Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Newton's Law of Gravitation

  1. Jun 6, 2005 #1
    Does any one know the proof for newton's law of gravity, because i looked in a lot of books for this proof but i didn't find it anywhere!!!
    Slowly i'm getting a little cautious about what we're easily accepting in school!
    Thanks for your reply.
  2. jcsd
  3. Jun 6, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    In perfect analogy with electrostatics,Gauss's law for the gravitostatic field is postulated.Using Gauss-Ostrogradski's theorem,one derives the Poisson equation for the gravitostatic field,whose solution for a delta-Dirac mass distribution is a gravity field identical with the one assumed by Newton.

    That's how it's done axiomatically.

  4. Jun 6, 2005 #3

    There is no proof at classical level!!

    because Newton law is not a theorem. It's postulated from the beggining.

    Note that dextercioby needs postulate first an analogous to Gauss's law of electrostatics. I prefer postulate Newton dynamical law and derive Gauss's law for the gravitostatic field.

    In any case one begins from an initial asumption.

    Regarding historical issues, Newton did a study of experimental data and an mathematical analysis of Kepler laws for planetary motion.
    Last edited: Jun 6, 2005
  5. Jun 6, 2005 #4

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Juan R. is right. There's no "proof" which doesn't rely on other assumptions.

    Newton essentially guessed at the law in order to fit observations. He guessed very well indeed.

    In the light of later theories and mathematical models, such as Gauss's law, which dextercioby mentioned, Newton's law fits in very nicely.

    It is possible to derive Newton's law as an approximation to Einstein's general theory of relativity in a "flat" spacetime, but Einstein's theory also rests on assumptions.

    The ultimate test of whether you should trust a physical theory or not is how well it predicts observations and experimental results. Newton's gravity does an excellent job. Einstein's gravity is even better.
  6. Jun 7, 2005 #5
    Newton theory is not rigorously reduced to GR

    As broadly explained in "Is GR a wrong approach to gravitation?" (last posts), in the theory development forum, there is no rigorous derivation of Newton gravitation from Einstein GR.

    Usual "metric" derivation (appears in textbooks) is not strictly correct and asumes many points without rigor. Moreover one does not derive Newton gravitation.

    For solving this, relativists developed other derivation, from so-called "afine" gravitation. This very modern derivation needs of a firsts rewriting of Einstein GR, a previous geometrization (covariant) of Newton theory, and the asumption of aditional equations. Here one "derive" Newton Cartan theory. This is not a derivation (see extensive comments in other post) because one need of aditional equations (does not contained in GR) regarding curvature tensor in the "new spacetime". Moreover, one authors use unphysical boundary equations for the derivation. Finally one derives a equation that look like Newton but is not exactly Newton theory.

    From a new more rigorous theory we can obtain Newton theory whereas explaining relativistic tests and other tests do not explained (or with difficulty) by GR.
  7. Jun 11, 2005 #6
    You mean newton's gravitational law is not proovable using only newton's three laws as axioms??
  8. Jun 11, 2005 #7

    Doc Al

    User Avatar

    Staff: Mentor

    That is correct.
  9. Jun 11, 2005 #8


    User Avatar
    Staff Emeritus
    Science Advisor

    In "defense" of Newton (as if he needed me!) he did show that in order that Kepler's laws be satisfied, the force keeping the planets in orbit about the sun must be directed toward the sun and must be an inverse square law.
  10. Jun 14, 2005 #9
    How can you proove what you're saying????? :rolleyes:
  11. Jun 14, 2005 #10

    Doc Al

    User Avatar

    Staff: Mentor

    I interpreted your question to be: "Is Newton's Law of gravity derivable from Newton's 3 laws of motion?" I assume you meant derivable solely from the laws of motion and nothing else, in which case the answer is no.

    As Halls stated, using his laws of motion along with Kepler's laws, Newton was able to deduce an inverse square law of gravity.
  12. Jun 14, 2005 #11
    As per my information , newton derived the newton's law of Gravitation using a bit of experience from Kepler's equation's , the three laws of motion and a bit of analysis .. like he did experiments and found out that the Force is proportional to product of the masses and follows the inverse square law , further G was calculated correctly through Cavendish Experiment .
  13. Jun 14, 2005 #12


    User Avatar
    Science Advisor
    Homework Helper

    Nope,from what i recall,Newton obtain his law without any measurements.Theorist work.He was an experimentalist,but with other subjects.

  14. Jun 14, 2005 #13


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Daniel is right; intially, Newton thought ought how it "ought" to be.
    When he compared it to available data, he found his theory to be lacking in accuracy, so he shoved his theory into the closet.

    The initial data were flawed, however (at least that set Newton initially used); once the empirical material was improved, Newton shook the dust off his old theory.

    (That's how I recall it..)
  15. Jun 14, 2005 #14
    Newton was an experimentalist

    The comments by arildno and dextercioby are not very accurate if claim that Newton was a theorist. The old idea of Newton discovering gravitation from a falling apple is a fantasy without historical rigor.

    Modern historical discoveries show that his theory of gravitation was basically like I outlined in a previous post. Moreover, one can add intersting details.

    For example, one can say that the basis for his theory was obtained from his previous research in chemistry, concretely in chemical affinity: attraction and repuslion between chemical bodies.

