How Do We Calculate the Gravity of Different Particles and Celestial Bodies?

[mvan4310]

Hello,

I have some questions regarding gravity. I was wondering if there was a certain formula to figure out the gravity of particles.

For instance, we have a single proton, how would we know its gravity? On the other end of the scale, we have a neutron star, how would I figure out its gravity? Does adding particles together essentially add up the total gravity, or does it work differently.

Could you provide examples, and also formulas?

Thank you,
Mike

 

[Bloodthunder]

\vec{g}=\frac{GM}{r^{2}}\hat{r}

This is the gravitational acceleration, the acceleration on an object caused by gravity from another object of mass M.

Does adding particles together essentially add up the total gravity

Yes.

 

[santo35]

Hello,

I have some questions regarding gravity. I was wondering if there was a certain formula to figure out the gravity of particles.

For instance, we have a single proton, how would we know its gravity? On the other end of the scale, we have a neutron star, how would I figure out its gravity? Does adding particles together essentially add up the total gravity, or does it work differently.

Could you provide examples, and also formulas?

Thank you,
Mike

i don think this is a valid question as it makes no sense to talk about gravity of a particle...you can talk about gravitational field of a particle as function of distance or you can talk about gravitational force of system of particle...to my knowldge i don't think there is anything called "gravity of a single proton"

 

[TurtleMeister]

If you're talking about active gravitational mass, then you can use the equation in Bloodthunder's post - but only for macro objects. However, when it comes to individual particles, then the answer is unknown. According to the equivalence principle, the active gravitational mass of a particle should equal it's inertial mass. But it is only a postulate, or assumption. Experimental tests of the active gravitational mass for samples of different compositions have been few and far between. The latest laboratory experiment that I know of was the Kreuzer experiment of 1966. And the sensitivity of that experiment is dwarfed by the sensitivity of modern torsion balance technology. Why there have been no new experiments since 1966 is a mystery to me. Well, actually I can think of one possible reason, which I think is ill founded, but I won't get into that since it is against forum rules to express personal theories. Suffice it to say that until experimental tests prove otherwise, it is a safe bet to side with the equivalence principle and say that a particles contribution to the active gravitational mass of a macro object is proportionally equivalent to it's contribution to the objects inertial mass.

 

[Vagn]

If you're talking about active gravitational mass, then you can use the equation in Bloodthunder's post - but only for macro objects. However, when it comes to individual particles, then the answer is unknown. According to the equivalence principle, the active gravitational mass of a particle should equal it's inertial mass. But it is only a postulate, or assumption. Experimental tests of the active gravitational mass for samples of different compositions have been few and far between. The latest laboratory experiment that I know of was the Kreuzer experiment of 1966. And the sensitivity of that experiment is dwarfed by the sensitivity of modern torsion balance technology. Why there have been no new experiments since 1966 is a mystery to me. Well, actually I can think of one possible reason, which I think is ill founded, but I won't get into that since it is against forum rules to express personal theories. Suffice it to say that until experimental tests prove otherwise, it is a safe bet to side with the equivalence principle and say that a particles contribution to the active gravitational mass of a macro object is proportionally equivalent to it's contribution to the objects inertial mass.

The equivalence principle has been tested further.
http://physicsworld.com/cws/article/news/20870
http://arxiv.org/abs/physics/0411052

 

[TurtleMeister]

Thanks for the links Vagn. However, the experiment that you sited is for the equivalence principle as it relates to passive gravitational mass. The Kreuzer experiment was for the equivalence principle as it relates to active gravitational mass. The two concepts are very different. Specifically, the Kreuzer experiment was to determine if the active gravitational mass of matter has any correlation to it's composition. This is not the same thing as testing how two objects of different composition free falls in a gravitational field, which is the equivalence principle for m_p = m_i.

In other words, if you have two objects (not necassarily single particles) of equal inertial mass but different compositions, will they both produce the same strength gravitational field? Is m_a = m_i true for all compositions of matter? As far as I know, the Kreuzer experiment stands alone as the only modern day, if you call 1966 modern day, laboratory experiment to put this question to the test. Why is that?

If you're interested you can read about the Kreuzer experiment via http://books.google.com/books?id=3U..."gravitational constant" composition&f=false" google books link. The link will take you to the II. Theory section, which you should read first. The actual experiment uses an unusual technique, but the experiment can be done with the ordinary torsion balance.