g/G = 1 AU. Discuss

[KeyOfDavid]

I observe that g/G is the distance to the sun.

Before I add own thoughts on this, I offer this up to discussion.

What might be the reason for this coincidence?

[Genady]

g/G has units of mass per area. 1 AU is a distance. How can they be equal?

[swansont]

1 hour ago, KeyOfDavid said:

I observe that g/G is the distance to the sun.

Let’s see the math

[Genady]

1 hour ago, swansont said:

Let’s see the math

1 AU = 1.5x10¹¹ m

g/G = 9.8 / (6.67x10^-11) = 1.47x10¹¹ kg/m² 

Close... 😉

Edited February 20, 2023 by Genady

[studiot]

2 hours ago, KeyOfDavid said:

I observe that g/G is the distance to the sun.

Before I add own thoughts on this, I offer this up to discussion.

What might be the reason for this coincidence?

You are correct.

It is a coincidence.

But Genady is also correct that the units don't match.

The numbers match in the case of Earth, but not in the case of say, Jupiter.

 

Let us look at some figures.

 

For Earth D_earth = 1.47 x 10¹¹ metres  -  distance to sun

For Jupiter D_jupiter = 7.41 x 10¹¹ metres  -  distance to sun

For Earth g_earth = 9.81 m/s

For Jupiter g_jupiter = 24.79 m/s

For both G = 6.7 x 10^-11 N-metre²/ kg²

 

So for Earth g_earth / G = 9.41/ 6.7 x 10^-11  = 1.47 x 10¹¹ kg/metre²    which is the same number of kg/metre² as the Earth is metres away from the sin.

BUT

For Jupiter g_jupiter / G  = 24.79 / 6.7 x 10^-11  = 3.7 x 10¹¹ kg/metre²  which is quite different numerically than 7.41 x 10¹¹ 

[Genady]

11 minutes ago, studiot said:

The numbers match in the case of Earth, but not in the case of say, Jupiter.

They will not match in the case of Earth, too, if length is in cm, or length in feet and mass in pounds, etc. (in case the OP does not realize what mismatched units mean.)

[swansont]

1 hour ago, Genady said:

1 AU = 1.5x10¹¹ m

g/G = 9.8 / (6.67x10^-11) = 1.47x10¹¹ kg/m² 

Close... 😉

My follow-up would be to do it in feet, if the OP returns.

If it depends on the unit system it’s not meaningful. (edit: as you point out; xpost)

[exchemist]

1 hour ago, Genady said:

They will not match in the case of Earth, too, if length is in cm, or length in feet and mass in pounds, etc. (in case the OP does not realize what mismatched units mean.)

Exactly.  

[studiot]

OOps!

I inadvertently gave g the wrong units.

It should of course be, m/s²  -  not m/s

Many thanks to @Sensei for pointing this out.

[KeyOfDavid]

OK, so my equation is out by 1 kg/m³.

What is physical interpretation of kg/m³?

Or units of G for that matter?

On 2/20/2023 at 9:01 PM, studiot said:

You are correct.

It is a coincidence.

But Genady is also correct that the units don't match.

The numbers match in the case of Earth, but not in the case of say, Jupiter.

 

Let us look at some figures.

 

For Earth D_earth = 1.47 x 10¹¹ metres  -  distance to sun

For Jupiter D_jupiter = 7.41 x 10¹¹ metres  -  distance to sun

For Earth g_earth = 9.81 m/s

For Jupiter g_jupiter = 24.79 m/s

For both G = 6.7 x 10^-11 N-metre²/ kg²

 

So for Earth g_earth / G = 9.41/ 6.7 x 10^-11  = 1.47 x 10¹¹ kg/metre²    which is the same number of kg/metre² as the Earth is metres away from the sin.

BUT

For Jupiter g_jupiter / G  = 24.79 / 6.7 x 10^-11  = 3.7 x 10¹¹ kg/metre²  which is quite different numerically than 7.41 x 10¹¹ 

Ok, so 3.7e11 is different from 7.4e11 by 3.7e11, or as we might say by a factor of 2.

[exchemist]

24 minutes ago, KeyOfDavid said:

OK, so my equation is out by 1 kg/m³.

What is physical interpretation of kg/m³?

Or units of G for that matter?

No. Your equation makes no sense, because you are trying to divide apples by sink plungers. G and g are different sorts of quantity. As has been pointed out, if you were to use different units the numerical relationship you have found would not arise. That means there is no significance in it.

