# The Naked Scientists Forum

### Author Topic: Where is r measured from in the gravitation equation GMm/r sqr?  (Read 2508 times)

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3770
• Thanked: 47 times
• The graviton sucks
##### Where is r measured from in the gravitation equation GMm/r sqr?
« on: 16/12/2013 02:56:12 »
In g = GM/r^2 where r=0 where is this zero point interpreted to be? Is it at the surface of the sphere or the centre of gravity?
« Last Edit: 02/01/2014 20:30:09 by chris »

#### Pmb

• Neilep Level Member
• Posts: 1838
• Physicist
##### Re: A question about g the gravitational field
« Reply #1 on: 16/12/2013 06:01:57 »
Quote from: jeffrey
In g = GM/r^2 where r=0 where is this zero point interpreted to be? Is it at the surface of the sphere or the centre of gravity?
The relationship g = GM/r^2 refers to the gravitational acceleration given to a body which is located at a distance r from the body. The expression you wrote is incomplete because g is really a vector quantity. The correct expression would have a unit vector multiplying it whose direction is from the place the source is to the source point.

The expression holds when the distance is very large compared to the dimensions of the source. If the distribution of matter is not spherically symmetric then that relationship is invalid when you're close to it. However if the body is a point object then the relationship holds no matter how close you are to it. If you’re too close though then you have to use Einstein's general theory of relativity.

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3770
• Thanked: 47 times
• The graviton sucks
##### Re: A question about g the gravitational field
« Reply #2 on: 16/12/2013 13:05:14 »
Quote from: jeffrey
In g = GM/r^2 where r=0 where is this zero point interpreted to be? Is it at the surface of the sphere or the centre of gravity?
The relationship g = GM/r^2 refers to the gravitational acceleration given to a body which is located at a distance r from the body. The expression you wrote is incomplete because g is really a vector quantity. The correct expression would have a unit vector multiplying it whose direction is from the place the source is to the source point.

The expression holds when the distance is very large compared to the dimensions of the source. If the distribution of matter is not spherically symmetric then that relationship is invalid when you're close to it. However if the body is a point object then the relationship holds no matter how close you are to it. If you’re too close though then you have to use Einstein's general theory of relativity.

Pete you have not answered the question at all. All I want to know is where the source is taken from.

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3770
• Thanked: 47 times
• The graviton sucks
##### Re: A question about g the gravitational field
« Reply #3 on: 16/12/2013 13:07:33 »
It's OK I worked it out myself.

#### Pmb

• Neilep Level Member
• Posts: 1838
• Physicist
##### Re: A question about g the gravitational field
« Reply #4 on: 16/12/2013 16:49:40 »
Quote from: jeffreyH
Pete you have not answered the question at all. All I want to know is where the source is taken from.
Sorry. I thought I was clear when I said the body was a distance
which is located at a distance r from the body.

You didnt' tell me anything about the source. That relation could hold for a point particle or for a spherically symmetric object. I any case the source object is centerred at r = 0.
The source is located at

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3770
• Thanked: 47 times
• The graviton sucks
##### Re: A question about g the gravitational field
« Reply #5 on: 16/12/2013 20:37:34 »
Quote from: jeffreyH
Pete you have not answered the question at all. All I want to know is where the source is taken from.
Sorry. I thought I was clear when I said the body was a distance
which is located at a distance r from the body.

You didnt' tell me anything about the source. That relation could hold for a point particle or for a spherically symmetric object. I any case the source object is centerred at r = 0.
The source is located at

Sorry Pete. I have some intractable problems to deal with. For instance mass-energy density with respect to radius. This can vary greatly an is not uniform for a given mass. I have calculated density for matter compressed at the Planck mass scale but the state of matter at that level I would consider having a more uniform density. You cannot easily reverse this. You need to consider averages at lower densities which is not ideal.

#### evan_au

• Neilep Level Member
• Posts: 3947
• Thanked: 227 times
##### Re: A question about g the gravitational field
« Reply #6 on: 18/12/2013 10:12:11 »
Quote
Is it at the surface of the sphere or the centre of gravity?
For roughly spherical astronomical objects like planets, stars and interstellar dust, distance r is measured from the center of the sphere (providing r >> radius of the sphere).

For a Plank mass whose quantum-theoretic uncertainty in position far exceeds the Plank length, measure r from the most likely point in the wavefunction.

Good luck with your theory of quantum gravity!

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3770
• Thanked: 47 times
• The graviton sucks
##### Re: A question about g the gravitational field
« Reply #7 on: 30/12/2013 15:16:00 »
Quote
Is it at the surface of the sphere or the centre of gravity?
For roughly spherical astronomical objects like planets, stars and interstellar dust, distance r is measured from the center of the sphere (providing r >> radius of the sphere).

For a Plank mass whose quantum-theoretic uncertainty in position far exceeds the Plank length, measure r from the most likely point in the wavefunction.

Good luck with your theory of quantum gravity!

This is immensely difficult stuff. Thanks for the encouragement. The density of matter is a very difficult concept to model. I am interested in density of solid bodies and although at the Planck scale you can find a fixed point there has to be a lower limit on density. This is becoming a mind twister.

#### jeffreyH

• Global Moderator
• Neilep Level Member
• Posts: 3770
• Thanked: 47 times
• The graviton sucks
##### Re: A question about g the gravitational field
« Reply #8 on: 31/12/2013 16:14:55 »
I am about to look into the Chandrasekhar limit. This as I understand it uses 4 values. The mass of a proton, the gravitational constant, Planck's constant and the speed of light. This may turn out to be a way to find my lower density limit with rs, the Schwarzschild radius, being an upper density limit. As I see it no matter the size of the mass involved g must go infinite at this radius along with time dilation and length contraction, except that that would be counter-intuitive. Sounds like a quantum state to me.

As for uncertainty and the Planck mass I would think that density may reduce uncertainty as at infinity there is no time or motion. the particle is effectively at every point in the wave function.

As a correction to that last sentence, the wave function may well cancel out completely and flat line. This in my opinion should be equivalent to an absolute zero state and being an absolute would mean the Schwarzschild radius is also an unattainable absolute. The big problem I am having is finding a function to relate density to field strength without loss of mass through a brane. This I really don't like as it starts running into complexity, which is what I am trying to avoid.
« Last Edit: 31/12/2013 23:10:06 by jeffreyH »

#### The Naked Scientists Forum

##### Re: A question about g the gravitational field
« Reply #8 on: 31/12/2013 16:14:55 »