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Inertial and gravitational mass

  1. Jun 24, 2003 #1
    What's the difference between inertial mass and gravitational mass?
  2. jcsd
  3. Jun 24, 2003 #2


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    See www.geocities.com/physics_world/mass_concept.htm

    n Einstein's words
    By the word “mass” of a body one denotes two things that are very different according to their definitions: on the one hand, the inertial resistance of the body and, on the other hand, the characteristic constant that is the determining factor for the effect of the gravitational field on the body.

    See also -- www.geocities.com/physics_world/mass_concept.htm

  4. Jun 27, 2003 #3
    Einstein discovered that there is none. This is called the equivalence of gravitational and inertial mass.
  5. Jun 27, 2003 #4
    I thought that this was just a hypothesis of einstein.

    Anyway, gravitational mass is the number that you plusg into gravity equations. Inertial mass is the number you plug into F = ma
  6. Jun 27, 2003 #5


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    At the time Einstein was writing, a great experimentalist named Eotvos had demonstrated the numerical equality of inertial and gravitational mass for many materials. Since that time this has continued to interest experimentalists and many measurements have confirmed the equality to high orders of accuracy.

    That doesn't prove it is so, of course, but it sets a high bar for those who might try to falsify it.
  7. Jun 27, 2003 #6
    Re: Re: inertial and gravitational mass

    Well, I knew that they are numerically the same. I was wondering actually what they are supposed to measure. The only way for it to be possible that they are numerically different is if they measure different quantities. Why else would a scientist have to conduct an experiment to show they are the same?
    In the book I'm reading now, Matter and Motion by Clerk Maxwell, he writes (in Article 50), "the force required to produce a given change of velocity in a given time is proportional to the number of units of mass* of which the body consists"
    The footnote reads: "Here mass means the measure of inertia rather than the quantity of matter; at extremely great speeds they would not be proportional, but connected by a law involving the speed, so that the momentum or impulse would then be the primary quantity and inertia a derived one."
    That's not where my question came from, but it seems to contain the answer. I would speculate that inertial mass is a measure of inertia, and gravitational mass is a measure of the quantity of matter. Then, from what is written in the footnote, I concluded that at high speeds these two quantities deviate from each other (ie, they would not be proportional). Is that correct?
  8. Jun 29, 2003 #7


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    Re: Re: inertial and gravitational mass

    Not quite - That fact was around long before Einstein. GR does not explain the equivalence - it postulates it
  9. Jun 29, 2003 #8
    Indeed, while so far nobody really disputes the difference (because if there is one, its incredibly small), there still is no real reason why inertial mass should be so close/equal to gravitational mass.

    Simply put, Intertial mass is the mass an object has with regards to resisting a force imparted on it (try and push a ball on a horizontal plane). Gravitational mass is the mass an object has with regards to attracting objects with a gravitational force.
  10. Jun 29, 2003 #9
    Re: Re: inertial and gravitational mass

    Einstein postulated that there was no difference in principle, and that is what lead him to a theory of gravity based on space-time curvature. And as I brought up in another thread, we can derive the property of inertia from simple considerations of quantum mechanics and special relativity, so that if C2 is constant the gravitation can be associated with the energy as easily as with the inertia.
  11. Jul 6, 2003 #10
  12. Jul 6, 2003 #11


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    Re: Re: Re: inertial and gravitational mass

    What led Einstein to a theory of gravity was not curved spacetime - that was simply something that happened along the way. What guided Einstein was the Equivalence Principle which was based on the equality of gravitational and inertial mass. And this implied that the gravitational force is an inertial force. I.e. According to Einstein

    If you want the original article I got that from then read this


  13. Jul 6, 2003 #12
    I was under the impression that mass was mass was mass.

    Isn't mass related to inertia by F = ma.
    Since gravity is a force then why should it cause confusion?
  14. Jul 6, 2003 #13
    Re: Re: Re: inertial and gravitational mass

    You sure know how to start an argument, Stephen.
    This question has been debated heatedly before in other circles; yet it is a very valid concern.
    Obviously, it hasn't been answered or even addressed here yet.

    Your assumption of gravitational and inertial mass deviation at high speeds is predicated on graviatational mass being, as you stated, a function of the'quantity of matter'. However, that is rather nebulous. What exactly is 'a quantity of matter'? Don't we measure the quantity of matter ultimately by inertial reaction? thus making gravitational mass identical to inertial mass? From that standpoint then, like PMB has pointed out with Einstein, they can be considered identical. But can't we measure it gravitationally also?

    However, now (and in answer to your question) we have a conceptual problem (hotly debated often) involving gravitational bodies moving at relativistic speeds. Does the increase in inertial mass (due to velocity) mean an increase in gravitation? Moving mass has greater gravity? If so does one observer at rest relative to a body see a gravitational acceleration that is different than an observer traveling quickly with respect to it?

    If so would not a moving observer measure planets as having a different orbital period than measured by a person at rest? How can that be? Now you've turned this into a full blown relativistic question. Shame on you.:wink:

    Last edited: Jul 6, 2003
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