What you are doing is like noting the approx height of a man is 6ft and there are 6 sides to dice.  Coincidence! Whereas if you work in metres, the height of a man is a bit less than 2metres and the coincidence disappears.

 

 

 

 

 

Edited February 23, 2023 by exchemist

[KeyOfDavid]

1 hour ago, exchemist said:

No. Your equation makes no sense, because you are trying to divide apples by sink plungers. G and g are different sorts of quantity. As has been pointed out, if you were to use different units the numerical relationship you have found would not arise. That means there is no significance in it.

What you are doing is like noting the approx height of a man is 6ft and there are 6 sides to dice.  Coincidence! Whereas if you work in metres, the height of a man is a bit less than 2metres and the coincidence disappears.

 

 

 

 

 

Ok, congratulations for your take down analysis 

Now explain to me the physical interpretation of G and how that makes sense.

[KeyOfDavid]

On 2/20/2023 at 8:27 PM, Genady said:

1 AU = 1.5x10¹¹ m

g/G = 9.8 / (6.67x10^-11) = 1.47x10¹¹ kg/m² 

Close... 😉

So it works in some sense only in SI units. But what are SI units, and why do we use them? Are there other formulae that only work in SI units?

[exchemist]

2 hours ago, KeyOfDavid said:

Ok, congratulations for your take down analysis 

Now explain to me the physical interpretation of G and how that makes sense.

No need to be sarky😀. Look, there have been half a dozen posts explaining why your equation is not valid, yet it is clear from your response that you have not taken in what was being said. So I've just been trying to explain it to you again, as clearly as I can.

G is the proportionality constant relating the force of gravity to the mass of the two objects concerned and the distance between them. It is observed that the force is proportional to the size of both masses, i.e. F is proportional to m x M and that it is inversely proportional to the square of the distance between them , i.e. F is proportional to 1/r².  

Putting the two observations together F is proportional to mM/r².

G is the scaling factor that tells you how much F you get for given values of m, M and r.  So the whole expression is F=GmM/r². This was worked out by Isaac Newton and is known as Newton's Law of Gravitation.

The dimensions of G are L³/MT², so in the SI system the units are m³/kg-sec². This funny collection of units is the result of relating force, which has dimensions of ML/T² (per F=ma), to the expression on the right which, apart from G, has dimensions of  M²/L². 

So we have  L³/MT² x  M²/L², which after simplifying by cancelling powers top and bottom as appropriate gives us  ML/T², which is what we want.  

6 minutes ago, KeyOfDavid said:

So it works in some sense only in SI units. But what are SI units, and why do we use them? Are there other formulae that only work in SI units?

Only wrong ones, like yours. If a formula giving the ratio of two physical quantities has a result that depends on the units chosen, then it must be dimensionally incorrect and tells you nothing about the world.   

SI is used in science because it is universal and simple to use. 

Edited February 23, 2023 by exchemist

[studiot]

9 minutes ago, KeyOfDavid said:

So it works in some sense only in SI units.

What works ?

I have shown you that it does not work on other planets for example Jupiter.

2 hours ago, KeyOfDavid said:

Ok, congratulations for your take down analysis 

Now explain to me the physical interpretation of G and how that makes sense.

I thought exchemist's die analogy was rather good. Didn't you?

 

For your information g is specific to local conditions, even on Earth.
It is derived from G by applying these local conditions.

This is why G is called the Universal Gravitational Constant  - it applies everywhere.
G is used to calculate something called gravitational potential, and also the gravitational force exerted between any two bodies with mass, and that calculation involves the values of both masses.

g is used to calculate the force on a singlebody with mass in the vicinity of Earth, but g already incorporates a factor for the mass of the Earth and varies fromplace to place on the Earth's surface or height above it.
 

[KeyOfDavid]

19 minutes ago, studiot said:

What works ?

I have shown you that it does not work on other planets for example Jupiter.

I thought exchemist's die analogy was rather good. Didn't you?

 

For your information g is specific to local conditions, even on Earth.
It is derived from G by applying these local conditions.

This is why G is called the Universal Gravitational Constant  - it applies everywhere.
G is used to calculate something called gravitational potential, and also the gravitational force exerted between any two bodies with mass, and that calculation involves the values of both masses.

g is used to calculate the force on a singlebody with mass in the vicinity of Earth, but g already incorporates a factor for the mass of the Earth and varies fromplace to place on the Earth's surface or height above it.
 

How do you know G is constant? What observations prove this?