    That from chemical experiments he derived the law of action and reaction, whereas rest of physicists and mathematicians were searching the law of motion of planets around Sun, etc.

    From his physico-chemical experiments, Newton did studies on densities and matter and after studied pendular motion with that and finally used the data for studying oscilatory motion of Jupiter satellites, etc.

    He could not make experiments on gravitatory affinity (like he did in chemical affinity with Fe, Cu, Ag...) and therefore he was forced to use available data from astronomers. But he was not a theoretician since his theory of gravitation is directly based in his previous work in chemical affinity.

    Last historical studies show that he devoted more than 30 years to experiments (especially chemistry and alchemy) and just one or two years to theory and math.
    Last edited: Jun 14, 2005
  16. Jun 14, 2005 #15


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Kindly refrain from making these types of insinuations.
    Nowhere have I stated that this myth is the origin of Newton's theory.
  17. Jun 14, 2005 #16
    The data flawed was actually "distance between the earth and moon " which was correctly calculated afterwards and this verified the newton's data....
  18. Jun 14, 2005 #17
    The data flawed was actually "distance between the earth and moon " which was correctly calculated afterwards and this verified the newton's data....

    Actually Law Of Gravitation came naturally to him . He was a man of considerable feeling for generalities .

    As per Feynamn:
    " Newton appreciated that the sun could be the seat of forces that govern the motion of the planets.Newton after analysing Kepler's Law proved to himself that equal areas are swept out in equal times is a precise sign post that all deviations are precisely radial..........Now by analyzing Keplers Laws , it was possible to show that farther away the planet , the weaker the forces .....With the combination of two laws , Newton concluded that there must be a force , inversely as the square of the distance , directly in line with the objects..."
  19. Jun 14, 2005 #18


    User Avatar
    Science Advisor
    Homework Helper

    Chemical affinity...?Hmm,i heard Newton was a known alchemist,but please come up with articles/books written by Newton on this specific subject.

  20. Jun 15, 2005 #19
    Well Newton was not a known alchemist. He was the alchemist. He was the most readed and studied alchemist of the epoque.

    Physicists presented to Newton like the great genious and when studied his work (when died) physicists discovered that the genious was an alchemist. Then they split his work into two parts: physics/math and the rest. The former was published, and the rest was burned...

    Well, fortunately the family doesn't burn other works and were rediscovered around 1960. They are so numerous that still today historians have studied only a small part of them, in fact, the database was still opened the last year. I don't know if now was already closed once all Newton articles recolected for further study.

    However, the vision of Newton like an alchemist/chemist with very, very small interest in physics or math (low level research in his words when compared with chemical sciences) is well proven. The interest is computed around 30/1. That is, 30 years of intense research for chemistry/alchemy for each year on math/physics.

    His derivation of gravitational affinity from his previous theory of chemical affinity is well-proven, including his laboratory notes in experiments with attraction and measure of masses, etc. The history of apple, so extended, is considered a mith without support today. It is really interesting that Brian Greene in his Elegant universe use a apple for illustrate the structure of matter. Casuality? Perhaps an attempt to suggest that from theoretical efforts only one can obtain a theory of nature?

    The popular idea of Newton like a pure theoretician, discovering natural laws from the falling of an apple, is a mith. I said is correct. Next recent words of Ludovico Geymonat (in Spanish)

    "La atención que dedican a estos estudios [it refers to Newton chemical studies] los más modernos historiadores ha modificado profundamente el esquema tradicional con el que se presentaba la figura de Newton. Ya no se nos presenta como el puro teórico prevalentemente dirigido a sistematizar las grandes leyes de la mecánica, sino sobre todo como un experimentador, empeñado desde los primeros años de su juventud en interrogar a la naturaleza, recoger con la máxima precisión los datos de la experiencia y controlar en ellos toda tentativa de explicación teórica."

    Some modern authors consider to Newton chemist and physicist, other consider that was the second physical chemist (Boyle was the 1º) of history.

    Isaac Newton, 1987, Principios matemáticos de la filosofía natural 1. Introducción y Libro I, (Introducción, traducción y notas de Eloy Rada García) Alianza Editorial S.A, Madrid.

    is one interesting book containing the latter historical discoveries on the topic. I also have notes in the last confgerence in the topic. If you cannot read in Spanish, don't worry. I prepared an educative article on the history of Newton and his research and was available in a previous web. I will post for open download again in


    since that history is one of research program of Center


    The case of Newton is not unique. Many historians of science claim openly that the history of physics was often rewritten and physics emphasized over other sciences.

    There are dozen of well-documented examples: for example the prediction of neutron was not done by physicists, the first study of quantum tuneling was not that of Gamow, one of Feynmann theorems was discovered years before, etc, etc.

    Unfortunately, this style of many physicists of hidde/ignore contributions of other fields/authors appears to be today observed in string theory literature. Some people claimed that several studies and claims of string theory were done in other theories before (a mathematician said to me that some recent work in M theory was done years before in other theory), but string theorists do not cite them (she contacted in several occasions with Witten and others). I have not historical confirmation of this fact, but i have a phrase from a string theorist supporting that interpretation.
    Last edited: Jun 15, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Newton's Law of Gravitation