.... Will you check my work?

    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...
  24. Ben S

    I How Can I Improve My 2D Newtonian Gravity Simulator?

    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...
  25. C

    B General relativity vs. Newtonian gravity

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  26. needved

    I Help with Newtonian Gravity as Limit of General Relativity

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  27. L

    I Galilean Equivalence Principle: Extended Objects

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  28. A

    Gravitation energy of a spherical shell

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  29. EnumaElish

    I (How) does the LIGO experiment falsify Newtonian gravity?

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  30. haushofer

    Insights The Revival of Newton-Cartan Theory - Comments

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  31. J

    Relativity versus Newtonian gravity

    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...
  32. C

    Newtonian gravity and differential equations

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  33. L

    Newtonian gravity theory and energy

    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...
  34. SpanishOmelette

    Is Newtonian gravity still relevant in modern physics?

    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.
  35. T

    Combining Special Relativity & Newtonian Gravity: Can We? Why?

    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.
  36. G

    Help Solve FORTRAN Post Newtonian Gravity Simulation

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  37. ellipsis

    Solving nonlinear differential to emulate Newtonian gravity

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  38. vlemon265

    When can we approximate General Relativity to Newtonian Gravity?

    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.
  39. A

    Newtonian gravity and Special Relativity

    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...
  40. BruceW

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  41. PsychonautQQ

    Calculating Final Velocity of a Spacecraft Crashing into the Moon

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  42. WannabeNewton

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  43. M

    Denominator in cosmological constant term in Newtonian gravity

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  44. J

    Newtonian Gravity involving spheres in a trigonal pyramid

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  45. inflector

    Are Distant Globular Clusters the Key to Testing Newtonian Gravity?

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  46. O

    Density of Atmospheric Gas Using Newtonian Gravity

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  47. Nabeshin

    What is the speed of Newtonian gravity?

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  48. P

    Any Laboratory Scale Test of GR's correction to Newtonian Gravity?

    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...
  49. S

    Newtonian Gravity: How GR Affects F=GMm/d^2

    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?
  50. N

    Newtonian Gravity: curved time

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