58 minutes ago, exchemist said:

No need to be sarky😀. Look, there have been half a dozen posts explaining why your equation is not valid, yet it is clear from your response that you have not taken in what was being said. So I've just been trying to explain it to you again, as clearly as I can.

G is the proportionality constant relating the force of gravity to the mass of the two objects concerned and the distance between them. It is observed that the force is proportional to the size of both masses, i.e. F is proportional to m x M and that it is inversely proportional to the square of the distance between them , i.e. F is proportional to 1/r².  

Putting the two observations together F is proportional to mM/r².

G is the scaling factor that tells you how much F you get for given values of m, M and r.  So the whole expression is F=GmM/r². This was worked out by Isaac Newton and is known as Newton's Law of Gravitation.

The dimensions of G are L³/MT², so in the SI system the units are m³/kg-sec². This funny collection of units is the result of relating force, which has dimensions of ML/T² (per F=ma), to the expression on the right which, apart from G, has dimensions of  M²/L². 

So we have  L³/MT² x  M²/L², which after simplifying by cancelling powers top and bottom as appropriate gives us  ML/T², which is what we want.  

Only wrong ones, like yours. If a formula giving the ratio of two physical quantities has a result that depends on the units chosen, then it must be dimensionally incorrect and tells you nothing about the world.   

SI is used in science because it is universal and simple to use. 

Except G is not a scaling factor as it not dimensionless.

Do you see where I'm going with this yet?

[exchemist]

36 minutes ago, KeyOfDavid said:

How do you know G is constant? What observations prove this?

Except G is not a scaling factor as it not dimensionless.

Do you see where I'm going with this yet?

Down some crank rabbit hole, by the look of it.😄

But as you are having trouble with fairly simple concepts, I am not expecting a particularly sophisticated form of crankery. Nevertheless, you can stop being coy and reveal your agenda now, Ta-Daa!

Edited February 23, 2023 by exchemist

[Genady]

(Speed of light) * (1 ns) = (1 ft)

(Avogadro number) = (number of stars in the observable universe)

g = (Human population in 2050)

[exchemist]

1 hour ago, Genady said:

(Speed of light) * (1 ns) = (1 ft)

(Avogadro number) = (number of stars in the observable universe)

g = (Human population in 2050)

Temperature of domestic fridge, in C deg / number of digits on one hand = 1. 

[Genady]

14 minutes ago, exchemist said:

Temperature of domestic fridge, in C deg / number of digits on one hand = 1. 

G/h = 10^{number of Crocodilian species}

[exchemist]

Just now, Genady said:

G/h = 10^{number of Crocodilian species}

That deserves some sort of prize! 

[John Cuthber]

7 hours ago, exchemist said:

Your equation makes no sense, because you are trying to divide apples by sink plungers.

I'm going to steal that. 

[exchemist]

Just now, John Cuthber said:

I'm going to steal that. 

Yeah I thought apples and oranges was getting a bit hackneyed, and that sink plungers would also obviate the tiresome rejoinder that both are at least types of fruit. 😁

[joigus]

On 2/20/2023 at 6:55 PM, Genady said:

g/G has units of mass per area. 1 AU is a distance. How can they be equal?

 

On 2/20/2023 at 10:01 PM, studiot said:

It is a coincidence.

But Genady is also correct that the units don't match.

 

On 2/20/2023 at 11:04 PM, swansont said:

If it depends on the unit system it’s not meaningful.

 

3 hours ago, exchemist said:

If a formula giving the ratio of two physical quantities has a result that depends on the units chosen, then it must be dimensionally incorrect and tells you nothing about the world.  

 

27 minutes ago, Genady said:

G/h = 10^{number of Crocodilian species}

LOL

...

[KeyOfDavid]

2 hours ago, exchemist said:

Down some crank rabbit hole, by the look of it.😄

But as you are having trouble with fairly simple concepts, I am not expecting a particularly sophisticated form of crankery. Nevertheless, you can stop being coy and reveal your agenda now, Ta-Daa!

 

2 hours ago, exchemist said:

Down some crank rabbit hole, by the look of it.😄

But as you are having trouble with fairly simple concepts, I am not expecting a particularly sophisticated form of crankery. Nevertheless, you can stop being coy and reveal your agenda now, Ta-Daa!

Except G is not a scaling factor as it not dimensionless.

So who's the crank?

The equation you are using is dimensionally incorrect. Why do you mock me for what you are doing?

42 minutes ago, Genady said:

G/h = 10^{number of Crocodilian species}

What's green, scaly and has 13 feet?